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NAME ___________________________________AP NOTES: UNIT 3 (1): EQUILIBRIUM & THE CONSTANT Let’s take a moment and reflect on how we’re constructing the coursework. To further our grasp as how chemists can predict and/or explain chemical phenomena: First, there was a review of nomenclature, writing empirical formula and dimensional analysis We began our advanced work, with the underlying process of kinetics (Big Idea 4). We segued to the study of substances, with a focused look at the gas laws … (Big Idea 2, in part) We are now moving on to another of the underlying processes … equilibrium (Big Idea 6) Equilibrium is a big, (I mean, big) topic. It links into other units such as Kinetics, Thermodynamics, Acid/Base Theory, Solution Theory, Bonding, and the behavior of matter, in terms of phase changes. It is another underlying process. To control the yield of a reaction chemists need to understand how the position of equilibrium is affected by conditions such as temperature and pressure. The regulation of chemical equilibria affects the yield of products in industrial processes and living cells struggle to avoid sinking into equilibrium Hmm! (Atkins p. 383) At this point we’ll cover ONLY, Enduring Understandings 6A and 6B & the following Learning Objectives. BIG IDEA 6: Any bond or intermolecular attraction, that can be formed, can be broken. These two processes are in dynamic competition sensitive to initial conditions and external perturbations. Enduring understanding 6.A: Chemical equilibrium is a dynamic, reversible state in which rates of opposing processes are equal. Essential knowledge 6.A.1: In many classes of reactions, it is important to consider both the forward and reverse reaction. Essential knowledge 6.A.2: The current state of a system undergoing a reversible reaction can be characterized by the extent to which reactants have been converted to products. The relative quantities of reaction components are quantitatively described by the reaction quotient, Q. Essential knowledge 6.A.3: When a system is at equilibrium, all macroscopic variables, such as concentrations, partial pressures, and temperature, do not change over time. Equilibrium results from an equality between the rates of the forward and reverse reactions, at which point Q = K. Essential knowledge 6.A.4: The magnitude of the equilibrium constant, K, can be used to determine whether the equilibrium lies toward the reactant side or product side. Enduring understanding 6.B: Systems at equilibrium are responsive to external perturbations, with the response leading to a change in the composition of the system. understanding 6.C: Enduring Chemical equilibrium plays an important role in acid-base chemistry and in solubility. Essential knowledge 6.B.1: Systems at equilibrium respond to disturbances by partially countering the effect of the disturbance (Le Chatelier’s principle). Essential knowledge 6.B.2: A disturbance to a system at equilibrium causes Q to differ from K, thereby taking the system out of the original equilibrium state. The system responds by bringing Q back into agreement with K, thereby establishing a new equilibrium state. Essential knowledge 6.C.1: Chemical equilibrium reasoning can be used to describe the proton-transfer reactions of acid-base chemistry. Essential knowledge 6.C.2: pH is an important characteristic of aqueous solutions that can be controlled with buffers. Comparing pH to pKa allows us to determine the protonation state of a molecule with a labile proton. Essential knowledge 6.C.3: The solubility of a substance can be understood in terms of chemical equilibrium. Enduring understanding 6.D: The Essential knowledge 6.D.1: When the difference in Gibbs free energy between reactants and products (ΔG°) is equilibrium constant is related to much larger than the thermal energy (RT), the equilibrium constant is either very small (for ΔG° > 0) or very large temperature and the difference in (for ΔG° < 0). When ΔG° is comparable to the thermal energy (RT), the equilibrium constant is near 1. Gibbs free energy between reactants and products 215 Learning objective 6.1 The student is able to, given a set of experimental observations regarding physical, chemical, biological, or environmental processes that are reversible, construct an explanation that connects the observations to the reversibility of the underlying chemical reactions or processes. [See SP 6.2; Essential knowledge 6.A.1] Learning objective 6.2 The student can, given a manipulation of a chemical reaction or set of reactions (e.g., reversal of reaction or addition of two reactions), determine the effects of that manipulation on Q or K. [See SP 2.2; Essential knowledge 6.A.2] Learning objective 6.3 The student can connect kinetics to equilibrium by using reasoning about equilibrium, such as Le Chatelier’s principle, to infer the relative rates of the forward and reverse reactions. [See SP 7.2; Essential knowledge 6.A.3] Learning objective 6.4 The student can, given a set of initial conditions (concentrations or partial pressures) and the equilibrium constant, K, use the tendency of Q to approach K to predict and justify the prediction as to whether the reaction will proceed toward products or reactants as equilibrium is approached. [See SP 2.2, 6.4; Essential knowledge 6.A.3] Learning objective 6.5 The student can, given data (tabular, graphical, etc.) from which the state of a system at equilibrium can be obtained, calculate the equilibrium constant, K. [See SP 2.2; Essential knowledge 6.A.3] Learning objective 6.6 The student can, given a set of initial conditions (concentrations or partial pressures) and the equilibrium constant, K, use stoichiometric relationships and the law of mass action (Q equals K at equilibrium) to determine qualitatively and/or quantitatively the conditions at equilibrium for a system involving a single reversible reaction. [See SP 2.2, 6.4; Essential knowledge 6.A.3] Learning objective 6.7 The student is able, for a reversible reaction that has a large or small K, to determine which chemical species will have very large versus very small concentrations at equilibrium. [See SP 2.2, 2.3; Essential knowledge 6.A.4] Learning objective 6.8 The student is able to use Le Chatelier’s principle to predict the direction of the shift resulting from various possible stresses on a system at chemical equilibrium. [See SP 1.4, 6.4; Essential knowledge 6.B.1] Learning objective 6.9 The student is able to use Le Chatelier’s principle to design a set of conditions that will optimize a desired outcome, such as product yield. [See SP 4.2; Essential knowledge 6.B.1] Learning objective 6.10 The student is able to connect Le Chatelier’s principle to the comparison of Q to K by explaining the effects of the stress on Q and K. [See SP 1.4, 7.2; Essential knowledge 6.B.2] As in the other units, we’ll begin with a sweep through of general ideas, basic vocabulary and quick reviews of work done in Honors Chemistry. In the unit on Kinetics (Big Idea 4), we studied chemists’ understanding as to how fast a chemical reaction occurs. In this unit we will study how far a chemical reaction can go. Not all go “to completion”. Some reactions can experience a reverse reaction. The extent …, the how far of a chemical reaction is determined by thermodynamics (a later unit). However, we can extract a piece of that unit for our current work, because we will study an experimentally measurable quantity called the equilibrium constant. In short, most reactions occur so as to produce products. A reaction with a large equilibrium constant proceeds, virtually to completion (the virtually complete consumption of reactants to make product). A small value for the equilibrium constant indicates that nearly all the reactants remain as reactants, producing very small quantities of product. (Tro p. 648) Physical changes (e.g. melting-freezing, dissolving-crystallization), and chemical reactions can achieve an equilibrium. A state of equilibrium unto itself is not, a “bad or good” thing. However, in the quest to manipulate matter and energy to our own ends, chemists wish to understand the issue, so as to control/change/affect/avoid/create equilibria, in most chemical systems which achieve equilibrium. 