Question

A closed container has a gas A at a pressure of 200 mm of Hg at 300 K. When the container is heated to 600 K, A starts decomposing via first order kinetics as,

$A\left(g\right)\to 3B\left(g\right)+2C\left(g\right)$

After 1 hour and 20 minutes, the total pressure of the gaseous mixture is 1900 mm of Hg. What is the half-life of the reaction (in min) at 600 K?

Answer 1

At 300 K, the initial pressure of A is 200 mmHg
At 600 K, the initial pressure of A would be twice as the temperatue is doubled, that is, 400 mmHg

$A\left(g\right)\to 3B\left(g\right)+2C\left(g\right)$
At, t = 0 400 0 0
At, t = 80 min 400-p 3p 2p

Total pressure at 80 mins = 1900 mmHg

400 + 4p = 1900 mm of Hg

Therefore, p = 375 mm of Hg

Pressure of A at 600 K, 400 - 375 = 25 mm of Hg

For 400 mm of Hg to become 25 mm of Hg, four half-lives should have passed.

Therefore, half-life= $\frac{timetaken}{4}$
=$\frac{80}{4}$= 20 mins