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Chemical EquilibriumChapter 14
Equilibrium: the extent of a reactionIn stoichiometry we talk about theoretical
yields, and the many reasons actual yields may be lower.
Another critical reason actual yields may be lower is the reversibility of chemical reactions: some reactions may produce only 70% of the product you may calculate they ought to produce.
Equilibrium looks at the extent of a chemical
reaction.
Equilibrium is a state in which there are no observable changes as time goes by.
Chemical equilibrium is achieved when:
• the rates of the forward and reverse reactions are equal and
• the concentrations of the reactants and products remain constant
Physical equilibrium
H2O (l)
Chemical equilibrium
N2O4 (g)
14.1
H2O (g)
2NO2 (g)
Rate of sale of Rate of sale of cookies cookies
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The Concept of EquilibriumThe Concept of Equilibrium• Consider colorless frozen N2O4. At room temperature, it
decomposes to brown NO2:
N2O4(g) 2NO2(g).
• At some time, the color stops changing and we have a mixture of N2O4 and NO2.
• Chemical equilibrium is the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. At that point, the concentrations of all species are constant.
• Using the collision model:
– as the amount of NO2 builds up, there is a chance that two NO2 molecules will collide to form N2O4.
– At the beginning of the reaction, there is no NO2 so the reverse reaction (2NO2(g) N2O4(g)) does not occur.
The Concept of EquilibriumThe Concept of Equilibrium• As the substance warms it begins to decompose:
N2O4(g) 2NO2(g)
• When enough NO2 is formed, it can react to form N2O4:
2NO2(g) N2O4(g).
• At equilibrium, as much N2O4 reacts to form NO2 as NO2 reacts to re-form N2O4
• The double arrow implies the process is dynamic.
N2O4(g) 2NO2(g)
The Concept of EquilibriumThe Concept of EquilibriumAs the reaction progresses
– [A] decreases to a constant,
– [B] increases from zero to a constant.
– When [A] and [B] are constant, equilibrium is achieved.
A B
N2O4 (g) 2NO2 (g)
Start with NO2 Start with N2O4 Start with NO2 & N2O4
equilibrium
equilibrium
equilibrium
14.1
14.1
constant
The Equilibrium ConstantThe Equilibrium Constant• No matter the starting composition of reactants and
products, the same ratio of concentrations is achieved at equilibrium.
• For a general reaction
the equilibrium constant expression is
where Kc is the equilibrium constant.
aA + bB(g) pP + qQ
ba
qp
cKBA
QP
N2O4 (g) 2NO2 (g)
= 4.63 x 10-3K = [NO2]2
[N2O4]
aA + bB cC + dD
K = [C]c[D]d
[A]a[B]bLaw of Mass Action
K >> 1
K << 1
Lie to the right Favor products
Lie to the left Favor reactants
Equilibrium Will
14.1
Homogenous equilibrium applies to reactions in which all reacting species are in the same phase.
N2O4 (g) 2NO2 (g)
Kc = [NO2]2
[N2O4]Kp =
NO2P2
N2O4P
In most cases
Kc Kp
aA (g) + bB (g) cC (g) + dD (g)
14.2
Kp = Kc(RT)Δn
Δn = moles of gaseous products – moles of gaseous reactants
= (c + d) – (a + b)
Homogeneous Equilibrium
CH3COOH (aq) + H2O (l) CH3COO- (aq) + H3O+ (aq)
Kc =‘[CH3COO-][H3O+][CH3COOH][H2O]
[H2O] = constant
Kc = [CH3COO-][H3O+]
[CH3COOH]= Kc [H2O]‘
General practice not to include units for the equilibrium constant.
14.2
The Equilibrium ExpressionThe Equilibrium Expression• Write the equilibrium expression for the
following reaction:
N2(g) + 3H2(g) 2NH3(g)
The equilibrium concentrations for the reaction between carbon monoxide and molecular chlorine to form COCl2 (g) at 740C are [CO] = 0.012 M, [Cl2] = 0.054 M, and [COCl2] = 0.14 M. Calculate the equilibrium constants Kc and Kp.
