Download Thermodynamics and Kinetics

Exam 1 Distribution
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Thermochemical Equations
•
Write the thermochemical equation for the reaction for
CuSO4(aq) + 2NaOH(aq)
50.0mL of 0.400 M CuSO4 at 23.35 oC
Tfinal 25.23oC
50.0mL of 0.600 M NaOH at 23.35 oC
Density final solution = 1.02 g/mL
CH2O = 4.184 J/goC
Cu(OH)2(s) + Na2SO4(aq)
Chemical Thermodynamics
• Chemical reactions obey two fundamental laws:
1. The law of conservation of mass


States that matter can be neither created nor destroyed
Explains why equations must balance and is the basis for
stoichiometry and equilibrium calculations



Stoichiometry that allows us to compare apples and oranges
Equilibrium predictions of reversible reactions which leads to
Kinetics allowing us to determine how fast the reaction will
occur
2. The law of conservation of energy


States that energy can be neither created nor destroyed
Energy takes various forms that can be converted from one to
the other
Some Thermodynamic Terms
Thermodynamics - The study of the relationship between heat, work, and other
forms of energy of a system at equilibrium. Predicts whether a particular reaction
is energetically possible in the direction as written and the composition of the
reaction system at equilibrium. Thermodynamics does not say whether an
energetically feasible reaction will actually occur as written. Thermodynamics tells
nothing about the rate of the reaction or the pathway by which it will occur.
Thermochemistry - A branch of thermodynamics which focuses on the study of
heat given off or absorbed in a chemical reaction.
Temperature - An intensive property of matter; a quantitative measurement of the
degree to which an object is either "hot" or "cold". There are 3 scales:
•Fahrenheit - relative
• 32 ◦F is the normal freezing point temperature of water;
212 ◦ F is the normal boiling point temperature of water.
•Celsius (centigrade) - relative
• 0 ◦ C is the normal freezing point temperature of water; 100
◦ C is the normal boiling point temperature of water.
•Kelvin - absolute
• 0 K is the temperature at which the volume and pressure of
an ideal gas extrapolate to zero.
Standard States and Standard
Enthalpy Changes
1.
Thermochemical standard state conditions
• The thermochemical standard T = 298.15 K.
• The thermochemical standard P = 1.0000 atm.
– Be careful not to confuse these values with STP.
2. Thermochemical standard states of matter
• For pure substances in their liquid or solid phase the standard
state is the pure liquid or solid.
• For gases the standard state is the gas at 1.00 atm of pressure.
• For gaseous mixtures the partial pressure must be 1.00 atm.
• For aqueous solutions the standard state is 1.00 M concentration.
Thermodynamics and Work
• A system is that part of the universe in which we are interested (in chemistry this
is the reactant side of the chemical equation); the surroundings are everything
else—the rest of the universe.
• System + surroundings = universe.
• A closed system can exchange energy but not matter with its surroundings; an
open system exchanges both, and an isolated system exchanges neither.
• State function — the property of a system that depends only on the present
state of the system and not on its history.
1.
State Functions are independent of pathway:
– T (temperature), P (pressure), V (volume), E (change in energy), H
(change in enthalpy – the transfer of heat), and S (entropy)
2.
Examples of non-state functions are:
– n (moles), q (heat), w (work)
• A change in state function depends only on the difference between the initial and
final states, not on the pathway used to go from one to the other.
• Thermodynamics is concerned with state functions and does not deal with how
the change between the initial and final state occurs.
Some Thermodynamic Terms
Latent Heat versus Sensible Heat
Sensible heat - Heat that can be detected by a change in the temperature of a
system.
Latent heat - Heat that cannot be detected because there is no change in
temperature of the system. e.g. The heat that is used to melt ice or
to evaporate water is latent heat.
There are two forms of latent heat:
•Heat of fusion - The heat that must be absorbed to melt a mole of a solid.
•e.g. melting ice to liquid water
•Heat of vaporization - The heat that must be absorbed to boil a mole of a liquid.
•e.g. boiling liquid water to steam
Thermochemical Equations
• Thermochemical equations are a balanced chemical reaction
plus the H value for the reaction.
– For example, this is an exothermic thermochemical equation.
C5 H12( )  8 O 2(g)  5 CO 2(g)  6 H 2 O (  )  3523 kJ
1 mole
8 moles
5 moles
6 moles
• The stoichiometric coefficients in thermochemical equations must be
interpreted as numbers of moles.
• 1 mol of C5H12 reacts with 8 mol of O2 to produce 5 mol of CO2, 6
mol of H2O, and releasing 3523 kJ is referred to as one mole of
reactions.
this is an endothermic thermochemical equation.
H2O(S) + 6.02 kJ →H2O(l)
Some Thermodynamic Terms
Heat (q) - A form of energy associated with the random motion of the elementary
particles in matter.
