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Calculating Equilibrium Pressures of Reactants and Products

Concentrations or gas pressures of reactants and products at equilibrium can be calculated from the initial concentrations or gas pressures of reactants and products and equilibrium constants. There are many variations of this procedure, but because our goal is only to introduce you to this category of calculations, we will restrict our examples to gas-phase reactions, for which you are given the initial partial pressures of reactants, the equation for the reaction, and the K_P that corresponds to the equation. The equations for the reactions of this kind that you will see will have one of two forms:

A(g)  +  B(g)        C(g)  +  D(g)

or      A(g)  +  B(g)        2C(g)

 

Sample Study Sheet: Calculating Equilibrium Pressures   

Tip-off – You are asked for the equilibrium partial pressures of reactants and products, and you are given the equation for the reaction, its K_P (or a table of K_P values), and the initial partial pressures of reactants.

General Steps –

• Write the equilibrium constant expression that corresponds to the chemical equation.
• Set up a table for displaying the initial pressures, the changes in pressure, and the equilibrium pressures.

For our examples, assign x to the decrease in pressure of each reactant. The equilibrium partial pressure of each reactant will be the given initial partial pressure minus x. The equilibrium partial pressure of product will be x for reactions that have the first general form below or 2x for reactions that have the second form.

A(g)  +  B(g)        C(g)  +  D(g)

or      A(g)  +  B(g)        2C(g)

• Plug the equilibrium concentration terms into the equilibrium constant expression.
• Solve for x.
• Use x to calculate the equilibrium concentrations of reactants and products.  

EXAMPLE – Calculating Equilibrium Pressures: 

Chloromethane, CH₃Cl, which has been used as a refrigerant and a local anesthetic, can be made from the following reaction.

CH₃OH(g)  +  HCl(g)        CH₃Cl(g)  +  H₂O(g)

K_P = 5.9 × 10³ at 120 °C

If enough methanol and hydrogen chloride are added to a container at 120 °C to yield an initial pressure of 0.75 atm for each, what will the equilibrium pressures of all of the reactants and products be?

Solution: 

We start by writing the equilibrium constant expression that corresponds to the given chemical equation:

Next, we set up a table describing the initial gas pressures, the changes in pressures, and the equilibrium pressures in terms of x. For our problem, we assign "x" to the decrease in pressure of CH₃OH and HCl.

We now plug in the terms for the equilibrium concentrations of each reactant and product into the equilibrium constant expression.

Next, we solve for x. (We can simplify our equation by taking the square root of both sides.)

x  =  77(0.75 – x)  =  58 – 77 x

78x  =  58                                      

We complete the problem by calculating the equilibrium concentrations of each reactant and product from the calculated x.