216 I) (Dynamic) Equilibrium: In short, an equilibrium exists when the * rate of the forward reaction equals the rate of the reverse reaction. The concentrations are not (probably) equal …. BUT the concentrations of all the reactants and products are constant. A) So, 3 issues define an equilibrium system: Reversible, Dynamic, Constant [reactant]:[product] B) In unit on kinetics we learned that reaction rates are dependent upon the required activation energy & rds. You also know that the rates generally increase with increasing concentration of the reactants (unless, the reaction order is *zero ) …. and the rates decrease with decreasing concentration of the reactants. Yet, reflection upon Big Idea 6, Any bond or intermolecular attraction, that can be formed, can be broken. These two processes are in dynamic competition sensitive to initial conditions and external perturbations. should suggest that as the reactant concentration decreases (and thus the rate), the products due to their inevitably increasing concentrations, could indeed begin to collide and rupture their newly formed bonds and engage in a reverse reaction. This activity, OVER TIME, could reconstitute the reactant concentration to such a point, that the two opposing rates (making product and the decomposition thereof) could eventually match each other…. http://www.history.com/encyclopedia/fwne/images/ChemicalReactionC3.gif 217 II) Most chemical reactions (and virtually all physical changes involved in chemistry) are reversible. A) We tend to write only 1 equation … but under the correct conditions, a reaction equation, could symbolize two possible reactions occurring, simultaneously. 1) Before launching into this conversation let’s assume that the ONLY collisions which can have an effect are summarized below: reactant colliding with reactant …. to make product product colliding with product …. to re-constitute reactant o reactant colliding with product is a non-effective collision & has no effect on the creation or shifting of the point of equilibrium 2) reactants collide and bond, giving the products (this is called the forward reaction … we read the FORWARD reaction from left to right) 3) products can react with each other, to reconstitute the reactants (This is called the reverse reaction and we read the REVERSE reaction equation from right to left … essentially making the products into reactants. 4) Think of it this way: Every synthesis reaction, can be seen as a decomposition when read backwards …. NO(g) + O2(g) 2 NO2(g) + 112.86 kJ can be read in reverse giving a complimentary reaction: 112.86 kJ + 2 NO2(g) NO(g) + O2(g) a) Initially students become a bit confused over the change in enthalpy being the same for both the forward and the reverse reaction … However, when you reflect upon that the change in enthalpy is the difference between products and reactants, or Hp –Hr then, it should make a bit more sense. e.g A + B → C + 40 kJ 100 A+B 60 40 kJ + C → B + A A+B 100 ∆H ∆H C 60 C 218 B) The nature of an equilibrium is interesting, in that whether you begin with only reactants or with only products, the reaction reaches equilibrium concentration at which the equilibrium constant is the same, at a specific temperature. 1) No matter what the initial concentrations are, the reaction * always goes in a direction that ensures that the equilibrium concentrations, when substituted into the equilibrium expression , give the same equilibrium constant (K) This idea is summarized very nicely in your B&L text (p. 632) B) A double-headed arrow () or double arrow ( ) indicate a reaction is a reversible reaction and that the two opposing reactions are already at equilibrium. 1) Given: 2 SO2(g) + O2(g) 2SO3(g) + 197.78 kJ a) What visual clue tells you the reaction is at equilibrium? *double/opposing arrows b) Write the forward reaction: * 2 SO2(g) + O2(g) → 2SO3(g) + 197.78 kJ c) Write the reverse reaction: * 2SO3(g) + 197.78 kJ → 2 SO2(g) + O2(g) d) Which reaction (forward or reverse) is exothermic? *forward reaction 219 2) Given: 2 H2O(l) + 571 kJ 2 H2(g) + O2(g) a) What visual clue tells you the reaction is at equilibrium? * double headed arrow b) Write the forward reaction: * 2 H2O + 571 kJ → 2 H2 + O2 c) Write the reverse reaction: * 2 H2 + O2 → 2 H2O + 571 kJ d) In terms of energy, (exothermic vs. endothermic) how should you categorize the reverse reaction? * exothermic III) There are three forms of equilibrium: A) phase equilibrium: When the rates of 2 opposing * physical at the same rate. (ice melts as fast as water freezes same rate as water vapor condenses) changes occur or water evaporates at the B) solution equilibrium: When the rate of dissolving occurs at the same rate as * crystallization A solution equilibrium exists only in saturated solutions, in which a small amount of solid is present, which is in equilibrium with the dissolved species. C) chemical equilibrium: When the rates of 2 opposing * chemical same rate. reactions occur at the Chemmaters Feb 1984 D) Chemical equilibrium is dynamic … there is a good deal of change going on. There could be a significant amount of bond making and bond breaking going on … It is just that in a dynamic equilibrium, the net effect of all of this change is a 0 change in the concentrations of reactants and products. 1) a static equilibrium would be akin to me pushing against a wall, or a tug of war in which neither party moves forward or back at all …. 