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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)

KP = 5.9 x 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.

 CH3OH HCl CH3Cl H2O Initial 0.75 0.75 0 0 Change -x -x x x Equilibrium 0.75 - x 0.75 - x x x

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.

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