Heat capacity - The amount of heat needed to raise the temperature of a defined
amount of a pure substance by one degree.
Specific heat - The amount of heat needed to raise the temperature of one gram of a
substance by 1 C (or 1 K)
•SI unit for specific heat is joules per gram-1 Kelvin-1 (J/g-K)
Calorie - The specific heat of water = 4.184 J/g-K
Molar heat capacity - The amount of heat required to raise the temperature of one
mole of a substance by 1 C (or 1 K)
•SI unit for molar heat capacity is joules per mole-1 Kelvin-1 (J/mol-K)
Btu (British thermal unit) - The amount of heat needed to raise the temperature of
1 lb water by 1 F.
NOTE: The specific heat of water (4.184 J/g-K) is very large relative to other
substances. The oceans (which cover over 70% of the earth) act as a giant "heat sink,"
moderating drastic changes in temperature.
Our body temperatures are also controlled by water and its high specific heat.
Perspiration is a form of evaporative cooling which keeps our body temperatures from
getting too high.
Some Thermodynamic Theories
Caloric Theory of Heat
•Served as the basis of thermodynamics.
•Is now known to be obsolete
•Based on the following assumptions
•Heat is a fluid that flows from hot to cold substances.
•Heat has a strong attraction to matter which can hold a lot of
heat.
•Heat is conserved.
•Sensible heat causes an increase in the temperature of an
object when it flows into the object.
•Latent heat combines with particles in matter (causing
substances to melt or boil)
•Heat is weightless.
The only valid part of the caloric theory is that heat is weightless.
Heat is NOT a fluid, and it is NOT conserved.
Some Thermodynamic Theories
Kinetic Theory of Heat
1. Divides the universe into two parts:
A.
System. - The substances involved in the chemical and
physical changes under investigation: In chemistry lab, the
system is the REACTANTS inside the beaker.
B.
Surroundings - Everything not included in the system, i.e.
the rest of the universe.
2. A BOUNDARY separates the system and the surroundings
from each other and can be tangible or imaginary.
A. Heat is something that is transferred back and forth across
boundary between a system and its surroundings
B. Heat is NOT conserved.
Some Thermodynamic Theories
The kinetic theory of heat is based upon the last postulate in the kinetic molecular
theory which states that the average kinetic energy of a collection of gas
particles is dependent only upon the temperature of the gas.
where R is the ideal gas constant (0.08206 L-atm/mol-K) and T is temperature
(Kelvin) The kinetic theory of heat can be summarized as follows:
When heat enters a system, it causes an increase in
the speed at which the particles in the system move.
•
•
The set of conditions that specify all of the properties of the system is called the
thermodynamic state of a system.
For example the thermodynamic state could include:
– The number of moles and identity of each substance.
– The physical states of each substance.
– The temperature of the system.
– The pressure of the system.
The Three Laws of Thermodynamics
There are two basic ideas of importance for
thermodynamic systems.
1. Chemical systems tend toward a state of
minimum potential energy.
2. Chemical systems tend toward a state of
maximum disorder.
When:
H > 0 disorder increases (which favors spontaneity).
H < 0 disorder decreases (does not favor spontaneity).
When:
S > 0 disorder increases (which favors spontaneity).
S < 0 disorder decreases (does not favor spontaneity).
The First Law of Thermodynamics
• The first law is also known as the
Law of Conservation of Energy.
Energy is neither created nor destroyed in
chemical reactions and physical changes.
•The energy of the universe does not change.
•The energy in a system may change, but it must be complemented by a change in the
energy of its surroundings to balance the change in energy.
The term internal energy is often used synonymously with the energy of a system. It is the
sum of the kinetic and potential energies of the particles that form the system. The change
in energy of the system is identical in magnitude but opposite in sign to the change in energy
of the surroundings.
The First Law of Thermodynamics
If a system is more complex than an ideal gas, then the internal energy must
be measured indirectly by observing any changes in the temperature of the
system. The change in the internal energy of a system is equal to the
difference between the final and initial energies of the system:
The equation for the first law of thermodynamics can be rearranged to show
the energy of a system in terms of the energy of its surroundings.
This equation indicates that the energy lost by one must equal the energy
gained by the other:
1.
2.
Esys = KEsys + PEsys
KE – kinetic energy: translational,
rotational, vibrational
PE – energy stored in bonds (Bond energy)
The First Law of Thermodynamics
The energy of a system can change by the transfer of work and or heat
between the system and its surroundings. Any heat that is taken, given
off, or lost must be complemented by an input of work to make up for
the loss of heat. Conversely, a system can be used to do any amount of
work as long as there is an input of heat to make up for the work done.