220 Visualize! The equilibrium between the decomposition of dinitrogen tetroxide and its synthesis 58 kJ + N2O4(g) 2 NO2(g) NO2 N2O4 http://www.cartage.org.lb/en/themes/Sciences/Chemistry/Miscellenous/Helpfile/Equilibrium/Equilibrium/eq.gif 1) The following reaction is at equilibrium N2O4(g) 2 NO2(g) Being at equilibrium, means: The rate of the forward reaction * equals the rate of the reverse reaction AND the [N2O4 ] and [NO2] are * constant but not necessarily *equal a) Translation: The product of the forward reaction (nitrogen dioxide) collides and combines to make N2O4(g) at the same rate as the dinitrogen tetroxide decomposes into NO2 Recall: Only 2 categories of collisions are ever considered ... The collisions between reactants (which result in products) & the collisions between products that result in re-constituting the reactants. For instance: Important: N2O4(g) Important: NO2(g) UN-important: N2O4(g) colliding with N2O4(g) colliding with NO2(g) colliding with NO2(g) 2) The following reaction is at equilibrium N2(g) + 3H2(g) 2NH3(g) Being at equilibrium, means: The rate of the forward reaction = the rate of the reverse reaction. OR: The rate of the effective collisions between N2 and H2 = the rate of effective collisions between molecules of NH3 & NH3 AND the [N2 ] , [H2] and [NH3] are * constant but not necessarily * equal a) Another way to look at it is : Ammonia is produced at the same rate as it is decomposed back into dinitrogen and dihydrogen 221 3) The reaction: 2 N2(g) + 3 O2(g) 2 N2O3(g) is at equilibrium. This means that the rate of producing * N2O3(g) equals the rate of * decomposing N2O3(g) back into N2(g) and O2(g) a) The concentrations of N2(g), O2(g) & N2O3(g) at equilibrium are constant / equal (circle one) b) Translation: Dinitrogen trioxide is made at the same rate as it is * decomposed OR the rate of effective collisions between N2(g) & O2(g) equals the rate of effective collisions between molecules of N2O3 4) The reaction: 2SO2(g) + O2(g) 2SO3(g) is at equilibrium. This means that the production of SO3 equals the rate of its decomposition ... OR the rate of effective collisions between SO2(g) & O2(g) = the rate of effective collisions between molecules of SO3 (or SO3 and other SO3 molecules) a) The concentration of each substance is constant / equal (circle one) III) D (continued) 2)A chemical equilibrium can be “shifted” (perturbed or stressed, as in Big Idea 6). When the perturbation (stress) is maintained, the chemical reaction will achieve a new point of equilibrium, in time. The concentrations of the reactants and products, will be different at this new point of equilibrium. a) During this time of perturbation (or stress), *one reaction is inevitably favored or made to be dominant … and runs at a higher rate. As the system works away under this stress, in time, under these different conditions a new equilibrium, at some point will be established. The role of the chemist is to understand the causative factor(s), consequence(s) and perhaps use it to her/his advantage. 222 b) Were we to assume a reaction at equilibrium, the point of equilibrium can be shifted (temporarily destroyed, stressed, perturbed) to favor one of the competing reactions over the other. It will shift in such a way as to reduce the stress, and reach a new point of equilibrium Learn this jargon … it is specific to equilibrium, and we use it pretty often… i) Shift the (point of) equilibrium to the right = favor the forward reaction and make more product. Shift the (point of) equilibrium to the left = favor the reverse reaction and make reactant e.g.) Given a system at equilibrium: 58 kJ + N2O4(g) 2 NO2(g) i) at equilibrium the rate of the forward reaction which makes NO2 is equal to the rate of the reverse reaction which is *the decomposition of NO2 or rather, the making of dimer, N2O4 ii) upon manipulation, the equilibrium is altered so as to produce more NO2 We would say that the equilibrium was *shifted to the right OR that we favored the forward reaction. OR… iii) upon manipulation, the equilibrium could be altered so as to produce more N2O4 … We would say that the equilibrium was *shifted to the left, OR that we favored the reverse reaction. 223 III) The Equilibrium Constant (Keq et. al.) A) There are many different types of equilibrium constants … each has a special designation depending upon the system it describes. Many of the commonly used symbols are listed in the following table. Equilibrium Constant TABLE OF EQUILIBRIUM CONSTANTS The Equilibrium Described by the Constant Kc A general designation, of c (concentration) in terms of molarity Keq A general designation, similar to Kc used for a chemical equilibrium Kp The partial pressure of a gas used to describe a gas’s concentration Ka The ionization of a(n) (weak) acid in water (a = acid) Kb The dissociation of a (weak) base in water (b = base) Kw The ionization for water = 1 x 10-14 [H2O(l) H3O+1(aq) + OH-1(aq) ] Ksp The dissociation of an ionic salt in water (sp = solubility product) B) The equilibrium constant of a reaction is a unit-less, temperature-dependent, ratio, which has a magnitude (size) indicating the relative amount of product to the amount of reactant at the point of equilibrium. The constant suggests the relative success of the forward reaction, before equilibrium is achieved. It is calculated using the Law of Mass Action. 1) Very generally … the larger the constant, the greater the production of product, before equilibrium is established. MEMORIZE a) Hence a large equilibrium constant (Keq ≫1) favors making product … and moves towards completion. Such reactions tend to have rather large, negative ∆H values b) A small equilibrium constant (Keq ≪1) indicates that very little product is produced by the time a point of equilibrium was reached … and that most of the reactants remain un-reacted. The forward reaction does not proceed (does not get) very far by the time an equilibrium system is reached. c) When K ≈ 1 neither the forward nor the reverse is favored, and the forward reaction goes “about half-way”…. The molar concentrations should reflect the equilibrium constant. d) The time it takes to reach a state of equilibrium is linked to the activation energy and the reaction rate … It is not linked to the size of the equilibrium constant. What I want to do now, is to take apart the above definition to show you why it is a ratio, temperature-dependent, etc. … To do that we need to take a nice long look at The Law of Mass Action…. 224 C) Using the Law of Mass Action to Write an Equilibrium Expression (The equation for Kc) 1) The Law of Mass Action is used to calculate the equilibrium constant, using experimentally obtained molar concentrations. a) When we write use the Law of Mass Action we are essentially writing out what is called the equilibrium expression … the equation used to calculate Kc 2) The Law of Mass Action has a highly prescribed format. It includes ONLY aqueous and/or gaseous components of a reaction. In the event of a heterogeneous equilibrium (in which multiple phases are present in the system, the Law of Mass Action NEVER, NEVER includes solids or liquids. Remember … include only gases or aqueous solutions! a) coef coef K = [Product] [Product] coef coef [Reactant] [Reactant] 3) K is a unit-less ratio expressing the molar concentration of the gaseous &/or aqueous * products vs the concentration of the gaseous &/or aqueous * reactants raised by an * exponent reaction equation. equal to each species' coefficient from the balanced 4) Note that the equilibrium expression used to calculate the equilibrium constant (K) depends only upon the reaction stoichiometry!!! (This is quite different from the rate constant of k) a) For this reason, it is convention to write out the stoichiometry using only whole numbers. Using fractions can change the equilibrium constant. For example: KEq = [C] [A][B]2 A + 2B C versus: ½A + B ½C KEq’ = [C]1/2 [A]1/2 [B] Now, let [A] = 2 M, [B] = 3 M and [C] = 4 M … when we solve the two above equilibrium expressions: KEq = [4] = 2 = 0.222 [2][3]2 9 That makes so much sense vs. KEq’ = [4]1/2 = 2 = 0.472 [2]1/2 [3] 4.24 This is one of the reasons why you are