Chapter 2, Problem 36P

Consider the following reaction having an equilibrium constant of $4.66\times {10}^{-3}$ at a certain temperature:

$\text{A}\left(\text{g}\right)+\text{13}\left(\text{g}\right)\rightleftharpoons \text{C}\left(\text{g}\right)$

If 0.300 mol of A and 0.100 mol of B are mixed in a container and allowed to reach equilibrium, the concentrations of $\text{A}=0.300-x$ and $\text{B}=0.100-x$ reaction that form the concentration of $\text{C}=2x$ are related to the equilibrium constant by the expression

$4.66\times {10}^{-3}=\frac{{\left(2x\right)}^2}{\left(0.300-x\right)\left(0.100-x\right)}$

(a) Write the quadratic equation for x. (h) Solve the quadratic equation found in part (a) by completing the square and the quadratic formula.

(c) Find the equilibrium concentration A, B, and C.