A) \[\frac{1}{n-1}\left( \frac{{{2}^{n-1}}-2}{{{a}^{n-1}}} \right)\frac{1}{k}\]
B) \[\frac{1}{n-1}\left( \frac{{{2}^{n-2}}-2}{{{a}^{n-1}}} \right)\frac{1}{k}\]
C) \[\frac{1}{n-1}\left( \frac{{{2}^{2n-2}}-1}{{{a}^{n-1}}} \right)\frac{1}{k}\]
D) \[\frac{1}{n-2}\left( \frac{{{2}^{2n-2}}-1}{{{a}^{2n-1}}} \right)\frac{1}{k}\]
Correct Answer: C
Solution :
[C]| for a nth order reaction : |
| \[kt=\frac{1}{n-1}\left[ \frac{1}{{{[A]}^{n-1}}}-\frac{1}{[A]_{0}^{n-1}} \right]\] |
| For 75% completion of reaction \[[A]=\frac{{{[A]}_{0}}}{4}\] |
| \[\Rightarrow t=\frac{1}{k(n-1)}\left[ \frac{{{4}^{n-1}}-1}{[A]_{0}^{n-1}} \right]\] |
| \[=\frac{1}{k\,(n-1)}\left( \frac{{{2}^{2n-2}}-1}{{{a}^{n-1}}} \right)\] |
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