Chemical Kinetics Question 203

Question: For a reaction, $ X(g)\to Y(g)+Z(g) $ the half life period is 10 min. In What period of time would the concentration of X be reduced to 10% of original concentration [DCE 2004]

Options:

A) 20 min

B) 33 min

C) 15 min

D) 25 min

Show Answer

Answer:

Correct Answer: B

Solution:

$ {x_{(g)}}\to {y_{(g)}}+{z_{(g)}} $ The reaction is a first order reaction hence, K=\frac{0.693}{{t_{1/2}}}=\frac{2.303}{t}\log \frac{a}{a-x} $

$ =\frac{0.693}{10\ \min } $

$ =\frac{2.303}{t}\log \frac{a}{a/10} $

$ =\frac{0.693}{10}=\frac{2.303}{t}\log 10 $
$ \therefore \ \ t=\frac{2.303\times 10}{.693}=33\min $ .



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