This equation can be used to explain the two types of heat that can be
added to a system:
1. Heat can increase the temperature of a system. This is sensible heat.
2. Heat that does ONLY WORK on a system is latent heat.
• Any machine that converts energy to work is designed to want to
maximize the amount of work obtained and to minimize the amount
of energy released to the environment as heat
The First Law of Thermodynamics
Most chemical reactions occur at constant P, so
Heat transferred at constant P = qp
qp = ∆H
where H = enthalpy
and so ∆E = ∆H + w (and w is usually small)
∆H = heat transferred at constant P ≈ ∆E
∆H = change in heat content of the system
∆H = Hfinal - Hinitial
∆Horxn =  ∆Hfo (prod) -  ∆Hfo (react)
-103.8 kJmol-1
0 kJmol-1
-393.5 kJmol-1
-241.8 kJmol-1
C3H8(g) + 5 O2(g) )  3 CO2(g) + 4 H2O(g)
The First Law of Thermodynamics
1.
2.
Exchange of heat (q) Endothermic and exothermic
Work is performed (w)
E = q + w
Solids, Liquids, Solutions
Gases
Why only gases?
Because changes in volume
results in work
w = Fd
E = q + 0 = H
F = Pressure x Area d = h
W = P (A h) = V
H is change in enthalpy which is the
transfer of heat and is measured
experimentally by determining changes
in temperature.
Changes in volume are negligible
Therefore w is effectively zero
The First Law of Thermodynamics
heat transfer in
(endothermic), +q
heat transfer out
(exothermic), -q
SYSTEM
∆E = q + w
w transfer in
(+w)
Compression of system
w transfer out
(-w)
Expansion of system
By convention except for some engineers whose frame
of reference is the work done on the surroundings.
hi
hf
hi hf
A(hf-hi)>0 V
w = -PV
E =H + w = H – PV = H – (PV)
A(hf-hi)<0 V
E = H – (PV)
Constant Volume
Constant Pressure
w = -PV
V = 0
E = q + 0 = H
Check the temperature change
Apply some stoichiometry
And the Ideal Gas Law
PV=nRT
(PV)=(nRT)
Hold Temperature constant k1
(PV)=(nRk1)
Combine constants and
multiply through by -1
-(PV) = -R1n
w = -PV = -R1n
E = H + w = H - R1n
E
H
n
E = H
exothermic
No change
E = H
endothermic
No change
E > H
exothermic
increase
E > H
endothermic
decrease
E < H
exothermic
decrease
E < H
endothermic
increase
Thermochemical Equations
Write the thermochemical equation for
CuSO4(aq) + 2NaOH(aq)
50.0mL of 0.400 M CuSO4 at 23.35 oC
50.0mL of 0.600 M NaOH at 23.35 oC
Tfinal 25.23oC
CH2O = 4.184 J/goC
Density final solution = 1.02 g/mL
Cu(OH)2(s) + Na2SO4(aq)
The Second Law of Thermodynamics
Enthalpy changes are not the only factors that determine whether a
process is spontaneous. Most spontaneous reactions are exothermic,
but there are many that are not exothermic, however, reactions can be
both spontaneous and highly endothermic.
•
The second law of thermodynamics states, “In spontaneous
changes the universe tends towards a state of greater
disorder.”
•
Spontaneous processes have two requirements:
1. The free energy change of the system must be negative.
2. The entropy of universe must increase.
• Fundamentally, the system must be capable of doing
useful work on surroundings for a spontaneous process
to occur.
Changes in S are usually quite small compared to E and H. Notice that S has units
of only a fraction of a kJ while E and H values are much larger numbers of kJ.
The Second Law of Thermodynamics
Entropy (S) – is the measure of the disorder in a system. Entropy
of the universe is unchanged in reversible processes and constitutes
part of the second law of thermodynamics: the entropy of the
universe remains constant in a reversible process, whereas the entropy
of the universe increases in an irreversible (spontaneous)
process. Entropy is a state function described by the equation:
where k is a proportionality constant equal to the ideal gas constant (R)
divided by Avogadro's number (6.022 x 10-23) and lnW is the natural log
of W, the number of equivalent ways of describing the state of a
system.
In this reaction, the number of ways of describing a system is directly
proportional to the entropy of the system.
The Second Law of Thermodynamics
Number of Equivalent Combinations for Various Types of Poker Hands
Hand
W
ln W
Royal flush (AKQJ10 in one suit)
Straight flush (five cards in sequence in one suit)
Four of a kind
Full house (three of a kind plus a pair)
Flush (five cards in the same suit)
Straight (five cards in sequence)
Three of a kind
Two pairs
One pair
No pairs
Total
4
36
624
3,744
5,108
10,200
54,912
123,552
1,098,240
1,302,540
2,598,960
1.39
3.58
6.44
8.23
8.54
9.23
10.91
11.72
13.91
14.08
The Second Law of Thermodynamics
Entropy of Reaction (S)
•The difference between the sum of the entropies of
the products and the sum of the entropies of the
reactants:
In the above reaction, n and m are the coefficients
of the products and the reactants in the balanced
equation.