CO (g) + Cl2 (g) COCl2 (g)
Kc = [COCl2]
[CO][Cl2]=
0.140.012 x 0.054
= 220
Kp = Kc(RT)Δn
Δn = 1 – 2 = -1 R = 0.0821 T = 273 + 74 = 347 K
Kp = 220 x (0.0821 x 347)-1 = 7.7
14.2
The equilibrium constant Kp for the reaction
is 158 at 1000K. What is the equilibrium pressure of O2 if the PNO = 0.400 atm and PNO = 0.270 atm?2
2NO2 (g) 2NO (g) + O2 (g)
14.2
Kp = 2PNO PO
2
PNO2
2
PO2 = Kp
PNO2
2
PNO2
PO2 = 158 x (0.400)2/(0.270)2 = 347 atm
Heterogenous equilibrium applies to reactions in which reactants and products are in different phases.
CaCO3 (s) CaO (s) + CO2 (g)
Kc =‘[CaO][CO2]
[CaCO3][CaCO3] = constant[CaO] = constant
Kc = [CO2] = Kc x‘[CaCO3][CaO]
Kp = PCO2
The concentration of solids and pure liquids are not included in the expression for the equilibrium constant.
14.2
PCO 2= Kp
CaCO3 (s) CaO (s) + CO2 (g)
PCO 2 does not depend on the amount of CaCO3 or CaO
14.2
Writing Equilibrium Constant Expressions
• The concentrations of the reacting species in the condensed phase are expressed in M. In the gaseous phase, the concentrations can be expressed in M or in atm.
• The concentrations of pure solids, pure liquids and solvents do not appear in the equilibrium constant expressions.
• The equilibrium constant is a dimensionless quantity.
• In quoting a value for the equilibrium constant, you must specify the balanced equation and the temperature.
• If a reaction can be expressed as a sum of two or more reactions, the equilibrium constant for the overall reaction is given by the product of the equilibrium constants of the individual reactions.
14.2
Calculating Equilibrium Concentrations
1. Express the equilibrium concentrations of all species in terms of the initial concentrations and a single unknown x, which represents the change in concentration.
2. Write the equilibrium constant expression in terms of the equilibrium concentrations. Knowing the value of the equilibrium constant, solve for x.
3. Having solved for x, calculate the equilibrium concentrations of all species.
14.4
At 12800C the equilibrium constant (Kc) for the reaction
Is 1.1 x 10-3. If the initial concentrations are [Br2] = 0.063 M and [Br] = 0.012 M, calculate the concentrations of these species at equilibrium.
Br2 (g) 2Br (g)
Br2 (g) 2Br (g)
Let x be the change in concentration of Br2
Initial (M)
Change (M)
Equilibrium (M)
0.063 0.012
-x +2x
0.063 - x 0.012 + 2x
[Br]2
[Br2]Kc = Kc =
(0.012 + 2x)2
0.063 - x= 1.1 x 10-3 Solve for x
14.4
Kc = (0.012 + 2x)2
0.063 - x= 1.1 x 10-3
4x2 + 0.048x + 0.000144 = 0.0000693 – 0.0011x
4x2 + 0.0491x + 0.0000747 = 0
ax2 + bx + c =0-b ± b2 – 4ac
2ax =
Br2 (g) 2Br (g)
Initial (M)
Change (M)
Equilibrium (M)
0.063 0.012
-x +2x
0.063 - x 0.012 + 2x
x = -0.00178x = -0.0105
At equilibrium, [Br] = 0.012 + 2x = -0.009 M or 0.00844 M
At equilibrium, [Br2] = 0.062 – x = 0.0648 M14.4
Example Problem: Calculate Concentration
Note the moles into a 10.32 L vessel stuff ... calculate molarity.Starting concentration of HI: 2.5 mol/10.32 L = 0.242 M
2 HI H2 + I2
222
][
]][[
HI
IHKeq
Initial:Change:Equil:
0.242 M 0 0 -2x +x +x0.242-2x x x
32
2
21026.1
]2242.0[]2242.0[
]][[
xx
x
x
xxKeq
What we are asked for here is the equilibrium concentration of H2 ... ... otherwise known as x. So, we need to solve this beast for x.
Example Problem: Calculate Concentration
32
2
1026.1]2242.0[
xx
x
232 ]2242.0[1026.1 xxx
]4968.00586.0[1026.1 23 xxx
2335 1004.51022.11038.7 xxxxx
01038.71022.1995.0 532 xxxx
And yes, it’s a quadratic equation. Doing a bit of rearranging:
a
acbbx
2
42
x = 0.00802 or –0.00925Since we are using this to model a real, physical system,we reject the negative root.The [H2] at equil. is 0.00802 M.
Example Problem: Calculate Keq
This type of problem is typically tackled using the “three line” approach:2 NO + O2 2 NO2
Initial:
Change:
Equilibrium:
Approximating
If Keq is really small the reaction will not proceed to the right very far, meaning the equilibrium concentrations will be nearly the same as the initial concentrations of your reactants.
