For the reaction, $2 N O (g) + 2 H_{2} (g) \to N_{2} (g) + 2 H_{2} O (g)$ the rate expression can be written in the following ways:
${d t [N_{2}] / d t} = k_{1} [N O] [H_{2}]; {d [H_{2} O] / d t) = k [N O] [H_{2}];$
${- d [N O] / d t} = k_{1}^{'} [N O] [H_{2}]; {- d [H_{2}] / d t} = k_{1}^{''} [N O] [H_{2}]$
The relation ship between $k, k_{1}, k_{1}^{'}$ and $k_{1}^{''}$ is:

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Solution

$2 N O_{(g)} + 2 H_{2} (g) \to N_{2} (g) + 2 H_{2} O (g)$
$- \frac{1}{2} \frac{d [N O]}{d t} = \frac{- 1}{2} \frac{d [H_{2}]}{d t} = \frac{d [N_{2}]}{d t} = \frac{1}{2} \frac{d [H_{2} O]}{d t}$
$- \frac{d [N O]}{d t} = \frac{- d [H_{2}]}{d t} = \frac{2 d [N_{2}]}{d t} = \frac{d [H_{2} O]}{d t}$
$\begin{matrix} \frac{d [N_{2}]}{d t} = k_{1} [N O] [H_{2}] \frac{d [H_{2} O]}{d t} = k [N O] [H_{2}] - \frac{d [N O]}{d t} = k_{1}^{'} [N O] [H_{2}] - \frac{d [H_{2}]}{d t} = k "_{1} [N O] [H_{2}] \end{matrix} ⎫ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎭ G i v e n$
put given data in equation (i)
$k_{1}^{'} [N O] [H_{2}] = k "_{1} [N O] [H_{2}] = 2 k_{1} [N O] [H_{2}] = k [N O] [H_{2}]$
$k_{1}^{'} = k "_{1} = 2 k_{1} = k$

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Similar questions

2 N O (g) + 2 H_{2} (g) \to N_{2} (g) + 2 H_{2} O (g)

\frac{d [N_{2}]}{d t} = k_{1} [N O] [H_{2}] \frac{d [H_{2} O]}{d t} = k [N O] [H_{2}] - \frac{d [N O]}{d t} = k_{1}^{'} [N O] [H_{2}] - \frac{d [H_{2}]}{d t} = k_{1}^{''} [N O] [H_{2}]

k, k_{1}, k_{1}^{'}

k_{1}^{''}

2 N O (g) + 2 H_{2} (g) \to N_{2} (g) + 2 H_{2} O (g)

\frac{d [N_{2}]}{d t} = k_{1} [N O] [H_{2}] \frac{d [H_{2} O]}{d t} = k [N O] [H_{2}] - \frac{d [N O]}{d t} = k_{1}^{'} [N O] [H_{2}] - \frac{d [H_{2}]}{d t} = k_{1}^{''} [N O] [H_{2}]

k, k_{1}, k_{1}^{'}

k_{1}^{''}

2 N O (g) + 2 H_{2} (g) \to N_{2} (g) + 2 H_{2} O (g)

\frac{d [N_{2}]}{d t} = k_{1} [N O] [H_{2}]; \frac{d [H_{2} O]}{d t} = k_{2} [N O] [H_{2}]; \frac{- d [N O]}{d t} = k_{3} [N O] [H_{2}]; \frac{d [H_{2}]}{d t} = k_{4} [N O] [N_{2}]

k_{1}, k_{2}, k_{3}, k_{4}

2 H_{2 (g)} + 2 N O_{(g)} \to N_{2 (g)} + 2 H_{2} O_{(g)}

\frac{d [N_{2}]}{d t} = k [H_{2}] [N O]^{2}

2 N H_{3} \to N_{2} + 3 H_{2}

- \frac{d [N H_{3}]}{d t} = k_{1} [N H_{3}], \frac{d [N_{2}]}{d t} = k_{2} [N H_{3}], \frac{d [H_{2}]}{d t} = k_{3} [N H_{3}]

k_{1}, k_{2}

k_{3}

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