For the reaction, $2 N O + 2 H_{2} \to N_{2} + 2 H_{2} O$ , the following kinetic data were obtained:
Expt.
No. $[H_{2}]$
$(m o l L^{- 1})$ $[N O]$
$(m o l L^{- 1})$ Rate of reaction
$(m o l L^{- 1} s^{- 1})$
$1.$ $0.12$ $0.12$ $0.25 \times 10^{- 4}$
$2.$ $0.12$ $0.24$ $1.0 \times 10^{- 4}$
$3.$ $0.24$ $0.24$ $2.0 \times 10^{- 4}$
Determine the rate law and the rate constant.

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Solution

Rate $= K {[A]}^{m} {[B]}^{n}$
$= K {[H_{2}]}^{m} {[N O]}^{n}$
${(\frac{0.12}{0.12})}^{m} {(\frac{0.12}{0.24})}^{n} = \frac{0.25 \times 10^{- 4}}{1.0 \times 10^{- 4}}$
${(0.5)}^{n} = 0.25$
$n = 2$
${(\frac{01.12}{0.24})}^{m} {(\frac{0.24}{0.24})}^{n} = \frac{1 \times 10^{- 4}}{2 \times 10^{- 4}}$
${(0.5)}^{m} = (0.5)$
$m = 1$
Rate $= K [H_{2}] {[N O]}^{2}$
$K = \frac{0.25 \times 10^{- 4}}{[0.12] {[0.12]}^{2}}$
$K = 0.0144 {m o l}^{- 2} l^{+ 2} S^{- 1}$

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