1. Tardigrade
  2. Question
  3. Chemistry
  4. textA(g) xrightarrow textB(g) is a first order reaction. The initial concentration of A is text0 text.2 textmol textL-1. After 10 min, the concentration of B is found to be text0 text.18 textmol textL-1. The rate constant (in min-1) for the reaction is

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Q. $ \text{A(g)}\xrightarrow{{}}\text{B(g)} $ is a first order reaction. The initial concentration of A is $ \text{0}\text{.2}\,\text{mol}\,{{\text{L}}^{-1}}. $ After 10 min, the concentration of B is found to be $ \text{0}\text{.18}\,\text{mol}\,{{\text{L}}^{-1}}. $ The rate constant $ (in\,mi{{n}^{-1}}) $ for the reaction is

EAMCETEAMCET 2008Chemical Kinetics

Solution:

Given, $ A(g)\xrightarrow{{}}B(g) $ (first order reaction) Initial concentration of $ A=0.2\text{ }mol\text{ }{{L}^{-1}} $ Concentration of $ \text{B}=0.18\text{ mol}\,{{\text{L}}^{-1}} $ Concentration of A after 10 min $ =0.2-0.18 $ $ =0.02\text{ mol }{{\text{L}}^{-1}} $ time (r)= 10 min Rate constant, $ k=\frac{2.303}{t}\log \frac{a}{a-x} $ $ =\frac{2.303}{10}\log \frac{0.2}{0.02} $ $ =0.2303\,{{\min }^{-1}} $