NEET Chemistry NEET PYQ-Chemical Kinetics

For a first order reaction \[A\xrightarrow[{}]{{}}B\,,\] the reaction rate at reactant concentration of 0.01 M is found to be \[2.0\times {{10}^{-5}}\,mol\,{{L}^{-1}}\,{{s}^{-1}}\]. The half-life period of the reaction is: [AIPMT (S) 2005]

A) 220 s

B) 30 s

C) 300 s

D) 347 s

Correct Answer: D

Solution :

[d] For first order reaction

\[A\xrightarrow[{}]{{}}B\]

Given that rate = \[k\times [A]\]

Rate = \[2.0\times {{10}^{-5}}\,\,mol\,{{L}^{-1}}\,{{s}^{-1}}\]

\[[A]=Conc.\,\,of\,A=0.01\,M\]

\[So\,\,\,\,2.0\times {{10}^{-5}}\,=k\times 0.01\]

\[k=\frac{2.0\times {{10}^{-5}}}{0.01}{{s}^{-1}}\]

\[=2.0\times {{10}^{-3}}\,{{s}^{-1}}\]

For first order reaction

\[{{T}_{1/2}}=\frac{0.693}{k}=\frac{0.693}{2.0\times {{10}^{-3}}}\]

\[=346.5\approx 347\,s\]