Chapter 2, Problem 37P

Consider the following reaction having an equilibrium constant of 1.00 at 1105° K temperature:

$\text{CO}\left(\text{g}\right)+{\text{H}}_{\text{2}}\text{O}\left(\text{g}\right){\text{ CO}}_{\text{2}}\left(\text{g}\right)+{\text{H}}_{\text{2}}\left(\text{g}\right)$

Suppose the feed to a reactor contains 1.000 mol of CO and 2.000 mol of H₂O(g), and the reaction mixture comes to equilibrium at 1105 K. The concentrations of $\text{CO}=\text{1}.000-x$ and ${\text{H}}_{\text{2}}\text{O}=2.000-x$ reaction that form the concentration of ${\text{CO}}_2=x$ and ${\text{H}}_{\text{2}}=x$ are related to the equilibrium constant as

$1.00=\frac{2x}{\left(1.000-x\right)\left(2.000-x\right)}$

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

(c) Find the equilibrium concentration of CO, H₂O, CO₂, and H₂.