Chemical Equilibrium

EQUILIBRIUM
• In many chemical reactions both a forward and
reverse reaction occur simultaneously.
• When the rate of forward and reverse reactions are
equalized, the system is at equilibrium.
• Not all reactions can reach equilibrium. Consider a
burning log. The products of the combustion (the
smoke and ashes) can never reunite to form the
reactants (the log and the oxygen)
• By contrast some common processes are
equilibrium systems, such as the formation of a
saturated solution or the vaporization of a liquid in
a sealed container.
2

RECOGNIZING EQUILIBRIUM
• When equilibrium systems do exist they may be
recognized by their apparent static nature (it looks as
if nothing is happening). Additionally, all equilibrium
systems must be closed, that is, nothing let in and
nothing let out including energy.
• While equilibrium appear unchanging when observed
on a large scale (macroscopically) they are in
constant change on the molecular level
(microscopically). Reactants are continually forming
products and products are continually forming
reactants at equal rates.
• Simply stated, equilibrium systems are
macroscopically static and microscopically
dynamic(changing). 3

SOLUBILITY EQUILIBRIUM
RATE OF DISSOLVING = RATE OF CRYSTALIZATION
RATE OF FORWARD PROCESS = RATE OF REVERSE PROCESS
The amount of substance dissolved remains constant
The system appears macroscopically static. 4

CHEMICAL EQUILIBRIUM
• When the rates of opposing processes are equal, equilibrium has been
established whether the system is physical or chemical.
• Given the reaction: a A + b B  c C + d D
when the rate at which A reacts with B equals the rate at which C
reacts with D the system is at equilibrium.
• Recall that the rate equation for a reaction is:
Rate = k x [reactants]n
• At equilibrium Rate forward = Rate reverse or:
kf [reactants] = kr[products] and rearranging the equation:
kf / kr = [products] / [reactants] and a constant divided by a
constant gives another constant so we get:
• Ke = [PRODUCTS] / [REACTANTS] at equilibrium for
the given reaction then is:
• Ke = ([C]c x [D]d) / ([A]a x [B]b) notice that in this
equation called the equilibrium expression, the
coefficients of the balanced equation serve as powers.
5

THE EQUILIBRIUM EXPRESSION
• For a system at equilibrium, the value of the equilibrium
constant (Ke) remains constant unless the temperature is
changed. The concentrations of products and reactants
may change as a result of “equilibrium shifts” but the ratio
of products to reactants as calculated using the equilibrium
expression remains unchanged.
• Let’s find the equilibrium expression for the following
reaction: 2 H2(g) + O2(g)  2 H2O(g)
(the double arrow  means equilibrium)
• Ke = [H2O] 2 / ([H2]2 x [O2])
• How about H2(g) + 1/2 O2(g)   H2O(g) ?
The reaction is the same but it is balanced with a different
set of coefficients and therefore the equilibrium expression
is different: Ke = [H2O] / ([H2] x [O2
]1/2) 7

THE EQUILIBRIUM EXPRESSION
• The coefficients used in balancing the reaction alters the equilibrium
expression and also the value of the equilibrium constant.
• For example, using the equilibrium equation
H2(g) + I2(g)  2 HI(g) the equilibrium expression is
Ke = [HI] 2 / ([H2] x [I2])
Let us assume the following equilibrium concentrations [H2] = 0.094
M, [I2] = 0.094 and [HI] = 0.012 M
Ke = (0.012)2 / ((0.094) x (0.094)) = 0.016
• If the equation was balanced as
½ H2(g) + ½ I2(g)  HI(g) the equilibrium expression would be:
Ke = [HI] / ([H2]1/2 x [I2] 1/2 ) and
Ke = (0.012) / ((0.094)1/2 x (0.094)1/2 ) = 0.127
• The numerical value of the equilibrium constant depends on the
coefficients used to balance the equation!
8

HOW ARE Ke VALUES RELATED?
• In our previous example when the coefficients of the
balanced equation were halved the Ke value changed. But
how?
• H2(g) + I2(g)  2 HI(g) ,
Ke = [HI] 2 / ([H2] x [I2]) = 0.016
• ½ H2(g) + ½ I2(g)  HI(g) ,
Ke = [HI] / ([H2]1/2 x [I2] 1/2 ) = 0.127
• Notice that the square root (half power) of 0.016 = 0.127
• If for some reason the equation was balanced as:
2 H2(g) + 2 I2(g)  4 HI(g), the constant would change to
the square of the original value or 0.0162 and Ke would
equal 0.064
• When the balancing coefficients of an equation are
changed by a factor, the Ke value changes by that factor
as a power of the original Ke
9

HOW ARE Ke VALUES RELATED?
• How else may the original balanced equation be
altered?
• Often equations are reversed (interchanging products
with reactants. For example:
H2(g) + I2(g)  2 HI(g) may be rewritten as:
2 HI(g)  H2(g) + I2(g)
The equilibrium expression for the first equation is:
Ke = [HI] 2 / ([H2] x [I2]) , for the second it is:
Ke = ([H2] x [I2]) / [HI] 2 , the reciprocal of the
first
• Therefore when an equation is reversed, the Ke
becomes the reciprocal of the original Ke value.
• Ke (reverse) = 1 / K (forward) 10

HETEROGENEOUS EQUILIBRIUM SYSTEMS
• Heterogeneous and homogeneous are terms that are
applied to the physical state (phases) of the components in
equilibrium systems. A system consisting of all gases is
heterogeneous while one including, for example, both solids
and gases is heterogeneous.
• H2(g) + I2(g)  2 HI(g) (homogeneous – all gases)
• H2(g) + ½ O2(g)  H2O(l) (heterogeneous – gas & liquid)
• Solids and liquids have concentrations which can vary only
slightly due to temperature changes. For all practical
proposes the concentrations of solids and liquids are fixed.
Only gases and dissolved substances can change
concentration. Since the equilibrium expression involves
only components which change concentration, solids and
liquids are not included in its format. 11