As with H, entropies have been measured and tabulated.
When:
S > 0 disorder increases (which favors spontaneity).
S < 0 disorder decreases (does not favor spontaneity).
The Second Law of Thermodynamics
Natural processes that occur in an isolated system are spontaneous when they lead to an
increase in the disorder, or entropy, of the system.
Isolated system - System in which neither heat nor work can be transferred between it and its
surroundings. This makes it possible to ignore whether a reaction is exothermic or endothermic.
If Ssys > 0, the system becomes more disordered through the
course of the reaction
If Ssys < 0, the system becomes less disordered (or more
ordered) through the course of the reaction.
There are a few basic principles that should be remembered to help determine
whether a system is increasing or decreasing in entropy.
• Liquids are more disordered than solids.
•WHY? - Solids have a more regular structure than liquids.
• Gases are more disordered than their respective liquids.
•WHY? - Gases particles are in a state of constant random motion.
• Any process in which the number of particles in the system increases
consequently results in an increase in disorder.
• In general for substances with the same molar mass and number of atoms in its
three states of matter, Sº values fall in the :
Sgas > Sliquid > Ssolid
The Second Law of Thermodynamics
Does the entropy increase or decrease for the following reactions?
• CaCO3(s) → CaO(s) + CO2(g)
• N2(g) + 3H2(g) → 2NH3(g)
→
• NH4NO3(s) → NH4+(aq) + NO3-(aq)
• H2O(g)→ H2O(l)
→
•
•
Entropy, S
The Third Law of Thermodynamics states, “The entropy of a pure, perfect,
crystalline solid at 0 K is zero.”
This law permits us to measure the absolute values of the entropy for
substances.
– To get the actual value of S, cool a substance to 0 K, or as close as
possible, then measure the entropy increase as the substance heats from
0 to higher temperatures.The coldest place in nature is the depths of
outer space. There it is 3 degrees above Absolute Zero.
– Notice that Appendix L has values of S not S.
Predicted 1924...
...Created 1995
Bose-Einstein Condensation in a gas: a
new form of matter at the coldest
temperatures in the universe...
A. Einstein S. Bose
Cornell and Wieman cooled a small
sample of atoms down to only a
few billionths (0.000,000,001) of a
degree above Absolute Zero
Entropy, S
BEC
When a gas expands into a vacuum, its entropy increases because the increased
volume allows for greater atomic or molecular disorder; the greater the number of
atoms or molecules in the gas, the greater the disorder.
The magnitude of the entropy of a system depends on the number of microscopic
states, or microstates, associated with it; the greater the number of microstates, the
greater the entropy.
Entropy and Temperature
S increases slightly with T
S increases a large
amount with phase
changes
Calculating S from Standard Molar Entropy Values
•
Similar molecular structures have similar Sº values
1.
2.
Those with the lowest entropies tend to be rigid crystals composed of small
atoms linked by strong, highly directional bonds
Those with higher entropies are soft crystalline substances that contain larger
atoms and increased molecular motion and disorder
•
Absolute entropy of a substance tends to increase with increasing
molecular complexity because the number of available microstates
increases with molecular complexity
•
Substances with strong hydrogen bonds have lower values of Sº,
reflecting a more ordered structure
•
To calculate Sº for a chemical reaction from standard molar
entropies, the “products minus reactants” rule is used; here the
absolute entropy of each reactant and product is multiplied by its
stoichiometric coefficient in the balanced chemical equation
Entropy, S
• Entropy changes for reactions can be
determined similarly to H for reactions.This is
only true, i.e. conserved, for the system. This is
not included for the surroundings.
S
o
298
  nS
o
products
n
-  nS
o
reactants
n
Entropy, S
• Calculate the entropy change for the following reactions at 25oC.
240 Jmol-1K-1
210.6 Jmol-1K-1
270.2 Jmol-1K-1
0 Jmol-1K-1
304.2 Jmol-1K-1
219.7 Jmol-1K-1
240 Jmol-1K-1
197.6 Jmol-1K-1
188.7 Jmol-1K-1
C3H8(g)+ 5O2(g)  3CO2(g) + 4H2O(g)
The Third Law of Thermodynamics
The entropy of any perfectly ordered,
crystalline substance at absolute zero is zero.
Absolute zero is an ideal temperature that is unobtainable, and a
perfect single crystal is an ideal that cannot be achieved, however,
the combination of these two ideals constitutes the basis for the
third law of thermodynamics.
• The third law of thermodynamics has two important
consequences:
1.
2.
