Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Vapor-compression refrigeration wikipedia , lookup
Solar air conditioning wikipedia , lookup
Stoichiometry wikipedia , lookup
Electrolysis of water wikipedia , lookup
Gas chromatography wikipedia , lookup
George S. Hammond wikipedia , lookup
Chemical equilibrium wikipedia , lookup
Equilibrium chemistry wikipedia , lookup
Internal energy wikipedia , lookup
Heat transfer wikipedia , lookup
Heat capacity wikipedia , lookup
Thermodynamics wikipedia , lookup
General Physical Chemistry I Lecture 7 Aleksey Kocherzhenko February 26, 2015" Last time…" The first law of thermodynamics" The change in the internal energy of a system: "dU = dA + dq Work performed on the system (positive) Heat transferred" or by the system (negative) " to the system (positive) or from the The first law of thermodynamics" system to the surroundings (negative)" Verbal statement: The " change in the internal energy of the system is the sum of the heat transferred to the system and the work performed on it" An isolated system does not exchange energy with its surroundings, neither as heat, nor as work: dq " = dA = 0 ) dU = 0 The first law of thermodynamics is the law of energy conservation: energy can be converted from one form to another, but it cannot be created or destroyed" à Perpetual motion machines that perform more work than they use energy cannot be created" Internal energy as a state function" The internal energy only depends on the initial and final state of the system (not on how it transferred from one to the other)" Ø Quantities like that are referred to as state functions! Ø Work is not a state function: as we have seen, it depends on the path by which the system got from the initial to the final state (it is a process function)! Enthalpy" Many processes, particularly chemical reactions, occur at constant pressure (in open vessels), not at constant volume" à Transferred heat ≠ change in internal energy" Ø Heat transfer in such processes is conveniently characterized in terms of the enthalpy, defined as:! H = U + pV Positive for endothermic reactions ! At constant pressure:" dH = dU + pdV Negative for exothermic reactions! At constant pressure, the heat transferred to the system is equal to the change in enthalpy " Ø The enthalpy is defined in terms of state functions only ( U, and thus it is itself a state function" p, V ), Ø Like the internal energy, the enthalpy is an extensive quantity: it depends on the amount of substance, and molar enthalpy can be defined" Heat capacity" Heat capacity" The heat capacity of a system is the amount of energy that needs to be transferred to a system" dq to achieve a unit change in its temperature:" C = dT Specific heat capacity (per unit mass):" C Cs = m Extensive property: heating more substance requires more energy" Molar heat capacity (per mole):" C Cm = ⌫ Heat capacity depends on the conditions under which the substance is heated" (the reasons for this are discussed in detail in PChem II) " à Commonly reported are the molar heat capacity @ constant pressure,"Cp,m or @ constant volume, CV,m (or respective specific heat capacities)" Ø Heat capacities for all monoatomic perfect gasses are similar" Ø The heat capacity of a sample can be measured using a calorimeter, where a known amount of energy is transferred to a sample and the change in its temperature is detected" Heat capacity at constant p and constant V! At constant volume:" CV = ✓ @q @T ◆ = V ✓ @U @T ◆ At constant pressure:" Cp = V The heat capacities at constant volume and constant pressure are tangents to functions U (T ) and H (T ), respectively" ✓ @q @T ◆ = p ✓ @H @T ◆ à generally, the heat capacity is temperature-dependent" p Heat capacity for a perfect gas! At constant volume:" CV = ✓ @q @T Enthalpy:" H ) ◆ = V ✓ @U @T ◆ At constant pressure:" Cp = V = U + pV (for a perfect gas only):" ✓ @q @T ◆ = p ✓ Perfect gas law:" pV @H @T @H @U = + ⌫R @T @T ) Cp = CV + ⌫R Or, for molar heat capacities:" Cp,m = CV,m + R This relation between heat capacities at constant pressure and constant volume is valid for perfect gasses only" p = ⌫RT H = U + ⌫RT Differentiating both sides with temperature:" ◆ Heat capacity for a perfect gas! At constant volume:" CV = ✓ @q @T ◆ = V ✓ @U @T ◆ At constant pressure:" Cp = V ✓ @q @T ◆ Relation between molar heat capacities of a perfect gas:" Cp,m = p ✓ @H @T ◆ = CV,m + R Calculate the actual values of the molar heat capacities at constant volume and at constant pressure for a monoatomic perfect gas! " (Hint: use the equipartition principle)" Energy per degree of freedom:" E1 = 12 kB T Energy per atom of perfect gas:" Eatom = 32 kB T Energy per mole of perfect gas:" Em = NA · 32 kB T = 32 RT For a perfect gas, "Um = Em ) CV,m = ) Cp,m = CV,m + p @Um 3 = @T V 2R R = 32 R + R = 52 R Thermochemistry" Thermochemistry" Some definitions:" Ø Heat of reaction: The heat change in the transformation of reactants at given fixed temperature and pressure to products at the same temperature and pressure" Ø Exothermic reaction: system transfers heat to the surroundings" Ø Endothermic reaction: system absorbs heat from the surroundings" The first law of thermodynamics requires that if a forward reaction is exothermic, the reverse reaction must be endothermic:" forward H = reverse H All reactants and products are in their standard states (at pressure 1 bar) at the same T " Changes in enthalpy in a reaction are reported under standard conditions (1 bar and some temperature): the standard enthalpy of the reaction, " r H Enthalpy of a phase transition" Ø Phase: is a state of matter that is uniform in composition and physical state" Ø Phase transition: a process in which a substance goes from one phase to another " Solid" Liquid" Only He has" two different" liquid states" Gas" All substances have just one gas phase" Many substances have more than one solid phase: e.g., C: graphite and diamond" All processes at same temperature" The enthalpy change of a process is the sum of enthalpy changes for the steps (observed or hypothetical) into which it may be divided" Enthalpies of some phase transitions" H2O (l) à H2O (g)" vap H (298 K) = 44 kJ/mol H2O (g) à H2O (l)" 44 kJ/mol cond H (298 K) = H2O (s) à H2O (l)" fus H (273 K) = 6 kJ/mol H2O (s) à H2O (g)" sub H (273 K) = 51.07 kJ/mol vap H (273 K) = sub H (273 K) fus H vap H (273 K) ? (273 K) Enthalpy of ionization" @ 1 bar and 25 °C" Enthalpy of ionization: Enthalpy that accompanies the removal of an electron from an atom in the gas phase" First, second, … enthalpies of ionization correspond to the removal of 1, 2, … e–’s" For atom in a solid: enthalpy of sublimation + enthalpy of ionization (in gas phase)" How much heat is necessary to turn 1 g of solid Mg into a gas of Mg2+ ions and e–’s @ 1 bar and 25 °C? " MMg = 24.31 g/mol Enthalpy of e– gain: enthalpy of adding an e– to form a negative ion" Standard enthalpy of formation" Change of enthalpy when 1 mole of a compound is formed from its constituent elements, with all substances in their standard states at 1 bar " reactants" products" aA + bB à cC + dD" Stoichiometric coefficients " r Hm =c f Hm (C) + d f Hm (D) a f Hm (A) f Hm (B) b Standard states for:" Ø A gas: a pressure of 1 bar" Ø A solute in an ideal solution: a concentration of exactly 1 M under p = 1 bar" Ø A pure substance or a solvent in a condensed state (liquid or solid): the pure liquid or solid under p = 1 bar" Ø For an element: the form in which the element is most stable under a pressure of 1 bar [Exception: P – most stable form at 1 bar is black P, but white P is used as the reference state for zero enthalpy of formation]" Bond enthalpy" Bond enthalpy: the enthalpy that accompanies the breaking of a chemical bond" Ø For polyatomic molecules, average bond enthalpy can be defined" Ø Hr estimated by counting the total number of bonds broken and formed " HCl (g) à H(g) + Cl(g)" Hr = +431 kJ Breaking a bond always requires energy à all bond enthalpies are positive" Complication: bond enthalpy depends on molecule in which a bond is broken" Mean bond enthalpy" Example: dissociation of water into atoms" H2O(g) à 2H(g) + O(g) " H2O(g) à HO(g) + H(g) " HO(g) à H(g) + O(g) " Hr = +927 kJ Hr1 = +499 kJ Hr2 = +428 kJ Mean bond enthalpy: average of bond enthalpies over a related series of compounds" Kirchhoff’s law" The difference between the enthalpies of a reaction at two temperatures, T1 and T2 , is the difference in the enthalpies of heating the products and reactants from T1 to" T2 rH Gustav Kirchhoff" (T2 ) rH (T1 ) = ZT2 r Cp,m dT = Cp,m (T2 ✓ ◆ T1 @H C = since we have established that" p @T p T1 ) Nearly constant within a wide range of T " r Cp,m = X i Sum over products" (i) ai Cp,m X (j) bj Cp,m j Sum over reactants" Stoichiometric coefficients "