To determine the equilibrium constant [tex]\( K_{\text{eq}} \)[/tex] for the given reaction, we follow these steps:
The equilibrium constant expression for the reaction
[tex]\[ 2 \, NOCl \, (g) \leftrightarrow 2 \, NO \, (g) + Cl_2 \, (g) \][/tex]
is given by:
[tex]\[ K_{\text{eq}} = \frac{[NO]^2 [Cl_2]}{[NOCl]^2} \][/tex]
Given the equilibrium concentrations:
[tex]\[ [NOCl] = 1.4 \times 10^{-2} \, M \][/tex]
[tex]\[ [NO] = 1.2 \times 10^{-3} \, M \][/tex]
[tex]\[ [Cl_2] = 2.2 \times 10^{-3} \, M \][/tex]
First, we square the concentration of NO:
[tex]\[ [NO]^2 = (1.2 \times 10^{-3})^2 = 1.44 \times 10^{-6} \, M^2 \][/tex]
Next, we multiply this value by the concentration of [tex]\( Cl_2 \)[/tex]:
[tex]\[ [NO]^2 [Cl_2] = 1.44 \times 10^{-6} \times 2.2 \times 10^{-3} = 3.168 \times 10^{-9} \, M^3 \][/tex]
Then, we square the concentration of [tex]\( NOCl \)[/tex]:
[tex]\[ [NOCl]^2 = (1.4 \times 10^{-2})^2 = 1.96 \times 10^{-4} \, M^2 \][/tex]
Finally, we calculate [tex]\( K_{\text{eq}} \)[/tex] by dividing the product [tex]\( [NO]^2 [Cl_2] \)[/tex] by [tex]\( [NOCl]^2 \)[/tex]:
[tex]\[ K_{\text{eq}} = \frac{1.44 \times 10^{-6} [Cl_2]}{1.96 \times 10^{-4}} = \frac{3.168 \times 10^{-9}}{1.96 \times 10^{-4}} = 1.6163 \times 10^{-5} \][/tex]
Therefore, the value of [tex]\( K_{\text{eq}} \)[/tex] for the reaction is:
[tex]\[ 1.6 \times 10^{-5} \][/tex]
The correct answer is:
[tex]\[ 1.6 \times 10^{-5} \][/tex]
