Question

What is the pressure of \(C{O_2}\)in a mixture at equilibrium that contains \(0.50atm\)\({H_2}\), \(2.0atm\)of \({H_2}O\), and \(1.0atm\)of \(CO\) at \(99{0^0}C\)?

\({H_2}(g) + C{O_2}(g) \rightleftharpoons {H_2}O(g) + CO(g)\)

\({K_P} = 1.6\,at\, 99{0^o}C\)

Short answer

The pressure of CO₂is 2.5atm

Step-by-step solution

Given information

\({H_2}(g) + C{O_2}(g) \rightleftharpoons {H_2}O(g) + CO(g)\)

1. Value of equilibrium constant \({K_{\rm{P}}} = 1.6\)
2. The pressure of \({H_2}\)in mixture is \(0.50\,atm\)
3. The pressure of \({{\rm{H}}_{\rm{2}}}{\rm{O}}\)in mixture is \(2.0atm\)

Determine the pressure of \(C{O_2}\):

\(\begin{array}{*{20}{c}}{{K_p}}&{ = \frac{{\left[ {{{\rm{H}}_2}{\rm{O}}} \right] \times [{\rm{CO}}]}}{{\left[ {{{\rm{H}}_2}} \right] \times \left[ {{\rm{CO}}{{\rm{O}}_2}} \right]}}}\\{\left[ {{\rm{C}}{{\rm{O}}_2}} \right]}&{ = \frac{{\left[ {{{\rm{H}}_2}{\rm{O}}} \right] \times [{\rm{CO}}]}}{{\left[ {{{\rm{H}}_2}} \right] \times {{\rm{K}}_p}}}}\\{}&{ = \frac{{2.0 \times 1.0}}{{0.50 \times 1.6}}}\\{}&{ = 2.5{\rm{atm}}}\end{array}\)