Equilibrium constants `(K)` for the reaction `2NO(g)+Cl_(2)(g)hArr2NOCl(g)` is correctly given by the expression

Options

A. (a) `([NOCl]^(2))/([NO]^(2)[Cl_(2)])`
B. (b) `([2NOCl])/([2NO][Cl_(2)])`
C. (c) `([NO]^(2)+[Cl_(2)])/([NOCl])`
D. (d) `([NO]^(2)[Cl_(2)])/([NOCl]^(2))`

Explanation

To derive the equilibrium constant expression for the reaction \(2NO(g) + Cl_2(g) \rightleftharpoons 2NOCl(g)\), we will follow these steps:

### Step 1: Write the balanced chemical equation
The balanced chemical equation is:
\[ 2NO(g) + Cl_2(g) \rightleftharpoons 2NOCl(g) \]

### Step 2: Identify the products and reactants
In the equation, the reactants are \(2NO\) and \(Cl_2\), and the product is \(2NOCl\).

### Step 3: Write the general form of the equilibrium constant expression
The equilibrium constant \(K\) is expressed in terms of the concentrations of the products and reactants. The general form is:
\[ K = \frac{[\text{products}]^{\text{stoichiometric coefficient}}}{[\text{reactants}]^{\text{stoichiometric coefficient}}} \]

### Step 4: Apply the stoichiometric coefficients
For our specific reaction:
- The product \(NOCl\) has a stoichiometric coefficient of 2.
- The reactant \(NO\) has a stoichiometric coefficient of 2.
- The reactant \(Cl_2\) has a stoichiometric coefficient of 1.

### Step 5: Write the equilibrium constant expression
Substituting the products and reactants into the general form, we get:
\[ K = \frac{[NOCl]^2}{[NO]^2 \cdot [Cl_2]^1} \]

### Step 6: Finalize the expression
Thus, the equilibrium constant expression for the reaction is:
\[ K = \frac{[NOCl]^2}{[NO]^2 \cdot [Cl_2]} \]

### Conclusion
The correct expression for the equilibrium constant \(K\) for the reaction \(2NO(g) + Cl_2(g) \rightleftharpoons 2NOCl(g)\) is:
\[ K = \frac{[NOCl]^2}{[NO]^2 \cdot [Cl_2]} \]

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