always encouraged to balance chemical reaction equations using whole numbers …. TN: Marshall.edu 225 5) In an equilibrium expression, ONLY gaseous and aqueous species are included, for they are the only species in solution capable of reacting... thus the only factors responsible for determining the success of the reaction. Solids and liquids are technically unavailable (un-ionized, or un-dissociated) for reaction, and thus solids and liquids have a constant concentration … as odd as it is to even think of the term concentration in this light…. TN See Langella equilibrium notes for an example, w/ H2O 6) The equilibrium constant changes with temperature …. Hence the equilibrium constant for a specific reaction is * temperature dependent (because rate constants, k are temperature dependent) a) *endothermic reactions are more highly favored with an increase in temperature, than are exothermic reactions …. (more later) 7) So we have here another temperature dependent K constant … Where have we seen this before? How about k as in the rate constant… Now here is an interesting point for making connections…. Take Home Message: Equilibrium connects to kinetics because: K = kforward kreverse Chemical reactions, whether reversible or non-reversible, follow the chemical kinetics. Thus we can gain better understanding of the equilibrium constant K by using the concept of chemical kinetics. Let kf be the rate of forward reaction and kr be the rate of reverse reaction as shown below. kf aA + bB ↔ cC + dD kr Then the forward rate is given by ratef = kf [A]a [B]b and the reverse rate by rater = kr [C]c [D]d At equilibrium, the forward rate becomes equal to reverse rate as a result of no net change in concentrations of either reactants or products. (We have seen this already, in when dealing with fast steps and having to re-write a fast elementary step. Thus ratef = rater or kf [A]a [B]b = kr [C]c [D]d After rearranging the above equation, it takes the following form: c d kf = [C] [D] a b kr [A] [B] 226 Since both kf and kr are constants at a given temperature, their ratio is also a constant that is equal to the equilibrium constant K. c d (see take home message) kf = K = [C] [D] a b kr [A] [B] The equilibrium constant K is a constant at a particular temperature regardless of equilibrium concentrations of the species involved because of quotient kf / kr. https://faculty.ncc.edu/LinkClick.aspx?fileticket=1nktvq0zylA%3D&tabid=1889 8) Practice Writing Equilibrium Expressions…. Write the equilibrium expression for 8a) – f) a) N2(g) + 3H2(g) 2NH3(g) Remember: products is/are in the numerator. Note that the exponents reflect the coefficients of the balanced equation. 2 Keq = * [NH3] [N2] [H2]3 +3 b) Al2(SO4)3(s) + H2O(l) 2 Al (aq) + 3 SO4 -2 (aq) Ksp = * [Al+3]2 [SO4-2]3 c) 3 O2(g) 2 O3(g) Keq = * [O3]2 [O2]3 d) 2 Fe2O3(s) + 3 C(s) 4 Fe(s) + 3 CO2(g) Remember: include only (g) and (aq) Remember: the product(s) is/are in the numerator. Note that solids and liquids are EXCLUDED ... thus the denominator is essentially equal to 1 Note that the exponents reflect the coefficients of the balanced equation. Note that this is a "Ksp" because it reflects a physical change (solubility issue) and not a chemical reaction.... Note: This is a nice twist… apply the rules, and think! Keq = * [CO2]3 227 e) NH3(g) Note: This provides a nice twist…apply the rules and think! + HCl(g) NH4Cl(s) 1 Keq = * [NH3][HCl] f) 4HCl(g) + O2(g) H2O(l) + 2Cl2(g) Keq =* [Cl2]2 [HCl]4 [O2] g) Given the equilibrium constant expression: K = [CO2]3[H2O]4 Write the balanced reaction equation: [C3H8] [O2]5 * C3H8(g) + 5 O2(g) 3 CO2(g) + 4 H2O(g) h) Given the reaction A(g) B(g) K = 10. A reaction mixture initially contains [A] = 1.1M and [B] = 0.0M. Which statement is true at equilibrium? and Think: When written correctly, the equilibrium expression, with the substituted concentrations at equilibrium, must = 10.. Does that give you a hint? 1) The reaction mixture will contain [A] = 1.0M and [B] = 0.1M 2) The reaction mixture will contain [A] = 0.1M and [B] = 1.0M 3) The reaction mixture will contain equal concentrations of A and B ans* 2 i) Given: Ksp = [Ca ][Cl ] This is essentially an equilibrium constant expression for a heterogeneous system. Write the equation which describes the equilibrium expression 2+ -1 2 Think! Look at the constant … does it give you any insight? * CaCl2(s) + H2O(l) Ca+2(aq) + 2 Cl-(aq) Why were some substances left out of the equilibrium expression in this heterogeneous equilibrium system? * In a heterogeneous equilibrium, substances in the solid and liquid phase are omitted, due to their constant state or concentration. Only those species in solution or in the gas phase can affect the equilibrium. 228 9) Simple Calculations for K: a) Consider the equilibrium: 2 SO2(g) + O2(g) 2 SO3(g) + 791kJ 2 SO2(g) + O2(g) Forward Reaction Reaction Rate Equilibrium: Rate of the Forward Rxn = Rate of the Reverse Rxn 2 SO3(g) + 791 kJ Reverse Reaction t0 Concentrations are measured at any point once equilibrium is reached & then plugged into the "mass action" equation. t1 Time Using the above reaction equation and the following experimentally determined molar concentrations, calculate the Keq. At a specific temperature, the equilibrium concentration of [SO2 ] = 0.75 mole/L, [O2 ] = 0.30 mole/L, and [SO3] = 0.15 mole/L ans: Keq = 1.33 x 10-1 Keq 2 Substituion : Keq =* [0.15]2 [0.75]2 [0.30] = * [SO3] 2 [SO2] [O2] b) Consider the equilibrium: N2O4(g) 2 NO2(g) At 100˚C, experimentation shows that 0.10 M = [N2O4(g)] and 0.20 M = [NO2(g)]. Calculate the Keq ans: Keq = 0.4 or 4 x 10-1 c) At 100°C, Keq = 0.0778 for the following reaction: SO2Cl2(g) SO2(g) + Cl2(g) In an equilibrium mixture of the three gases the concentrations of SO2Cl2 and SO2 are 0.136 M and 0.0720 M, respectively. What is [Cl2] in the equilibrium mixture? ans: [Cl2] = 0.147 M *Keq = [SO2][Cl2] [SO2Cl2] or * 0.0778 = [0.0720 M] [x] [0.136 M] *0.010608 = 0.0720x 229 D) Significance of K …a follow up to 1) Recall, back in III) B1: I wrote: Very generally … the larger the constant, the greater the production of product, before equilibrium is established. a) Hence a large equilibrium constant (Keq ≫ 1) favors more product … and moves towards completion. b) A small equilibrium constant (Keq ≪ 1) indicates that very little product was produced by the time a point of equilibrium was reached … and that most of the reactants remain un-reacted. c) When K ≈ 1 neither the forward nor the reverse is favored,& the forward reaction goes about half-way We must now look at what this implies…and what we may infer from the value of K 2) A large equilibrium constant indicates that the numerator (the concentration of the products) *quite large, indicating that by the time the equilibrium was reached, a good deal of product existed… …. and, vice versa …. 