A) \[2.303\times {{10}^{-5}}\ {{\sec }^{-1}}\]
B) \[2.303\times {{10}^{-4}}\ {{\sec }^{-1}}\]
C) \[4.606\times {{10}^{-3}}\ {{\sec }^{-1}}\]
D) \[2.606\times {{10}^{-5}}\ {{\sec }^{-1}}\]
E) \[2.603\times {{10}^{-4}}\ {{\sec }^{-1}}\]
Correct Answer: C
Solution :
For first order reaction \[K=\frac{2.303}{t}\log \frac{a}{a-x}\] Given: \[a=\frac{1}{10}=.1m\]; \[a-x=\frac{1}{100}=.01m\]; t = 500 sec \[\therefore \ \ K=\frac{2.303}{500}\log \frac{.10}{.01}=\frac{2.303}{500}\log 10\] \[=\frac{2.303}{500}=0.004606=4.6\times {{10}^{-3}}{{\sec }^{-1}}\].
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