It defines as positive the sign of the entropy of any substance at
temperatures above absolute zero
It provides a fixed reference point that allows the measurement of
the absolute entropy of any substance at any temperature
G and Spontaneity
•
•
In the mid 1800’s J. Willard Gibbs determined the relationship
of enthalpy, H, and entropy, S, and temperature, T, that best
describes the maximum useful energy obtainable in the form of
work from a process at constant temperature and pressure. G
is the difference between the heat released during a process (via
a reversible or an irreversible path) and the heat released for the
same process occurring in a reversible manner
– The relationship also describes the spontaneity of a system.
The relationship is a new state function, G, the Gibbs Free
Energy.
H = q whether a process is reversible or irreversible
TS = qrev (Suniv = 0)
G = q – qrev
G = H-TS
at constant T and P
Free Energy Change, G, and
Spontaneity
•
•
The change in the Gibbs Free Energy, G, is a reliable indicator
of spontaneity of a physical process or chemical reaction.
– G does not tell us how quickly the process occurs.
• Chemical kinetics, the subject of Chapter 16, indicates
the rate of a reaction.
Sign conventions for G.
– G > 0 reaction is nonspontaneous
– G = 0 system is at equilibrium
– G < 0 reaction is spontaneous
The Temperature Dependence of
Spontaneity
• Free energy has the relationship
G = H -TS.
• Because 0 ≤ H ≥ 0 and 0 ≤ S ≥ 0, there
are four possibilities for G.
Forward reaction
H
<0
<0
>0
>0
S
>0
<0
>0
<0
G
<0
T dependent
T dependent
>0
spontaneity
at all T’s.
at low T’s.
at high T’s.
Nonspontaneous
at all T’s.
Equilibrium . .
..
G < 0
Spontaneous . .
Spontaneity is favored when
G > 0
Non Spontaneous . .
)
G = 0
)
)
H < 0 and/or S > 0
G = H -TS
G
..
)
..
)
High T
..
..
..
..
..
)
)
)
)
..
)
)
Low T
)
..
S
)
..
H
G and Spontaneity
• Changes in free energy obey the same type of relationship
we have described for enthalpy and entropy changes.
Calculate Go298 for the reaction in
-23.56 kJmol-1
0 kJmol-1
-394.4 kJmol-1
-237.2 kJmol-1
The Temperature Dependence of
Spontaneity
•
Determine the temperature at which the following system is at
equilibrium, spontaneous, non-spontaneous.
C3H8(g) + 5 O2(g) )  3 CO2(g) + 4 H2O(g)
1.
2.
3.
We know that So298= -1077.4 kJmol-1K-1,
We know that Ho298= -2219.9 kJmol-1,
and that Go298= -2108.5 kJmol-1.
Chemical Kinetics
– Study of reaction rates, or the changes
in the concentrations of reactants and
products with time
– By studying kinetics, insights are gained
into how to control reaction conditions
to achieve a desired outcome, its
mechanism
– Reaction rate = change in concentration
of a reactant or product with time. Three
“types” of rates
1. initial rate
2. average rate
3. instantaneous rate
– Chemical kinetics of a reaction depend on
various factors
1. Physical states and surface areas of
reactants
2. Reactant concentrations
3. Temperature
4. Solvent and catalyst properties
The Rate of Reaction
• Consider the hypothetical reaction,
A(g)  B(g)
• equimolar amounts of reactant A will be consumed while product B will be
formed as indicated in this graph:
The Rate of Reaction
• Mathematically, the rate of a reaction can be written as:
aA(g) + bB(g)  cC(g) + dD(g)
1. Differential rate law
– Expresses the rate of a reaction in
terms of changes in the concentration
of one or more reactants, [R], over a
specific time interval, t
– Describes what is occurring on a
molecular level during a reaction
2. Integrated rate law
– Describes the rate of a reaction in
terms of the initial concentration,
[R]0, and the measured concentration
of one or more reactants, [R], after a
given amount of time, t
– Used for determining the reaction
order and the value of the rate
constant from experimental
measurements
The Rate of Reaction
In general, for
a A + b B → x X with a catalyst C
Rate = k [A]m[B]n[C]p
The exponents m, n, and p
• are the order of reactant
• The overall order of reaction is the sum of the order of
reactants
• can be 0, 1, 2 or fractions
• must be determined by experiment
Rate law must provide a rate with the units M/s
The proportionality constant, k, is called the rate constant.
1. Value is characteristic of the reaction and reaction conditions
2. A given reaction has a particular value of the rate constant under a given
set of conditions, such as temperature, pressure, and solvent
The Rate of Reaction
• The rate of a simple one-step reaction is directly proportional
to the concentration of the reacting substance.
A (g)  B(g) + C(g)
Rate  A or Rate = kA
• [A] is the concentration of A in molarity or moles/L.
• k is the specific rate constant.
– k is an important quantity in this chapter.
