Problem

For the reaction,

2\text{NO}(\text{g}) + 2\text{H}_2(\text{g}) \rightarrow \text{N}_2(\text{g}) + 2\text{H}_2\text{O}(\text{g})

the rate expression can be written in the following ways:

\begin{aligned} \frac{d[\text{N}_2]}{dt} &= k_1 [\text{NO}][\text{H}_2]; \\ \frac{d[\text{H}_2\text{O}]}{dt} &= k[\text{NO}][\text{H}_2]; \\ -\frac{d[\text{NO}]}{dt} &= k'_1 [\text{NO}][\text{H}_2]; \\ -\frac{d[\text{H}_2]}{dt} &= k''_1 [\text{NO}][\text{H}_2] \end{aligned}

The relationship between

k, k_1, k'_1

and

k''_1

is: (a)

k = k_1 = k'_1 = k''_1

(b)

k = 2k_1 = k'_1 = k''_1

(c)

k = 2k'_1 = k_1 = k''_1

(d)

k = k_1 = k'_1 = 2k''_1