Lesson 13.1 The Equilibrium Constant I
Suggested Reading
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Zumdahl Chapter 13 Section 13.1 - 13.4
Essential Question
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What are the characteristics of chemical equilibrium?
Learning Objectives:
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Differentiate between the kinetic and equilibrium regions of a chemical reaction.
Define chemical equilibrium.
Outline the characteristics of chemical and physical systems in a state of equilibrium.
Define the equilibrium constant.
Deduce the equilibrium constant expression (Kc or Kp) for the equation for a
homogenous reaction.
Write equilibrium expressions for heterogeneous equilibria.
Introduction
Chemical reactions often seem to stop before they are complete. Such reactions are reversible.
That is, the original reactants form products, but then the products react to give back the original
reactants. The reaction mixture ceases to change in any of its properties and consists of both
reactants and products in definite concentrations. Such a reaction mixture is said to have
reached chemical equilibrium. In this lesson we will look at some of the basic properties of
chemical equilibria.
Kinetics vs. Equilibrium
If we study a chemical reaction over time, we will see it has two distinct phases. In the first part
of the reaction the concentration of the reactants are decreasing while the concentrations of the
products are increasing. This is the kinetics phase of a chemical reaction.
However, at some point the concentrations of the products and reactants will cease to change.
That is, there is no net change in the concentrations of reactants and products if conditions
remain constant. This is the equilibrium phase of a chemical reaction.
Thus, the study of kinetics focuses on the first part of a chemical reaction while the study of
equilibrium focuses on the second part.
Chemical Equilibrium Defined
The equilibrium condition for chemical reactions is a dynamic equilibrium. This dynamic
equilibrium consists of a forward reaction, in which substances react to give products, and a
reverse reaction, in which products react to give the original reactants. Both forward and reverse
reactions occur at the same speed. Chemical equilibrium is defined as the state reached by a
reaction mixture when the rates of forward and reverse reactions have become equal.
Please read the following article about irreversible vs. reversible reactions.
Thornley outlines characteristics of equilibrium:
Watch the following YouTube Video:
https://www.youtube.com/watch?v=hSxTNEyTogU
The Equilibrium Constant Expression
A mathematical expression called the equilibrium constant expression is used to study chemical
equilibrium. Lets take a look at this. Consider the general reaction
aA + bB ⇌ cC + dD
where A, B, C, & D denote products and reactants and a, b, c, & d are coefficients in the
balanced chemical equation. The equilibrium-constant expression for a reaction is an
expression obtained by multiplying the concentrations of products, dividing by the reactants, and
raising each term to the power equal to the coefficient in the balanced chemical equation. The
equilibrium constant, Kc (often denoted by just K), is the value obtained from the equilibrium
constant expression when equilibrium concentrations are substituted.
The square brackets denote the molar concentrations of reactants and products. The subscript
c on the equilibrium constant means that it is defined in terms of molar concentrations.
The law of mass action states that the values of the equilibrium-constant expression are
constant for a particular reaction at a given temperature, regardless of the equilibrium
concentrations substituted. This means that for different starting concentrations of reactants, the
value for Kc should be essentially the same when the temperature is constant. The equilibrium
constant expression is sometimes referred to as the law of mass action because of this.
Example: Writing the Equilibrium-Constant Expression
Write the equilibrium-constant expression, Kc, for catalytic methanation.
CO(g) + 3H2(g) ⇌ CH4(g) + H2O(g)
Solution: Check to see if the reaction is balanced. If it is substitute the reactants and products
into the expression above raising each term to its coefficient in the balanced chemical equation
(products go on top).
Writing the equilibrium constant expression:
Watch the following YouTube Video:
https://www.youtube.com/watch?v=SL8Q0YmbhoE
The Equilibrium Constant Kp
For gas-phase equilibria, it is often convenient to write the equilibrium constant expression in
terms of partial pressures of gases rather than concentrations. Recall that the partial pressure of
a gas is proportional to its concentration. You can see this by looking at the ideal gas law, PV =
nRT. If you solve for molar concentration n/V you get n/V = P/RT. Thus, the molar concentration
equals the partial pressure divided by RT, which is constant at a given temperature.
When you express an equilibrium constant for a gaseous reaction in terms of partial pressures,
you call it Kp. For catalytic methanation in the example above
CO(g) + 3H2(g) ⇌ CH4(g) + H2O(g)
the equilibrium expression inter terms of partial pressures becomes
Notice that square brackets are not used with this expression of the equilibrium constant,
because pressure is not expressed in concentration units.
Homogeneous versus Heterogeneous Equilibria
A homogeneous equilibria is an equilibrium that involves reactants and products in a single
phase. Catalytic methanation is an example of a homogeneous equilibrium because it only
involves gaseous reactants and products. A heterogeneous equilibrium is an equilibrium
involving reactants and products in more than one phase. For example, the reaction of iron
metal filings with steam to produce iron oxide, Fe3O4, and hydrogen involves solids and gases.
3Fe(s) + 4H2O(g) ⇌ Fe3O4(s) + 4H2(g)
In writing the equilibrium expression for heterogenous equilibria, you omit concentration terms
for pure solids and liquids. Thus, for the reaction above you would write
The reason for this is, because whereas the concentration of a gas can have various values, the
concentration of a pure solid or a pure liquid is a constant at a given temperature. Thus, pure
solids and liquids are omitted from the equilibrium constant expression because then do not
have any impact of the equilibrium constant. The equilibrium is not affected by the amounts of
pure solids and liquids, as long as some is present.
Example: Writing Kc for a Reaction with Pure Solids
Quicklime, CaO, is prepared by heating a source of calcium carbonate, such as limestone or
seashells. Write the expression for Kc.
CaCO3(s) ⇌ CaO(s) + CO2(g)
Solution: Kc = [CO2]
This video expands on and summarizes some of the concepts of this lesson.
Watch the following YouTube Video:
https://www.youtube.com/watch?v=4z4_rc6nsKU
Homework: Practice exercises 15.1-15.6