Zeroth-Order Reactions
– Reaction whose rate is independent of concentration
– Its differential rate law is rate = k
– One can write their rate in a form such that the exponent of the
reactant in the rate law is 0
rate = – [A] = k[reactant]0 = k(1) = k
t
– Since rate is independent of reactant concentration, a graph of the
concentration of any reactant as a function of time is a straight line with
a slope of –k (concentration decreases with time); a graph of the
concentration of any product as a function of time is a straight line with
a slope of +k
First-Order Reactions
– Reaction rate is directly proportional to the concentration of one of the
reactants
– Have the general form A  products
– Differential rate for a first-order reaction is
rate = – [A] = k[A]
t
– If the concentration of A is doubled, the rate of the reaction doubles;
– If the concentration of A is increased by a factor of 10, the rate
increases
by a factor of 10
– Units of a first-order rate constant are inverse seconds, s–1
– First-order reactions are very common
The order of a reaction can be expressed in terms of either each reactant
in the reaction or the overall reaction.
•
For example:
Second-Order Reactions
• Two kinds of second-order reactions
1. The simplest kind of second-order reaction is one whose rate is proportional to
the square of the concentration of the reactant and has the form 2A  products.
– Differential rate law is rate = – [A]
2t
– Doubling the concentration of A quadruples the rate of the reaction
– If the [A] is halved the rate of the reaction will decrease by a factor of 4. (½)2 = ¼
– Units of rate constant is M–1s–1 or L/mols
– Concentration of the reactant at a given time is described by the following integrated
rate law:
2. The second kind has a rate that is proportional to the product of the
concentrations of two reactants and has the form A + B  products.
– Reaction is first order in A and first order in B
– Differential rate law for the reaction is
rate = – [A] = – [B] = k[A] [B]
t
t
– Reaction is first order both in A and in B and has an overall reaction order of 2
Factors That Affect Reaction Rates
•
1.
2.
3.
4.
•
There are several factors that can influence the
rate of a reaction:
The nature of the reactants.
The concentration of the reactants.
The temperature of the reaction.
The presence of a catalyst.
We will look at each factor individually.
Phase and Surface Area Effects
• If reactants are uniformly dispersed in a single homogeneous solution,
the number of collisions per unit time depends on concentration and
temperature.
• If the reaction is heterogeneous, the
reactants are in two different phases,
and collisions between the reactants can
occur only at interfaces between phases;
therefore, the number of collisions between
the reactants per unit time is reduced, as
is the reaction rate. The rate of a
heterogeneous reaction depends on the
surface area of the more condensed phase.
Nature of Reactants
• This is a very broad category that encompasses the different reacting
properties of substances.
• For example sodium reacts with water explosively at room temperature to
liberate hydrogen and form sodium hydroxide.
• Calcium reacts with water only slowly at room temperature to liberate hydrogen and
form calcium hydroxide.
Nature of Reactants
• The reaction of magnesium with water at room temperature is so slow that
that the evolution of hydrogen is not perceptible to the human eye.
• However, Mg reacts with steam rapidly to liberate H2 and form magnesium
oxide.
• The differences in the rate of these three reactions can be attributed to the
changing “nature of the reactants”.
Nature of Reactants
34
Rb
85
Dr Bunhead and some Pub tricks 1
Dr, Bunhead and some more Pub tricks
Just blowing things up
A tent
A trailer
A grand piano
melons
Flour
Fun with your Wii
Orchestra on helium
Human Beatbox on Helium
Some things You might want to consider
when fueling your car
Concentrations of Reactants
• Two substances cannot react with each other unless their constituent particles
come into contact; if there is no contact, the rate of reaction will be zero.
• The more reactant particles that collide per unit time, the more often a reaction
between them can occur.
• The rate of reaction usually increases as the concentration of the reactants
increases.
– The increase in the molecule numbers is indicative of an increase in
concentration. A(g) + B (g)  Products
A
B
A B
4 different possible
A-B collisions
A B
B
A B
A B
A B
A B
6 different possible
A-B collisions
9 different possible
A-B collisions
Concentrations of Reactants:
The Rate-Law Expression
• Example 16-1: The following rate data were obtained at
25oC for the following reaction. What are the rate-law
expression and the specific rate-constant for this reaction?
2 A(g) + B(g)  3 C(g)
Experiment
Number
Initial [A]
(M)
Initial [B]
(M)
Initial rate of
formation of C
(M/s)
1
0.10
0.10
2.0 x 10-4
2
0.20
0.30
4.0 x 10-4
3
0.10
0.20
2.0 x 10-4
Concentrations of Reactants:
The Rate-Law Expression
• The following data were obtained for the following reaction at
25oC. What are the rate-law expression and the specific rate
constant for the reaction?
