Question

# The reaction $A(s) \to 2B(g) + C(g)$ is first order. The pressure after 20 min and after a very long time was 150mm Hg and 225nm Hg. The value of rate constant and pressure after 40 min are:A.$0.05\ln 1.5{\min ^{ - 1}},200mm$B.$0.05\ln 2{\min ^{ - 1}},300mm$C.$0.05\ln 3{\min ^{ - 1}},300mm$D.$0.05\ln 3{\min ^{ - 1}},200mm$

Hint: A first order reaction is a reaction that proceeds at a rate that depends linearly on only one reactant concentration. The reaction rate or rate of reaction is the speed at which a chemical reaction takes place.
Formula used:
$k = \dfrac{{2.303}}{t}\log \dfrac{{{A_0}}}{{{A_t}}}$

Now according to the question,
After 20 min,
$k = \dfrac{{2.303}}{{20}}\log \dfrac{{225}}{{75}}$
Now,
$k = 0.05$
The pressure after 40 min will be,
Using the formula
$0.05 = \dfrac{{2.303}}{{40}}(\log 225 - \log (225 - x))$
$0.8685 - \log 225 = - \log y$
$0.8684 - 2.3522 = - \log y$
$y = anti\log (1.4838)$
${[A]_t} = 200mm$ (Taken antilog)

Hence option A is correct.

Note:
When the pressure increases the molecules have less space in which they can move. Hence greater density of molecules increases the number of collisions. When the pressure decreases molecules donâ€™t hit each other as often and the rate of reaction decreases.