3) Consider the following: 3H2(g) + N2g) 2 NH3(g) where K = 6.7 x 105 @ 400°C Write the equilibrium constant as a fraction… K = [NH3]2 = 6.7 x 105 3 [H2] [N2] or 670,000 1 This may be seen, relatively as: 1 : 670,000 ….. product is definitely favored 3H2(g) + N2g) 2 NH3(g) 4) Consider the following: N2(g) + O2(g) 2 NO(g) where K = 4.1 x 10-31 @ 25°C Write the equilibrium constant as a fraction… K = [NO]2 = 4.1 x 10-31 [N2][O2] or 1 41,000,000,000,000,000,000,000,000,000,000 This may be seen, relatively as: 41,000,000,000,000,000,000,000,000,000,000 N2(g) + O2g) : 1 at equilibrium, there is far more reactant, than product 2 NO(g) This reaction does not get very far… and thankfully for that … since NO is highly toxic, and that N2 and O2 are the major constituents of our atmosphere … Imagine the consequences of the two gases reacting easily with each other!!!!! Yet again here is an example as to the role chemistry can play in explaining the “how” of life on this, our planet … 230 5) Thus: the magnitude of the equilibrium constant K is useful in assessing the status of the equilibrium: If K = 1, [C]c [D]d = [A]a [B]b , the reaction is in equilibrium If K >>1, [C]c [D]d >> [A]a [B]b, the equilibrium lies to the right of the reaction and favors the products If K <<1, [C]c [D]d << [A]a [B]b, the equilibrium lies to the left of the reaction and favors the reactants Review the problem in the section practicing the equilibria expression. Given the reaction A(g) B(g) K = 10. A reaction mixture initially contains [A] = 1.1M and [B] = 0.0M. Which statement is true at equilibrium? Were you to apply the “re-write the equilibrium expression as a fraction” … interpretation, might it help you get the same answer? Where K = 10 1 and [B] [A] 1 10 thus: A(g) B(g) 1) The reaction mixture will contain [A] = 1.0M and [B] = 0.1M 2) The reaction mixture will contain [A] = 0.1M and [B] = 1.0M 3) The reaction mixture will contain equal concentrations of A and B Kind’a cool… ain’t it? Understanding what the concepts imply can help…. 231 BASIC PRACTICE FOR THE MEANING OF K ___1) Given the equilibrium A + B C. The greatest concentration of C would be produced if the equilibrium constant of the reaction were equal to 1) 1 x 10 3 2) 1 x 10 -3 3) 1 x 10 9 4) 1 x 10 -9 ___2) Given : A + B C, The greatest concentration of C would be produced if the equilibrium constant of the reaction were equal to 1) 5.0 x 10-8 3) 1.0 x 10-13 2) 2.5 x 104 4) 8.9 x 101 ___3) Given : A + B C, which Keq value suggests that the favored reaction is the forward reaction ? -1 -7 1) 8.0 x 10 -4 2) 1.5 x 10 1 3) 5.5 x 10 4) 6.4 x 10 __4) Which of the following values indicates the least soluble salt at 25 ˚C? 1) Mg(OH)2 Ksp = 8.9 X 10 2) Ca(OH)2 Ksp = 1.3 X 10 -12 -6 -4 3) Sr(OH)2 Ksp = 3.2 X 10 4) Ba(OH)2 Ksp = 5.0 X 10 -3 ___5) Which equilibrium system will contain the largest concentration of products at 25˚C? + - -17 1) AgI(s) ↔ Ag (aq) + I (aq) + 2) CH3COOH(aq) ↔ H (aq) + CH3COO (aq) 3) Pb 2+ Keq = 8.5 x 10 -5 Keq = 1.8 x 10 - (aq) + 2Cl (aq) ↔ PbCl2(s) + 4) Cu(s) + 2Ag (aq) ↔ Cu 2+ (aq) Keq = 6.3x 10 + 2Ag(s) Al(OH)3(s) ___6) Consider the reaction: 4 Keq = 2.0 x 10 Al 3+ (aq) + 15 -1 3 OH [hint:: never include (s) and (l)] (aq) Which of the following is the correct equilibrium expression for the reaction? 3+ -1 1) Ksp = [Al ] 3[OH ] 3+ -1 3 2)Ksp = [Al ] [OH ] ___7) Given the equilibrium expression: 3+ -1 3 3) Ksp = [Al ] + 3[OH ] 3+ -1 4) Ksp = [Al ] [OH ] Keq = [A] [B] [C] [D] Which pair represents the reactants in the forward reaction? 1) A and B 2) B and D 3) C and D 4) A and C 232 ___8) For the system 2A(g) + B(g) 3C(g) , the expression for the equilibrium constant Keq is 2 1) Keq = [2A] [B] [3C] 3) Keq = [A] [B] 3 [C] 3 2) Keq = [3C] [2A] [B] 4) Keq = [C] 2 [A] [B] ___9) Which reaction has the equilibrium expression : 1) 2 C(g) 3 AB(g) 2) 2 C(g) 3 A(g) + B(g) Keq = [B] [C] 3 [A] 2 ? 3) 3 A(g) B(g) + 2 C(g) 4) 3 AB(g) 2 C(g) ___10 In order for an aqueous solution to be at equilibrium, it must be: 1) dilute 2) saturated 3) concentrated 4) supersaturated ___11) Which of the following statements is FALSE? 1) The larger the value for K the longer the period of time it requires the overall reaction to reach a a point of equilibrium 2) A small value for K indicates that a reaction will reach a point of equilibrium quite quickly in the reaction, having a significant amount of unreacted reactant, and very little product. 3) The value for K is temperature dependent 4) A large value for K indicates that a reaction will proceed far to the right, favoring the production of product, prior to the point of equilibrium Answers: 1) 3 2) 2 3) 4 4) 1 5) 4 6) 2 7) 3 8) 4 9) 3 10) 2 11) 1 233 MORE PRACTICE ABOUT K … This practice deals principally with Ksp … or the solubility product. The solubility product addresses the extent to which (principally) an ionic compound dissociates into ions. Some deal with Ka which simply expresses the extent of ionization of a weak acid, in water. But they are really all predicated upon our work with K, regardless of the sytem, they describe …Okay? For questions 1 - 2 use the choices: 1) 2) 3) 4) 5) when only I is correct when only II is correct when only I and II are correct when only II and III are correct when I, II, and III are each correct _____1) Use the following table of Ksp values. Substance PbCrO4 Ksp 2.8 x 10 PbCO3 1 x 10 AgI 8.3 x10 -13 -14 -17 Assuming the same temperature, volume of water and pressure: I. PbCrO4 is more soluble than is PbCO3 II. PbCrO4 is more soluble than is AgI III. PbCO3 is more soluble than is AgI _____2) Use the following table of Ka values. Compound HCl Compound + Water +1 -1 HCl + H2O H (aq) + Cl (aq) HF HF+ H2O H H2S H2S + H2O H +1 (aq) +1 (aq) -1 Ka very large … greater than 1 + F (aq) 3.5 x 10 + HS -1 (aq) 9.5 x 10 -4 -8 +1 An Arrhenius acid is any substance which is the only significant source of H in solution. The +1 more H produced as the molecules ionize into ions, the stronger the acid. Thus, the larger the +1 Ka, the greater the amount of H produced, when added to water, and the stronger the acid. Which of the following is (are) accurate assuming the same conditions of temperature and pressure ? When dissolved in water: I) H2S is the strongest acid of the choices. II) HCl is a stronger acid than is HF. III) HF is the weakest acid of the choices. 234 3) Note that the equations from question 2's table, for HF and H2S have double headed arrows. The equation for HCl does not have a double headed arrow. Assuming a typist didn't make an error, explain the significance. *The single arrow for HCl suggests that it ionizes in water 100% or rather, the addition of HCl to water proceeds to completion (the complete ionization of the molecule into its hydrated ions). This means that HCl must be a strong acid. The other acids (HF and H2S) do NOT ionize completely in water, and this change reaches an equilibrium, thus the need for the double arrows. ____ 4) Which salt is the MOST soluble in water at 25˚C ? -14 1) lead carbonate (Ksp = 7.4 x 10 ) -8 2) calcium carbonate (Ksp = 8.7 x 10 ) -11 3) zinc carbonate (Ksp = 1.4 x 10 ) -9 4) barium carbonate (Ksp = 8.1 x 10 ) Defend your answer: (Be sure to have an argument, proof and to include any appropriate setting) -8 * It has the largest equilibrium constant Ksp = 8.7 x 10 . Since the equilibrium constant indicates the relative amount of reactant to product at equilibrium, the larger the constant indicates the most product that is made. In this case, the largest constant indicates the greatest ability of the compound to dissolve in water, or the most soluble compound. _____5) The expression : 3 Keq = [C] best represents which of the following reactions ? 