A) \[\frac{1}{5.7}\text{hou}{{\text{r}}^{-1}}\]
B) \[\frac{\ln \,2}{5.7}\text{hou}{{\text{r}}^{-1}}\]
C) \[\ln \frac{2}{5.7}\text{hou}{{\text{r}}^{-1}}\]
D) \[0.5\,\,\text{hou}{{\text{r}}^{-1}}\]
Correct Answer: B
Solution :
The thermal dissociation of \[{{N}_{2}}{{O}_{5}}\] is a first order reaction. Hence, for it \[k=\frac{1}{t}\ln \,\frac{a}{(a-x)}\] For half-change, \[k=\frac{1}{{{t}_{1/2}}}\ln \,\frac{a}{\left( a-\frac{a}{2} \right)}\] \[=\frac{1}{{{t}_{1/2}}}\cdot \ln 2\] \[\therefore \] \[k=\frac{\ln \,2}{5.7}\text{hou}{{\text{r}}^{-1}}\]
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