HETEROGENEOUS EQUILIBRIUM SYSTEMS
• When solids or liquids are encountered in an
equilibrium equation, a “1” is substituted in the
equilibrium expression for that component.
• 2 H2(g) + O2(g)  2 H2O(l)
Ke = 1 / ([H2]2 x [O2])
• For a system such as:
CaCO3(s)  CaO(s) + CO2(g)
The equilibrium expression is:
Ke = 1 x [CO2] / 1 or simply Ke = [CO2]
notice that since both CaCO3(s) and CaO(s) are solids
they have been replaced by ones in the equilibrium
expression.
12

THE MAGNITUDE OF Ke AND
EQUILIBRIUM CONCENTRATIONS
Equilibrium means that the rate of the forward reaction
and the rate of the reverse reaction are equal.
The concentrations of the products and the reactants need
not be equal and rarely are equal at equilibrium
When the equilibrium constant is small, the concentrations
of the reactants are large as compared to the products at
equilibrium. (The equilibrium favors the reactants).
13

When the equilibrium constant is large, the concentrations
of the reactants are small as compared to the products at
equilibrium. (The equilibrium favors the products).
14

When the equilibrium constant is about one, the
Concentrations of the reactants and the products are
about equal at equilibrium.
15

MEASURING Ke VALUES
• Since concentration may be measured for solutions in moles per liter
and for gases in terms of pressures (atms) or moles per liters two unit
systems are possible for Ke.
• When the concentration values used in calculating Ke are in terms of
molar units the constant is referred to as Kc (for concentration units
– moles per liter). When concentration of gases is measured in
pressure units (atms) the constant is referred to as Kp (for pressure
units – atms).
• The equilibrium constant in concentration terms (Kc) can be converted
to an equivalent value in pressure units (Kp).
• Kp = Kc(R x T) n , in this equation:
R = 0.0821 atm l / moles K, T = Kelvin temperature
n = moles of gaseous products – moles of gaseous reactants in the
balanced equation.
16

CONVERTING KP AND KC VALUES
• Problem: For the reaction:
N2(g) + 3 H2(g)  2 NH3(g) , Kc = 0.105 at 472 0C. Find
Kp at this temperature.
• Solution:
Kp = Kc(R x T) n , R = 0.0821 atm x l / mole x K
T= 472 + 273 = 745 K, n = 2 – 4 = - 2 (two
moles of NH3(g) product gases) – (one mole of N2(g) and
three moles of H2(g) a total of four moles of reactant
gases)
• Kp = 0.105 x (0.0821 x 745)-2 = 2.81 x 10-5
17

CALCULATING THE EQUILIBRIUM
CONSTANT
• Problem: If 0.20 moles of PCl3(g) and 0.10 moles of Cl2(g) are
placed in a 1.0 liter container at 200 0C the equilibrium
concentration of PCl5 is found to be 0.012 molar. What is Kc for
the reaction:
PCl3(g) + Cl2(g)  PCl5(g)
• Solution: Since one PCl3 and one Cl2 must be consumed to form
one PCl5, (0.20 M, the starting molarity of PCl3 – 0.012 M, the
molarity of PCl5 formed) = 0.188 M PCl3 remains and
(0.10 M, the starting molarity of Cl2 – 0.012 M the molarity of
PCl5 formed) = 0.088 M Cl2 remaining..
• Kc = [PCl5] / ([PCl3] x [Cl2])
• Kc = (0.012) / (0.188 x 0.088) = 0.725
• NOTE: The temperature given in the problem is not used in
the calculation. It is refer data only. Temperatures are not
used in equilibrium calculations of this type!
18

USING THE EQUILIBRIUM CONSTANT
• Problem: For the reaction: H2(g) + I2(g)  2 HI(g) ,
Kc = 0.016 at 793 K. If 1.00 mole of hydrogen and 1.00
mole of iodine are mixed in a 10.0 liter container, what
is the equilibrium concentration of all components?
• Solution: H2(g) + I2(g)  2 HI(g) and therefore,
Ke = [HI] 2 / ([H2] x [I2])
The starting [H2] and [I2] both equal 1.00 mole / 10.0
liters or 0.100 M.
• The concentration of HI at equilibrium is unknown (X).
• In order to form 2 HI, only 1 H2 and 1 I2 (half as
many of each) are needed. The equilibrium [H2] and
[I2] are both then (0.10 - .5X). This represents the
starting concentrations of each minus the concentration
used to form the HI. 19

USING THE EQUILIBRIUM CONSTANT
(cont’d)
• Substituting the equilibrium concentrations into the equilibrium
expression we get:
• Kc = X2 / (0.10 – 0.5 X)(0.10 – 0.5X) = 0.016 or
• X2 / (0.10 – 0.5X)2 = 0.016, taking the square root of both sides of the
equation we get:
• X / (0.10 – 0.5X) = 0.126 and X = 0.0126 – 0.008X
• Rearranging the equation to solve for X we get:
• 1.008X = 0.0126, X = 0.0126 / 1.008 = 0.0125
• [HI]e = 0.0125 M,
• [H2]e = [I2]e = 0.10 – .5(0.0125) = 0.0938 M
• CHECK – Placing the equilibrium concentrations back into the
equilibrium expression should give the correct constant!
• (0.0125)2 / (0.938)2 = 0.017 a very close approximation of Kc (0.016)
considering the rounding errors! 20

Chemical Equilibrium

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Chemical Equilibrium