2 [A] [B] 1) C(g) A(g) + B(g) 3) 2) 3 C(g) 2 A(g) + B(g) 4) 2 A(g) A(g) + B(g) C(g) + B(g) 3 C(g) 235 ____6) A saturated solution exists when the maximum amount of solute is dissolved completely, in a specific volume of water, at a specific temperature and pressure. A saturated solution is an expression of a physical equilibrium. A saturated solution may be dilute (having the maximum amount of dissolved species, but that amount is very small, compared to the amount of water) … Or a saturated solution may be concentrated (having the maximum amount of dissolved species and that amount is relatively high compared to the amount of water). Which sulfide compound forms the most concentrated saturated solution at 1 atm and 25 ˚C? -29 -17 1) CdS (Ksp = 3.6 x 10 ) 3) FeS (Ksp = 1.3 x 10 ) -52 4) HgS (Ksp = 2.4 x 10 ) -26 2) CoS (Ksp = 3.0 x 10 ) ____7) Using the choices from #6 .. .which sulfide compound produces the most saturated, yet dilute solution at 1 atm and 25 °C? +2 -1 2 _____ 8) The equilibrium expression : Ksp = [Pb ] [I ] 1) PbI2(s) Pb(s) + +2 3) Pb -1 (aq) + 2I (aq) I2(s) 4) Pb(s) + I2(s) +2 2) PbI2(s) + H2O(l) best represents which of the following reactions ? Pb -1 (aq) + 2I (aq) PbI2(s) + H2O(l) PbI2(s) ____ 9) Which equilibrium system will contain the LARGEST CONCENTRATION of products at 25 ˚C ? ↔ 1) AgI(s) + H2O(l) 2) CH3COOH(aq) ↔ H +2 3) Pb (aq) + 2 Cl -1 (aq) +1 4) Cu(s) + 2 Ag +1 Ag +1 -1 (aq) -17 (aq) -1 + CH3COO (aq) ↔ Cu (aq) (Ksp = 8.3 x 10 ) -5 (aq) ↔ PbCl2(s) + H2O(l) +2 (aq) + I + 2 Ag(s) (Ka = 1.8 x 10 ) 4 (Kc = 6.3 x 10 ) 15 (Kc = 2.0 x 10 ) Defend your answer: (Be sure to have an argument, proof and to include any appropriate setting) 15 * 4 must be correct because has the largest equilibrium constant at 2.0 x 10 . The equilibrium constant indicates the relative amount of reactant to product, we may infer that the larger the constant greater the amount of product (or the farther to the right the reaction will procee4). Since the question asks for the largest concentration of product, the answer must therefore be that with the largest value 236 for K _____ 10) Which of the following correctly expresses the Keq for the reaction +1 Cu(s) + 2 Ag +2 2 1) [Cu ] [Ag] +1 2 [Cu] [Ag ] 2) [Cu ] +1 2 [Ag ] +2 +2 (aq) ↔ Cu (aq) + 2 Ag(s) 2 3) [Ag] [Cu] 4) [Ag ] +2 [Cu ] +1 2 _____ 11) Which of the following correctly expresses the Keq for the system: 1) 2) 1 [CO2(g)] [CO2(g)] [CO2(s)] 3) [CO2(g)] 4) [CO2(s)] [CO2(g)] CO2(g) CO2(s) Answers: 1) 5 The greater the value of Ksp, the more soluble the compound (the more ion or dissolved molecule) 2) 2 It is the only accurate statement. The Ka value is the largest … thus it is the strongest acid, producing the most H+1 in water. 3) given on the page … highlight and check. 4) 2 it is the largest of these very small Ksp values. 5) 4 recall that the equilibrium constant is derived from the equilibrium expression of the Law of Mass Action. The Law of Mass Action has products (raised to an exponent equivalent to the coefficient of the balanced equation) divided by the reactants … raised to an exponent …..etc 6) 3 7) 4 8) 2 The Law of mass action has products over reactants and includes ONLY (g) and (aq), never (s) or (l) 9) 4 10) 2 11) 1 237 E) 3 Important Manipulations (pay attention): The relationship between K & the Chemical Equation When a chemical equation is modified in some way, then the equilibrium constant for the equation changes because of the modification. The following 3 modifications are relatively common. 1) Were you to reverse the equation, invert the equilibrium constant. (Take the inverse…) a) e.g. A(g) + 2B(g) 3C(g) Kforward = [C]3 [A][B]2 where you to reverse the reaction, then the Kreverse should equal 1 . Kforward because Kreverse = [A][B]2 [C]3 …. Piece o’ cake! b) When Kforward = 3.7 x 102 …. then Kreverse = 1 3.7 x102 or 0.0027 or 2.7 x 10-3 2) If you were to multiply the coefficients, in the equation by a factor, then you should raise the equilibrium constant exponentially to the same factor. a) Essentially, here is the rule of thumb: When the mole ratio is doubled, then square the value of K, when it is tripled, cube the value of K …. OR when the ratio is cut in half … take the square root. b) e.g. A(g) + 2B(g) 3C(g) K = [C]3 [A][B]2 Were you to multiply the balanced equation by some common factor … then you must account for that by raising the Law of Mass Action, exponentially by that factor nA + 2n B 3n C … K’ = [C]3n [A]n[B]2n = [C]3 [A][B]2 n = Kn Not Bad! 238 TRY THIS! (The next 3 problems ultimately combine both of the aforementioned manipulations …but first try a pretty straight forward one….) 1) The reaction A(g) 2B(g) has an equilibrium constant of K = 0.010. What is the equilibrium constant for the reverse reaction …. 2B(g) A(g) ? (hint: use manipulation 1) ans:100 This is tougher…both manipulation 1 and 2 are required … think … push forward…. 2) The reaction A(g) 2B(g) has an equilibrium constant of K = 0.010. What is the equilibrium constant for the reaction …. B(g) ½A(g) ? Hint 1: * Notice that the 2nd reaction a) 1 b) 10 is the reverse of the first reaction, and the ratio is only ½ of the original. c) 100 d) 0.0010 Hint 2: * Since it is a reverse reaction, take the inverse of K Hint 3: * Since the values have been cut by ½ , take the square root of the inverse of K ans:*b) or 10 3) Consider the chemical equation and equilibrium constant for the decomposition of ammonia at 25°C Given: NH3(g) 1⁄2 N2(g) + 3⁄2 H2(g) K = 1.34 x 10-3 Calculate the equilibrium constant for the following reaction at 25 °C N2(g) + 3H2(g) 2NH3(g) K’ = * 5.57 x 105 Hint 1:* Notice that the reaction is the reverse of the given reaction AND that the molar ratio values (while in the same ratio) have though, been doubled. Hint 2: * Because it is the reverse reaction, take the inverse of K… or 1/1.34 x 10-3 Hint 3: * Since the coefficients have been doubled … square the answer to the inverse of K …when doubled, square, when cut in half …take the square root. 239 3) If you add two or more individual chemical equations to obtain an overall equation, then multiply the corresponding equilibrium constants by each other to obtain the overall equilibrium constant…. (The Rule of Multiple Equilibria) a) Simplified … Koverall = (K1) x (K2) b) consider: A(g) 2B(g) K1 = [B]2 [A] and 2B(g) 3C(g) K2 = [C]3 [B]2 The two equations sum as follows: Thus the Koverall = [C]3 [A] In theory: A(g) 2B(g) 2B(g) 3C(g) A(g) 3C(g) …no big problem … Rather, do you see why manipulation 3 states what it states? Koverall = (K1) x (K2) because: [B]2 x [C]3 [A] [B]2 = [C]3 (which is the same answer [A] as the above addition) c) For such problems, you may need to run the sum, and use the sum to determine a Koverall …just as the above problem (and the following one….) requires you to do… TRY THIS! 1) Predict the equilibrium constant for the first reaction shown here given the equilibrium constants for the second and third reactions: CO2(g) + 3H2(g) CH3OH(g) + H2O(g) CO(g) + H2O(g) CO2(g) + H2(g) CO(g) + 2H2(g) CH3OH(g) K1 =???? K2 = 1.0 x 105 K3 = 1.4 x 107 * 2CO(g) + 4H2(g) 2CH3OH(g) notice that this is twice the third equation…. *Koverall = (1.4 x 107)2 or rather 1.96 x 1014 * Koverall = (K1)(K2)(K3) or …. Hint 1: * Add the reactions, by cancelling out like species, in order to get to an overall reaction Hint 2: *Since the sum is twice that of the third reaction, square the value of K3 in order to derive the overall K Hint 3: *Use Koverall and set it equal to the product of the other constants, with K1 being your “x”, or unknown value. Solve for that “x” ans: *K1 = 1.40 x 102 *1.96 x 1014 = (x)( 1.0 x 105)( 1.4 x 107) * K1 = 140 or 1.40 x 102 Check out the Trivedi flash, sections 14.4 – 14.6 for some support refresher…regarding the effects on equilibrium of “changing the chemical equation”. 