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Arrhenius Equation

Order of reac...

Question

Order of reaction for $C_{6} H_{6} + 3 H_{2} ⇌ C_{6} H_{12}$ is first order for $C_{6} H_{6}$ and first order for $H_{2}$ . The rate of reaction for backward reaction is:

K_{b} [C_{6} H_{12}]

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\frac{K_{b} [C_{6} H_{12}]}{[H_{2}]}

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\frac{K_{b} [C_{6} H_{12}]}{[H_{2}]^{2}}

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\frac{K_{b} [C_{6} H_{12}]}{[H_{2}]^{3}}

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Solution

The correct option is C $\frac{K_{b} [C_{6} H_{12}]}{[H_{2}]^{2}}$
$K_{c} = \frac{[C_{6} H_{12}]}{[C_{6} H_{6}] [H_{2}]^{3}} = \frac{K_{f}}{K_{b}}$
At equilibrium $r_{f} = r_{b}$
$∴ K_{f} [C_{6} H_{6}] [H_{2}] = r_{b}$
$∴ r_{b} = K_{f} [C_{6} H_{6}] [H_{2}]$
$= \frac{K_{b} [C_{6} H_{12}]}{[C_{6} H_{6}] [H_{2}]^{3}} \times [C_{6} H_{6}] [H_{2}] = \frac{K_{b} [C_{6} H_{12}]}{[H_{2}]^{2}}$

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