Question

At $ 250{}^\circ C, $ the time for half-change for the thermal dissociation of $ {{N}_{2}}{{O}_{5}} $ is 5.7 hours. The specific rate constant is given by:

• 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}} $

Answer 1

Answer: (B)

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}} $