240 III) K and its expression in terms of pressure …. Assignment: Read / Do: Trivedi: 14.10 KC vs KP A) The role of gases (as seen in Unit 2) is quite important. For gaseous reactions, the partial pressure of a particular gas is proportional to its molar concentration. Therefore we can express the equilibrium constant in terms of the partial pressure of the reactants and products. (Tro p. 658) B) Common expressions of K are Keq is Kc, in which the equilibrium constant is expressed with respect to molar concentration [ ]. Essentially, there is a relationship between the equilibrium constant in molar concentration and the equilibrium constant of gases, measured in atmospheres (KP) 1) Ultimately this work will lead us to an equation relating moles of gas and equilibrium expressions: Given: aA(g) + bB(g) ↔ cC(g) + dD(g) Think about using either of these two equations when having to deal with Partial Pressures of gases and equilibrium KP = (PC)c (PD)d (PA)a(PB)b Where P = partial pressures (This equation is on your tables, and it apes the Law of Mass Action) a) It is linked to a relationship, which IS NOT found on your tables … Where: Kp = the value for the partial pressure of a gas Kc = the equilibrium constant, for molar concentrations ∆n = the difference between the number of moles of gaseous products and gaseous reactants: Products - Reactants Kp = Kc(RT)∆n 2) The expression for KP takes the form of the expression for Kc, except that it uses the partial pressure of each gas in lieu of its concentration. a) e.g.) Consider the equilibrium: 2SO3(g) 2SO2(g) + O2(g) Kc = [SO2]2[O2] [SO3]2 vs KP = (PSO2)2 PO2 (PSO3)2 b) Partial pressure in atm and molar concentration are NOT necessarily equal! * So KP ≠ Kc, necessarily. They are equivalent only when ∆n = 0 c) Okay, they aren’t necessarily equivalent ….but, we can relate the two …. i) When you are given partial pressures in atm you may substitute right into: KP = (PC)c (PD)d (PA)a(PB)b ii) But if given Kc and asked for Kp (or vice versa) you need to convert from one to the other using Kp = Kc(RT)∆n Again, when the total number of moles of gas is the same after the reaction as before the reaction, then ∆n =0 and that means that Kp = Kc Because, Kp = Kc(RT)0 converts RT to 1 .. AND remember that the expression to find Kp mimics the equilibrium expression based upon the Law of Mass Action, which is quite convenient for gaseous systems. 241 TRY THIS 1) Consider the equilibrium N2(g) + 3H2(g) 2NH3(g) Kc = 9.60 at 300°C. Calculate Kp for this reaction Hint 1* Consider using Kp = Kc(RT)∆n , because Kc is given. Hint 2: *∆n = Prod – Reactants * Kp = Kc(RT)∆n *Kp = (9.60)(0.08206 x 573)-2 *Kp = (9.60) (0.08206 x 573)2 ans: 4.34 x 10-3 atm = 2) Dinitrogen tetroxide in its liquid state was used as one of the fuels on the lunar lander for the NASA Apollo missions. In the gas phase, it decomposes to gaseous nitrogen dioxide. N2O4(g) 2 NO2(g) Consider an experiment in which gaseous N2O4(g) was placed in a flask and allowed to reach equilibrium at a temperature where Kp = 0.133. At equilibrium, the pressure of dinitrogen tetroxide was found to equal 2.71 atm. Calculate the equilibrium pressure of NO2(g). (Zumdahl p 623) *Kp = (PNO2)2 (PN2O4) thus 0.133 = (PNO2)2 (2.71) *0.360 = (PNO2)2 *thus √0.360 = 𝑃NO2 or 0.600 atm Hint 1:* Kp is given …there is no Kc given so use the partial pressure equivalent of the Law of Mass Action, setting the partial pressure of nitrogen dioxide (the product) raised to its coefficient of 2, divided by the partial pressure of dinitrogen tetroxide. Hint 2: *Plug and Chug … you are given Kp and the partial pressure of dinitrogen tetroxide. ans: 0.600 atm 242 3) Slightly More Challenging: At 327°C the equilibrium concentrations are [CH3OH] = 0.150 M, [CO] = 0.240 M and [H2] = 1.10 M for the reaction: CH3OH(g) ↔ CO(g) + 2 H2(g) Calculate KP at this temperature 2 *Kc =[CO][H2] [CH3OH] = Hint 1: *Kp and Kc are not necessarily equivalent. 2 (0.240)(1.10) 0.150 = 1.94 ∆n *Kp = Kc(RT) *Kp = (1.94)(0.08026 • 600.15)2 = 4.50 x 103 Hint 2: *Write the equilibrium expression solving for Kc …. Hint 3: *Calculate Kc Hint 4: * Use the value for Kc to find Kp … did you convert Celsius to Kelvin??? ans: 4.70 x 103 4) For which of the following reactions is KP = Kc? (more than one choice may be a correct answer) Defend your reasoning. (Be sure to have an argument, proof and to include any appropriate setting) 1) 2 NH3(g) + CO2(g) ↔ N2CH4O(s) + H2O(g) 2) 2 NBr3(s) ↔ N2(g) + 3Br2(g) 3) 2 KClO3(s) ↔ 2 KCl(s) + 3O2(g) 4) CuO(s) + H2(g) ↔ Cu(𝓁) + H2O(g) * When ∆n=0 in the equation linking Kp and Kc: Kp =Kc (RT)∆n , then the expression RT is converted to a value of 1, giving an conversion of Kp = Kc(1) or rather Kp = Kc. (setting) The reaction in #4 gives a sum of 0 change in the number of moles ….based upon #moles of product - #moles of reactant (proof) Choice 4 is the only one of the examples which meets the requirement for Kp = Kc (answer) 243 IV) Using ICE Tables to Calculate K from Measured (experimentally determined) Concentrations A) For any reaction, the equilibrium concentrations depend on the initial concentrations (hence the I of ICE) … But the equilibrium constant is always the same at a specific temperature, regardless of the initial concentrations. Take a look at the following table and questions… Study the concentrations and the calculations … what are they telling the scientist in you? Initial and Equilibrium Concentrations for the Reaction: H2(g) + I2(g) 2 HI(g) at 445 °C Initial Concentrations [H2] [I2] [HI] Equilibrium Concentrations [H2] [I2] [HI] Equilibrium Constant Kc = [HI]2 [H2][I2] 1 0.50 0.50 0.0 0.11 0.11 0.78 (0.78)2 = 50 (0.11)(0.11) 2 0.0 0.0 0.50 0.055 0.055 0.39 (0.39)2 = 50 (0.055)(0.055) 3 0.50 0.50 0.50 0.165 0.165 1.17 (1.17)2 = 50 (0.165)(0.165) 4 1.0 0.50 0.0 0.53 0.033 0.934 (0.934)2 = 50 (0.53)(0.033) 5 0.50 1.0 0.0 0.033 0.53 0.934 (0.934)2 = 50 (0.033)(0.53) 1) Study trials 1 and 2 … what may you infer regarding the initial concentrations being all reactant or all product? * The reaction goes in a direction which establishes an equilibrium, with the same equilibrium constant. 2) Study trials 4 and 5, must the molar concentrations of the products be equal to each other at equilibrium? * No …. the product concentrations depend upon the initial concentrations and the stoichiometric ratio of the balanced reaction equation. 3) The synthesis of hydrogen iodide is an endothermic process, with a ∆Hformation of +26.5 kJ/mol. Were the temperature of the reaction lowered from 445°C to 100°C, which reaction (the forward or the reverse) should be favored? *The endothermic reaction depends upon energy … A lower temperature should hamper the endothermic reaction. Hence, the exothermic decomposition of HI would be favored. 