JEE Main 2016 · Chemistry · Chemical Kinetics · easy

The gas-phase reaction A(g)→ 2B(g)+C(g) is first order in A. Starting with pure A at 100 mm Hg, the total pressure is 220 mm Hg after 20 min. The…

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The gas-phase reaction

\mathrm{A(g)\to 2B(g)+C(g)}

is first order in A. Starting with pure A at

100

mm Hg, the total pressure is

220

mm Hg after

20

min. The half-life of the reaction (in minutes) is nearly

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Answer: (D) $15.1$

Let

x

be the pressure of A that reacted. Total pressure

=(100-x)+2x+x=100+2x=220

, so

x=60

and

p_A=40

mm Hg.

k=\dfrac{1}{t}\ln\dfrac{p_0}{p_A}=\dfrac{1}{20}\ln\dfrac{100}{40}=0.0458\ \mathrm{min^{-1}}

t_{1/2}=0.693/k=15.1

min. Using

\ln(220/100)

instead gives

17.6

min, while using

p_A=60

mm Hg (treating

x

as the remaining pressure) gives

27.2

min.

Original question written in the JEE Main 2016 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake