5I.29

[Amy Luu 2G]

At 25 C, K 5 3.2 x 10^-34 for the reaction 2HCl(g) H2(g) + Cl2(g). If a reaction vessel of volume 1.0 L is filled with
HCl at 0.22 bar, what are the equilibrium partial pressures of HCl, H2, and Cl2?

In the answer key, they said to assume that x << 0.22. Why do they do this?

[Brooke Yasuda 2J]

X must be smaller than .22 because the initial concentration of HCL is .22 M. If the x is larger than .22, then the final equilibrium concentration of HCl would be negative and negative concentrations are not possible.

[Daniel Honeychurch1C]

Since K is so small (3.2 x 10^-34), there is very little of the products at equilibrium. Therefore, we know that x is going to be very low. Using this assumption, we can simplify the expression 3.2 x 10^-34 = (x^2) / (0.22 -2x)^2 to 3.2 x 10^-34 = x^2 / (0.22)^2, since x is so small that it will have no effect on this calculation.