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In gaseous reactions important for the understanding of the upper atmosphere $H_{2} O$ and O react to form two OH radicals. $Δ H$ for this reaction is 72 kJ at 500 K and $E_{a}$ is $77 k J . m o l^{- 1}$ , then $E_{a}$ for the bimolecular recombination of two OH radicals to form $H_{2} O$ and O is:

A

3 k J . m o l^{- 1}

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B

4 k J . m o l^{- 1}

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C

5 k J . m o l^{- 1}

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D

7 k J . m o l^{- 1}

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Solution

The correct option is C $5 k J . m o l^{- 1}$
$H_{2} O + O \to 2 O H; Δ H = 72 k J$ at 500 K; $E_{a} = 77 k J m o l^{- 1}$
$2 O H \to H_{2} O + O; E_{a_{B . R .}}$
For a reaction, $E_{a_{F . R .}} = Δ H + E_{a_{B . R .}}$
$77 = 72 + E_{a_{B . R .}}$
$E_{a_{B . R .}} = 5 k J m o l^{- 1}$ .

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