Question

At equilibrium, the concentration of $ {N_2} = 3.0 \times {10^{ - 3}}M $ . $ {O_2} = 4.2 \times {10^{ - 3}}M $ and $ NO = 2.8 \times {10^{ - 3}}M $ in a closed vessel at $ 800K $ . Calculate $ {K_C} $ .
 $ {N_2} + {O_2} \rightleftharpoons 2NO $ .

Answer 1

Hint :The equilibrium constant of concentration of a chemical reaction at equilibrium is defined as the ratio of the concentration of products to the concentration of reactants with each of them raised to the power of their stoichiometric coefficients. It is denoted by $ {K_C} $ .

Complete Step By Step Answer:
As we already mention above the definition of equilibrium constant of the concentration of chemical reaction, so we can write its formula that is $ {K_C} = \dfrac{{Concentration{\text{ of product}}}}{{Concentration{\text{ of reactant}}}} $ .
Let the number of moles of nitrogen be x, number of moles of oxygen be y and number of moles of nitric oxide be z. Therefore the value of $ x = 1,y = 1,z = 2 $ . Now the complete formula of $ {K_C} $ is given below.
 $ {K_C} = \dfrac{{{{\left( {NO} \right)}^Z}}}{{{{\left( {{N_2}} \right)}^X}{{\left( {{O_2}} \right)}^Y}}} $
Now putting the values of x, y, and z in the above equation we get,
 $ {K_C} = \dfrac{{{{\left[ {NO} \right]}^2}}}{{{{\left[ {{N_2}} \right]}^1}{{\left[ {{O_2}} \right]}^1}}} $
Now putting the values of the concentration of nitrous oxide, nitrogen and oxygen in the above equation we get,
 $ {K_C} = \dfrac{{{{\left[ {2.8 \times {{10}^{ - 3}}} \right]}^2}}}{{\left[ {3.0 \times {{10}^{ - 3}}} \right]\left[ {4.2 \times {{10}^{ - 3}}} \right]}} $
By solving the above equation we get, $ {K_C} = 0.622 $ .

Note :
Nitric oxide is also known as nitrogen monoxide. It is a colorless gas. Nitrogen monoxide is a free radical which means that it contains unpaired electrons. It is the simplest form of the oxides of nitrogen. The other oxides of nitrogen are nitrogen dioxide $ \left( {N{O_2}} \right) $ . It is also known as brown gas. It is one of the major pollutants of the air. The other one is nitrous oxide $ \left( {{N_2}O} \right) $ . It is also known as the laughing gas and also used as anesthetic.