2 A(g) + B(g) + 2 C(g)  3 D(g) + 2 E(g)
Experiment
Initial [A]
(M)
Initial [B]
(M)
Initial [C]
(M)
Initial rate of
formation of D
(M/s)
1
0.20
0.10
0.10
2.0 x 10-4
2
0.20
0.30
0.20
6.0 x 10-4
3
0.20
0.10
0.30
2.0 x 10-4
4
0.60
0.30
0.40
1.8 x 10-3
Concentrations of Reactants:
The Rate-Law Expression
• Consider a chemical reaction between compounds A and
B that is first order with respect to A, first order with
respect to B, and second order overall. From the
information given below, fill in the blanks.
Experiment
Initial Rate
(M/s)
Initial [A]
(M)
Initial [B]
(M)
1
4.0 x 10-3
0.20
0.050
2
1.6 x 10-2
?
0.050
3
3.2 x 10-2
0.40
?
Concentration vs. Time: The
Integrated Rate Equation
Zeroth-Order Reactions
•
The integrated rate equation relates time and concentration for chemical and
nuclear reactions.
– From the integrated rate equation we can predict the amount of product
that is produced in a given amount of time.
– Integrated rate law for a zeroth-order reaction produces a straight line and
has the general formula
[A] = [A]0 – akt,
where [A]0 is the initial concentration of reactant A; the rate constant
must have the same units as the rate of the reaction, M/s, in a zerothorder reaction
– Equation has the form of the equation for a straight line
(y = mx + b); y = [A], mx = – akt, and b = [A]0
– Occur most often when the reaction rate is determined by available
surface area
Concentration vs. Time: The
Integrated Rate Equation
First-Order Reactions
•
These reactions are 1st order in the reactant and 1st order overall.
or
Rearranging the logarithmic expression : ln[A] = ln[A]0 – kt; the equation has the form of
the equation for a straight line; y = ln[A] and b = ln[A]0; and a plot of ln[A] vs. t for a
first-order reaction gives a straight line with a slope of –ak and an intercept of ln[A]0
– Integrated rate law for a first-order reaction can be written in two different
ways, one using logarithms and one using exponentials
Exponential form, [A] = [A]0e–kt, where [A]0 is the initial concentration of reactant A at t = 0;
k is the rate constant, and e is the base of the natural logarithms, which has the value 2.718.
Concentration of A will decrease in a smooth exponential curve over time
Concentration vs. Time: The
Integrated Rate Equation
First-Order Reactions
• An example of a reaction that is 1st order in the reactant
and 1st order overall is:
a A  products
This is a common reaction type for many chemical
reactions and all simple radioactive decays.
• Two examples of this type are:
2 N2O5(g)  2 N2O4(g) + O2(g)
238U  234Th + 4He
Concentration vs. Time: The
Integrated Rate Equation
•
Solve the first order integrated rate equation
for t.
• Define the half-life, t1/2, of a reactant as the
time required for half of the reactant to be
consumed, or the time at which
[A]=1/2[A]0.
14.4 Using Graphs to Determine Rate Laws, Rate
Constants, and Reaction Orders
For a zeroth-order reaction, a
plot of the concentration of any
reactant versus time is a straight
line with a slope of – k.
For a first-order reaction, a plot
of the logarithm of the
concentration of a reactant
versus time is a straight line with
a slope of – k.
For a second-order reaction, a
plot of the inverse of the
concentration of a reactant
versus time is a straight line with
a slope of k.
Properties of reactions that obey
zeroth-, first-, and second-order
rate laws are summarized in the
following table.
Concentration vs. Time: The
Integrated Rate Equation
• Cyclopropane, an anesthetic, decomposes to propene
according to the following equation.
The reaction is first order in cyclopropane with k = 9.2 s-1 at
10000C. Calculate the half life of cyclopropane at 10000C.
Concentration vs. Time: The
Integrated Rate Equation
• Refer to Previous Example: How much of a 3.0 g sample of cyclopropane
remains after 0.50 seconds?
– The integrated rate laws can be used for any unit that represents moles or
concentration.
– In this example we will use grams rather than mol/L.
Concentration vs. Time: The
Integrated Rate Equation
• The half-life for the following first order reaction is 688 hours at 10000C.
Calculate the specific rate constant, k, at 10000C and the amount of a 3.0 g
sample of CS2 that remains after 48 hours.
CS2(g)  CS(g) + S(g)
Concentration vs. Time: The
Integrated Rate Equation
Second-Order Reactions
• For reactions that are second order with respect to a particular reactant and
second order overall, the rate equation is:
• Where: [A]0= mol/L of A at time t=0; [A] = mol/L of A at time t; k = specific rate
constant; t = time elapsed since beginning of reaction; and a = stoichiometric
coefficient of A in balanced overall equation.
Rearranging the logarithmic expression : 1/[A] = 1/[A]0 + akt; the equation has the form
of the equation for a straight line; y = 1/[A] and b = 1/[A]0; and a plot of 1/[A] vs. t
for a first-order reaction gives a straight line with a slope of ak and an intercept of
1/[A]0
Temperature Effects
• Increasing the temperature of a system increases the average
kinetic energy of its constituent particles.
