question_answer 1)

The reaction, \[CO(g)+3{{H}_{2}}(g)\rightleftharpoons C{{H}_{4}}(g)+{{H}_{2}}O(g)\] is at equilibrium at 1300Kin a 1 L flask. It also contains 0.3mole of CO, 0.1 mole of \[{{H}_{2}}\] and 0.02 mole of \[{{H}_{2}}O\]and an unknown amount of in the flask. Determine the concentration of\[C{{H}_{4}}(g)\] in the mixture. The equilibrium constant, \[{{K}_{c}}\] for the reaction at a given temperature, is 3.90.

Answer:

The given reaction is: \[\underset{At\,equilibrium}{\overset{{}}{\mathop{{}}}}\,\underset{\frac{0.3}{1}M}{\mathop{CO(g)}}\,+\underset{\frac{0.1}{1}M}{\mathop{3{{H}_{2}}(g)}}\,\rightleftharpoons \underset{\frac{x}{1}M}{\mathop{C{{H}_{4}}(g)}}\,+\underset{\frac{0.02}{1}M}{\mathop{{{H}_{2}}O(g)}}\,\] \[{{K}_{c}}=\frac{[C{{H}_{4}}][{{H}_{2}}O]}{[CO]{{[{{H}_{2}}]}^{3}}}\] \[3.90=\frac{x\times 0.02}{0.3\times {{(0.1)}^{2}}}\] \[x=0.0585M\] \[\therefore \]Concentration of CH4 will be 0.0585 M.