0.20 – x is just about 0.20 is x is really dinky.
If the difference between Keq and initial concentrations is around 3 orders of magnitude or more, go for it. Otherwise, you have to use the quadratic.
Example
Initial Concentration of I2: 0.50 mol/2.5L = 0.20 MI2 2 I
Initialchangeequil:
0.20 0-x +2x0.20-x 2x 10
2
10
2
2
1094.2]20.0[
]2[
1094.2][
][
xx
x
xI
IKeq
With an equilibrium constant that small, whatever x is, it’s neardink, and 0.20 minus dink is 0.20 (like a million dollars minus a nickel is still a million dollars).
0.20 – x is the same as 0.20
102
1094.220.0
]2[ xx
x = 3.83 x 10-6 M
More than 3orders of mag.between thesenumbers. The simplification willwork here.
Example
Initial Concentration of I2: 0.50 mol/2.5L = 0.20 MI2 2 I
Initialchangeequil:
0.20 0-x +2x0.20-x 2x 209.0
]20.0[
]2[
209.0][
][
2
2
2
x
x
I
IKeq These are too close to
each other ... 0.20-x will not betrivially close to 0.20here.
Looks like this one has to proceed through the quadratic ...
A + B C + D
C + D E + F
A + B E + F
Kc =‘[C][D][A][B]
Kc =‘‘[E][F][C][D]
[E][F][A][B]
Kc =
Kc ‘Kc ‘‘Kc
Kc = Kc ‘‘Kc ‘ x
If a reaction can be expressed as the sum of two or more reactions, the equilibrium constant for the overall reaction is given by the product of the equilibrium constants of the individual reactions.
14.2
N2O4 (g) 2NO2 (g)
= 4.63 x 10-3K = [NO2]2
[N2O4]
2NO2 (g) N2O4 (g)
K = [N2O4]
[NO2]2‘ =
1K
= 216
When the equation for a reversible reaction is written in the opposite direction, the equilibrium constant becomes the reciprocal of the original equilibrium constant.
14.2
The reaction quotient (Qc) is calculated by substituting the initial concentrations of the reactants and products into the equilibrium constant (Kc) expression.
IF
• Qc > Kc system proceeds from right to left to reach equilibrium
• Qc = Kc the system is at equilibrium
• Qc < Kc system proceeds from left to right to reach equilibrium
14.4
If an external stress is applied to a system at equilibrium, the system adjusts in such a way that the stress is partially offset as the system reaches a new equilibrium position.
Le Châtelier’s Principle
• Changes in Concentration
N2 (g) + 3H2 (g) 2NH3 (g)
AddNH3
Equilibrium shifts left to offset stress
14.5
Le Châtelier’s Principle
• Changes in Concentration continued
Change Shifts the Equilibrium
Increase concentration of product(s) left
Decrease concentration of product(s) right
Decrease concentration of reactant(s)
Increase concentration of reactant(s) right
left14.5
aA + bB cC + dD
AddAddRemove Remove
Le Châtelier’s Principle
• Changes in Volume and Pressure
A (g) + B (g) C (g)
Change Shifts the Equilibrium
Increase pressure Side with fewest moles of gas
Decrease pressure Side with most moles of gas
Decrease volume
Increase volume Side with most moles of gas
Side with fewest moles of gas
14.5
Le Châtelier’s Principle
• Changes in Temperature
Change Exothermic Rx
Increase temperature K decreases
Decrease temperature K increases
Endothermic Rx
K increases
K decreases
14.5colder hotter
uncatalyzed catalyzed
14.5
Catalyst lowers Ea for both forward and reverse reactions.
Catalyst does not change equilibrium constant or shift equilibrium.
• Adding a Catalyst• does not change K• does not shift the position of an equilibrium system• system will reach equilibrium sooner
Le Châtelier’s Principle
Example
Chemistry In Action
Life at High Altitudes and Hemoglobin Production
Kc = [HbO2]
[Hb][O2]
Hb (aq) + O2 (aq) HbO2 (aq)
Chemistry In Action: The Haber Process
N2 (g) + 3H2 (g) 2NH3 (g) H0 = -92.6 kJ/mol
Le Châtelier’s Principle
Change Shift EquilibriumChange Equilibrium
Constant
Concentration yes no
Pressure yes no
Volume yes no
Temperature yes yes
Catalyst no no
14.5