L3 - Equilibrium Constants

objectives

Understandings

• The equilibrium law describes how the equilibrium constant (Kc) can be determined for a particular chemical reaction.
• The magnitude of the equilibrium constant indicates the extent of a reaction at equilibrium and is temperature dependent.
• The reaction quotient (Q) measures the relative amount of products and reactants present during a reaction at a particular point in time. Q is the equilibrium expression with non-equilibrium concentrations. The position of the equilibrium changes with changes in concentration, pressure, and temperature.

Applications and skills:

• Deduction of the equilibrium constant expression (Kc) from an equation for a homogeneous reaction.
• Determination of the relationship between different equilibrium constants (Kc) for the same reaction at the same temperature.

Guidance:

• Physical and chemical systems should be covered.
• Relationship between Kc values for reactions that are multiples or inverses of one another should be covered.
• Specific details of any industrial process are not required.

Introducing the Reaction Quotient (Q)

• Now that we have a symbol (⇌) to designate reversible reactions, we will need a way to express mathematically how the amounts of reactants and products affect the equilibrium of the system.
• A general equation for a reversible reaction may be written as follows:

• We can write the reaction quotient (Q) for this equation.
• When evaluated using concentrations, it is called Qc.
• We use brackets to indicate molar concentrations of reactants and products.

• The reaction quotient is equal to the molar concentrations of the products of the chemical equation (multiplied together) over the reactants (also multiplied together), with each concentration raised to the power of the coefficient of that substance in the balanced chemical equation.
• For example, the reaction quotient for the reversible reaction 2NO₂(g)⇌N₂O₄(g)2NO2(g)⇌N2O4(g) is given by this expression:

How Q Changes over Time

• The numeric value of Qc for a given reaction varies; it depends on the concentrations of products and reactants present at the time when Qc is determined.
• When pure reactants are mixed, Qc is initially zero because there are no products present at that point.
• As the reaction proceeds, the value of Qc increases as the concentrations of the products increase and the concentrations of the reactants simultaneously decrease (Figure 1).
• When the reaction reaches equilibrium, the value of the reaction quotient no longer changes because the concentrations no longer change.

The Equilibrium Constant Kc

• When a mixture of reactants and products of a reaction reaches equilibrium at a given temperature, its reaction quotient always has the same value.
• This value is called the equilibrium constant (K) of the reaction at that temperature.
• As for the reaction quotient, when evaluated in terms of concentrations, it is noted as Kc.
• That a reaction quotient always assumes the same value at equilibrium can be expressed as:

• This equation is a mathematical statement of the law of mass action: When a reaction has attained equilibrium at a given temperature, the reaction quotient for the reaction always has the same value.

Magnitude of Kc

• The magnitude of an equilibrium constant is a measure of the yield of a reaction when it reaches equilibrium.
• A large value for Kc indicates that equilibrium is attained only after the reactants have been largely converted into products.
• A small value of Kc—much less than 1—indicates that equilibrium is attained when only a small proportion of the reactants have been converted into products.
• Once a value of Kc is known for a reaction, it can be used to predict directional shifts when compared to the value of Qc.
• A system that is not at equilibrium will proceed in the direction that establishes equilibrium.
• The data in Figure 2 illustrates this.
• When heated to a consistent temperature, 800 °C, different starting mixtures of CO, H2O, CO2, and H2 react to reach compositions adhering to the same equilibrium (the value of Qc changes until it equals the value of Kc).
• This value is 0.640, the equilibrium constant for the reaction under these conditions.

• It is important to recognize that an equilibrium can be established starting either from reactants or from products, or from a mixture of both.
• For example, equilibrium was established from Mixture 2 in Figure 2 when the products of the reaction were heated in a closed container.
• In fact, one technique used to determine whether a reaction is truly at equilibrium is to approach equilibrium starting with reactants in one experiment and starting with products in another.
• If the same value of the reaction quotient is observed when the concentrations stop changing in both experiments, then we may be certain that the system has reached equilibrium.

Solution

Experiment 1:

The reaction will shift to the right.

Experiment 2:

The reaction will shift to the left.

Experiment 3:

The reaction will shift to the right.