244 B) ICE table: a decidedly nice process to analyze the changes between initial concentrations, and the equilibrium concentrations. ICE stands for: Initial, Change, Equilibrium [A] [B] Initial Change Equilibrium Follow this process 1) an ICE table can help you analyze the initial [ ], the change and the final equilibrium [ ] a) Use the balanced equation (as a guide) to start an ICE table and use the problem information, to fill in as much of the table as you can. This includes the “change” of the reactant or product…. b) Use the change and the stoichiometric ratio from the balanced chemical equation to complete the table. … Be sure the columns add up to reflect the correct equilibrium concentrations. c) Use the balanced reaction equation to write an equilibrium expression and sub in the appropriate values to calculate K 2) Assume the equilibrium: A(g) 2 B(g) A sealed container has been charged with 1.00 M of A, and an initial concentration of 0.00 M of B. At equilibrium, the concentration of A is 0.75 M. a) Calculate the equilibrium concentrations of A and B b) Calculate the equilibrium constant (Kc) Solution to a) … Study the stoichiometry of the balanced equation. It is 1:2 … That is for every molar change in A, B is TWICE the change [A] [B] 1.00 *0.00 Change *-0.25 *+0.50 Equilibrium *0.75 *0.50 Make an ICE table Initial Solution to b) …. Write the equilibrium expression … plug and chug Kc = * [B]2 [A] = (0.50)2 = 0.33 (0.75) 245 2) NO2, a brown gas, and N2O4, a colorless gas, exist in equilibrium 2NO2(g) N2O4(g) Chemistry is a “way” a) For an ICE Table Use the balanced equation (as a guide) & fill in as much of the table as you can. b) Use the change and the ratios of the balanced chemical equation to complete the table. c) Write an equilibrium expression to plug and chug A closed container at 25°C is charged with NO2 at a partial pressure of 0.56 atm and with N2O4 at a partial pressure of 0.51 atm. At equilibrium the partial pressure of N2O4 is found to be 0.54 atm. a) What is the partial pressure of NO2 at equilibrium? (ans: 0.50 atm) b) What is the value of Kp? (ans: 2.2) Initial (NO2) atm *0.56 (N2O4) atm *0.51 Change *-0.06 *+0.03 Equilibrium *0.50 *0.54 *Kp = (PN2O4) (PNO2)2 = 0.54 atm = 2.16 or 2.2 (0.50 atm)2 Hint 1: * You are given the partial pressure of the gases, in atmospheres … This means that you can write the equilibrium expression by using the Law of Mass Action, substituting in pressures, for concentrations. Hint 2: * This is a perfect time to use an ICE table … Take a look at the change in partial pressure and please be sure to note that there is a stoichiometric effect here of 2 to 1 … Hint 3: * Write the equilibrium expression, using the partial pressure version and be sure to plug in the equilibrium pressures, from your ICE table. 3) Consider the following reaction, at equilibrium: CO(g) + 2 H2(g) CH3OH(g) A reaction mixture at 780°C initially contains [CO] = 0.500 M and [H2] =1.00 M. At equilibrium the CO concentration is experimentally determined to be 0.150 M. What is the value of Kc? *Kc = [CH3OH] [CO] [H2]2 *remove [CO] [H2] [CH3OH] Initial 0.500 1.00 0.00 Change -0.350 -0.700 +0.350 Equilibrium 0.150 0.300 0.350 Hint 1: * It asks for the equilibrium constant, so write the equilibrium expression … hopefully you will recognize that you require the equilibrium concentrations … and thus need to figure those concentration out … How ???? Hint 2: * Create an ICE table Hint 3: * Follow our process re: ICE tables … be sure to watch those stoichiometric ratios … . ans: 25.9 246 4) Determine the value of the equilibrium constant for the reaction: A + 2 B ↔ 2C when 1.0 mol of A, 2.0 mol of B, and 3.0 mol of C are placed in 1.0 L vessel and allowed to come to equilibrium, The final or equilibrium concentration of C = 1.4 mol/L remove * Initial Change Equilibrium [A] [B] [C] 1.0 2.0 3.0 +0.80 +1.6 -1.6 1.8 3.6 1.4 *Kc = [C]2 [A] [B]2 = Hint 1: * Write the equilibrium expression using the Law of Mass Action. Hint 2:* Use an ICE Table. Find the change in moles and final moles at equilibrium. You should then convert all mole values to molarities but this problem is easier since the volume is a 1 L flask. … Hint 3: * In the ICE table, don’t forget that the coefficients of the balanced equation must be used to determine the C the change in concentration for the species. (1.4)2 = 0.084 (1.8) (3.6)2 Chemistry is a “way” 5) Given: 2 CH4(g) C2H2(g) + 3 H2(g) A reaction mixture at 1700 °C initially contains [CH4] = 0.115 M. At equilibrium, the mixture contains [C2H2] = 0.035 M. What is the value of the equilibrium constant? ans: 0.020 *remove [CH4] [C2H2] [H2] Initial 0.115 0.00 0.00 Change -0.070 +0.035 +0.105 Equilibrium 0.045 0.035 0.105 *Kc = [C2H2] [H2]3 [CH4]2 = (0.035)(0105)3 (0.045)2 a) For an ICE Table: Use the balanced equation (as a guide) & fill in as much of the table as you can. b) Use the change and the ratios of the balanced chemical equation to complete the table. c) Write an equilibrium expression to plug and chug = 0.020 6) Which of the following equations has Kc = KP? (one, or more than one answer may be applicable) 1) PCl5(g) PCl3(g) + Cl2(g) 2) 2NO(g) N2(g) + O2(g) 3) CaCO3(s) CaO(s) + CO2(g) 4) H2O (g) + CO(g) H2(g) + CO2(g) 5) 2 NOCl(g) 2 NO(g) + Cl2(g) ans: * 2 and 4 247 7) At a certain temperature, a 1.00 L flask initially contained 0.298 mole of PCl3(g) and 8.70 x 10-3 mole of PCl5(g). After the system had reached equilibrium, 2.00 x 10-3 mole of Cl2 was found in the flask. Gaseous phosphorus pentachloride decomposes according to the following reaction. Calculate Kc (Zumdahl p. 624) PCl5(g) PCl3(g) + Cl2(g) Hint 1:* Write the equilibrium expression *remove Initial Change Equilibrium [PCl5] [PCl3] [Cl2] 8.7 x 10-3 0.298 0.00 -2.00 x 10-3 +2.00 x 10-3 +2.00 x 10-3 6.7 x 10-3 0.300 2.00 x 10-3 Hint 2: * Convert moles to molarity … Luckily the volume is 1 L, so the conversion is a direct one … and run an ICE Table. Think about this … You do NOT have any chlorine at the start, so it is 0. The stoichiometric ratios are easy, since everything is in a 1:1 Hint 3: * Run the Law of Mass Action *Kc = [PCl3(g)] [Cl2(g)] [PCl5(g)] = (0.300)( 2.00 x 10-3) (6.70 x 10-3) ans: 8.96 x 10-2 8) 3.0 mol of iodine and 4.0 mol of bromine are placed in a 2.0 L flask at 150°C. The reaction comes to equilibrium, at which point 3.2 mol of iodine bromide are present. a) Write the balanced reaction equation for the synthesis of iodine bromide from its elements. * I2(g) + Br2(g) 2 IBr(g) b) Determine the equilibrium constant for the reaction. *remove iodine bromine concentrations iodineafter bromide This one is a bit different … I converted to equilibrium working with the mole values … because the overall volume was a 2 L flask …not a 1 L flask as in prior examples Initial 3.0 mol 4.0 mol 0.00 Change -1.6 mol -1.6 mol +3.2 mol Equilibrium 1.4 mol 2.4 mol 3.2 mol 0.7 M 1.2 M 1.6 M *Kc = [IBr]2 = (1.6)2 = 3.0 [I2][Br2] (0.7)(1.2) Hint 1: * Write the equilibrium expression and Run an ICE table finding the change in moles. Remember to take into account the stoichiometric ratios of the balanced equation. Hint 2:* Once you have the final mol values at equilibrium, convert them to molarity values. Note the volume of the flask is 2 L Hint 3: * Plug and chug the molarities calculated from the results of the ICE table into the equilibrium expression. ans: *3.0 248