• As the average kinetic energy increases, the particles move faster,
so they collide more frequently per unit time and possess greater
energy when they collide, causing increases in the rate of the
reaction.
• Rate of all reactions increases with increasing temperature and
decreases with decreasing temperature.
Temperature:
The Arrhenius Equation
• Svante Arrhenius developed this relationship among (1) the temperature (T),
(2) the activation energy (Ea), and (3) the specific rate constant (k).
• If the Arrhenius equation is written for two temperatures, T2 and T1 with T2 >T1.
Temperature:
The Arrhenius Equation
• Consider the rate of a reaction for which Ea=50 kJ/mol, at 20oC (293 K) and
at 30oC (303 K). How much do the two rates differ?
• For reactions that have an Ea50 kJ/mol, the rate approximately doubles for
a 100C rise in temperature, near room temperature.
• Consider:
2 ICl(g) + H2(g)  I2(g) + 2 HCl(g)
• The rate-law expression is known to be R=k[ICl][H2].
Solvent Effects
• The nature of the solvent can affect the reaction rates of solute particles.
• Solvent viscosity is also important in determining reaction rates.
1. In highly viscous solvents, dissolved particles diffuse much more slowly
than in less viscous solvents and collide less frequently per unit time.
2. Rates of most reactions decrease rapidly with increasing solvent viscosity.
Catalyst Effects
• Catalyst is a substance that
participates in a chemical
reaction and increases the rate
of the reaction without
undergoing a net chemical
change itself.
• Catalysts are highly selective
and often determine the
product of a reaction by
accelerating only one of
several possible reactions that
could occur.
Catalysts
• Catalysts change reaction rates by providing an alternative reaction pathway
with a different activation energy.
• Homogeneous catalysts exist in same phase as the reactants. At least one of
the reactants interacts with the solid surface (in a physical process called
adsorption) in such a way that a chemical bond in the reactant becomes weak
and then breaks.
• Heterogeneous catalysts exist in different phases than the reactants. the
number of collisions between reactants and catalyst is at a maximum because
the catalyst is uniformly dispersed throughout the reaction mixture
– Catalysts are often solids.
Enzymes
• Enzymes are catalysts that occur naturally in living organisms and are almost
all protein molecules with typical molecular masses of 20,000–100,000 amu.
• Some are homogeneous catalysts that react in aqueous solution within a
cellular compartment of an organism.
• Some are heterogeneous catalysts embedded within the membranes that
separate cells and cellular compartments from their surroundings.
• A reactant in an enzyme-catalyzed reaction is called a substrate.
• Enzymes can increase reaction rates by enormous factors and tend to be very
specific, typically producing only a single product in quantitative yield.
• Enzymes are expensive, and often cease functioning at temperatures higher
than 37ºC, and have limited stability in solution.
• Enzyme inhibitors cause a decrease in the rate of an enzyme-catalyzed
reaction by binding to a specific portion of an enzyme and thus slowing or
preventing a reaction from occurring.
Comparing Thermodynamics and
Kinetics
• Thermodynamics
– Deals with state functions and can be used to describe the overall
properties, behavior, and equilibrium composition of a system
– Provides a significant constraint on what can occur during a reaction
process
• Kinetics
– Concerned with the particular pathway by which physical or chemical
changes occur, so it can address the rate at which a particular process will
occur
– Describes the detailed steps of what actually occurs on an atomic or
molecular level
Comparing Thermodynamics and
Kinetics
• The following table gives the numerical values of the equilibrium
constant K that correspond to various values of Gº
– If Gº  + 10 kJ/mol or Gº  –10 kJ/mol, an equilibrium is ensured to lie all the
way to the left or to the right, respectively
– If Gº is quite small (10 kJ/mol), significant amounts of both products and
reactants are present at equilibrium
Comparing Thermodynamics and
Kinetics
• Most reactions have equilibrium constants greater than 1, with the
equilibrium strongly favoring either products or reactants
• In many cases, reactions that are strongly favored by thermodynamics
do not occur at a measurable rate, and reactions that are not
thermodynamically favored do occur under certain nonstandard
conditions
• A reaction that is not thermodynamically spontaneous under standard
conditions can be made to occur spontaneously by varying reaction
conditions, by using a different reaction to obtain the same product, by
supplying external energy, or by coupling the unfavorable reaction to
another reaction for which Gº<< 0
Rescuers Search for Six Missing From Georgia Sugar Refinery Blast
AP Friday, February 08, 2008
PORT WENTWORTH, Ga. — Six people remained missing early Friday after an
explosion and fire at a sugar refinery that left dozens injured.
Officials had not determined what caused the explosion but said they suspect sugar dust,
which can be volatile.
Feb. 7: Smoke billows from behind the main plant of the Imperial Sugar Company during a fire at the plant in Port
Wentworth, Ga.