| Following are two first order reactions with their half times given at\[25{}^\circ C\]. |
| \[A\xrightarrow{{{t}_{1/2}}=30\,\min }\text{Product}\] |
| \[B\xrightarrow{{{t}_{1/2}}=40\,\min }\text{Product}\] |
| The temperature coefficients of their reaction rates are 3 and 2, respectively, between \[25{}^\circ C\]and\[35{}^\circ C\]. If the above two reactions are carried out taking \[0.4\text{ }M\]of each reactant but at different temperature: \[25{}^\circ C\] for the first order reaction and \[35{}^\circ C\] for the second order reaction, find the ratio of the concentrations of A and B after an hour. |
A) \[1\]
B) \[2\]
C) \[3\]
D) \[4\]
Correct Answer: B
Solution :
[b] \[0.4M\] of \[A\xrightarrow{30\,\min }0.2M\xrightarrow{30\,\min }0.1M\] (for A) \[0.4M\]of \[B\xrightarrow{20\,\min }0.2M\xrightarrow{20\,\min }0.1M\xrightarrow{20\,\min }0.05\] (for B) \[\frac{-d[B]}{d}\] will be doubled and hence \[{{t}_{1/2}}\] will be halved \[\therefore \,\,\,\,\frac{[A]}{[B]}=2\]
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