Q33 / 180 · KCET 2011 · Chemistry

The folllowing data were obtained during the first order decomposition of $2 A(g) \rightarrow B(g)+C(s)$ at a constant volume and at a particular temperature
Figure
The rate constant in $\mathrm{min}^{-1}$ is

  • Correct answer
    A
    $0.0693$
  • B
    $69.3$
  • C
    $6.93$
  • D
    $6.93 \times 10^{-4}$

Solution

$$ \begin{array}{lc} 2 A(g) \longrightarrow B(g)+C(s) \\ 2-2 x & x \end{array} $$ At the end of reaction, only 1 mole of gas is present whose pressure is 200 Pascal. $\therefore$ At the beginning of the reaction 2 moles of gas should have a pressure of 400 Pascal. After time $10 \mathrm{~min}$ No. of moles present, $$ 2-2 x+x=2-x $$ The pressure of 2 moles $=400$ $\therefore \quad 400-x=300$ $\therefore \quad x=100$ $\therefore$ Pressure due to $2-2 x$ moles of $A$ $$ =400-200=200 $$ $\begin{aligned} \therefore \quad k &=\frac{2.303}{t} \log \left(\frac{a}{a-x}\right)=\frac{2.303}{10} \log \left(\frac{400}{200}\right) \\ &=\frac{2.303}{10} \log 2=\frac{0.693}{10} \\ &=0.0693 \mathrm{~min}^{-1} \end{aligned}$

Hence, the correct answer is option: 'A'.

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