Question

consider the reaction in chemical equilibrium.
cocl₂(g) ⇌ co(g) + cl₂(g)
which is the correct equation for k?
k = \frac{cocl₂^2}{cocl₂}
k = \frac{cocl₂}{cocl₂}
k = \frac{cocl₂}{cocl₂}
k = \frac{cocl₂}{cocl₂^2}

Explanation:

Step1: Recall Equilibrium Constant Formula

For a reaction \( aA + bB
ightleftharpoons cC + dD \), \( K = \frac{[C]^c[D]^d}{[A]^a[B]^b} \), where concentrations are at equilibrium.

Step2: Apply to Given Reaction

Reaction: \( \text{COO}_2(g)
ightleftharpoons \text{CO}(g) + \text{O}_2(g) \). Here, \( a = 1 \) (for \( \text{COO}_2 \)), \( c = 1 \) (for \( \text{CO} \)), \( d = 1 \) (for \( \text{O}_2 \)). So \( K = \frac{[\text{CO}]^1[\text{O}_2]^1}{[\text{COO}_2]^1} = \frac{[\text{CO}][\text{O}_2]}{[\text{COO}_2]} \).

Answer:

\( K = \frac{[\text{CO}][\text{O}_2]}{[\text{COO}_2]} \) (Assuming the reactant is \( \text{COO}_2 \) and products are \( \text{CO} \) and \( \text{O}_2 \); the correct option should be the one with products' concentrations in numerator and reactant in denominator without any incorrect exponents. From the options, the third option (if we consider the options as presented: first option has \( [\text{COO}_2]^2 \), second has reactant over products, third has products over reactant (single \( \text{COO}_2 \)), fourth has \( [\text{COO}_2]^2 \)) so the correct \( K \) expression is \( K=\frac{[\text{CO}][\text{O}_2]}{[\text{COO}_2]} \) which matches the third option's structure (assuming the options are ordered as: 1. \( K=\frac{[\text{COO}_2]^2}{[\text{CO}][\text{O}_2]} \), 2. \( K=\frac{[\text{COO}_2]}{[\text{CO}][\text{O}_2]} \), 3. \( K=\frac{[\text{CO}][\text{O}_2]}{[\text{COO}_2]} \), 4. \( K=\frac{[\text{CO}][\text{O}_2]}{[\text{COO}_2]^2} \))