Chapter 24.3, Problem 24.4.2PE

Consider the hypothetical reaction A(g) + 2B(g) ⇌ 2 C(g), for which K_c = 0.25 at a centain temperature. A 1.00-L reaction vessel is loaded with 1.00 mol of compound C, which is allowed to reach equilibrium. Let the variable x represent the number of mol/L of compound A present at equilibrium.
a. In terms of x, what are the equilibrium concentrations of compounds B and C?
b. What limits must be placed on the value of x so that all concentrations are positive?
c. By putting the equilibrium concentrations (in terms of x ) into the equilibrium- constant expression, derive an equation that can be solved for x.
d. The equation from part(c ) is a cubic equation (one that has the form ax³ + bx² + cx + d =0). In general, cubic equations cannot be solved in closed form. However, you can estimate the solution by plotting the cubic equation in the allowed range of x that you specified in part (b). The point at which the cubic equation crosses the x-axis is the solution.
e. From the plot in part (d), estimate the equilibrium concentrations of A, B, and C. (Hint : You can check the accuracy of your answer by substituting these concentrations into the equilibrium expression.)