Question

The reaction $A\left(s\right)\to 2B\left(g\right)+C\left(g\right)$ is first order. The pressure after $20$ min and after very long time as $150mm$ $Hg$ and $225mm$ $Hg$. The value of rate constant and pressure after $40$ min are:

• A. $0.05\ln 1.5{min}^{-1},200mm$
• B. $0.5\ln 2{min}^{-1},300mm$
• C. $0.05\ln 3{min}^{-1},300mm$
• D. $0.05\ln 3{min}^{-1},200mm$

Answer 1

The correct option is A $0.05\ln 1.5{min}^{-1},200mm$

Pressure of gaseous product is synonymous to concentration.

For first order reaction

$k=\frac{2.303}{t}\log \frac{{\left[A\right]}_o}{{\left[A\right]}_t}$

After 20 min

$k=\frac{2.303}{20}\log \left[\frac{225}{75}\right]=0.05$

Pressure after 40 minutes

$0.05=\frac{2.303}{40}(\log 225-\log (225-x))0.8684-\log 225=-\log y0.8684-2.3522=-\log y+1.4838=+\log yy=antilog\left(1.4838\right){\left[A\right]}_t=200mm$

Therefore answer is [A]