Question

For first order reaction:
2A(g) → 4B(g) + C(g)
Total pressure at \( t = 30 \, \text{sec} \) and \( t = \infty \) are 300 torr and 600 torr respectively. Calculate pressure of C(g) at 30 sec (in torr).

Hint:

For a first-order reaction, the total pressure is related to the change in the number of moles of gas. Use stoichiometry to relate the change in pressure to the amount of substance reacted.

Answer 1

Correct Answer: 20

Step 1: Understanding the reaction.
For the given first-order reaction, the stoichiometry is as follows: \[ 2A(g) \rightarrow 4B(g) + C(g) \] This means that for every 2 moles of A that react, 4 moles of B and 1 mole of C are formed.
Step 2: Relating pressure change to moles of gas.
The total pressure is directly related to the number of moles of gases present in the system. Let \( x \) be the amount of A that has reacted at time \( t \). From the stoichiometry, the moles of B formed will be \( 2x \), and the moles of C formed will be \( x \). At \( t = 30 \, \text{sec} \), the total pressure is 300 torr. At \( t = \infty \), the total pressure is 600 torr, which corresponds to the pressure when the reaction has gone to completion. The total change in pressure from \( t = 0 \) to \( t = \infty \) is due to the formation of B and C: \[ \text{Total pressure at} \, t = \infty = \text{pressure due to B} + \text{pressure due to C} \] Thus, the pressure at \( t = \infty \) is due to 2 moles of B and 1 mole of C for every 2 moles of A that reacted.
Step 3: Set up the relation.
The total pressure at \( t = \infty \) can be expressed as: \[ P_{\infty} = \text{Initial pressure} + \text{Pressure due to B and C} = 600 \, \text{torr} \] The pressure due to the reaction at time \( t = 30 \, \text{sec} \) is 300 torr. The fraction of the reaction completed can be found by comparing the change in pressure at \( t = 30 \, \text{sec} \) to the change in pressure at \( t = \infty \).
Step 4: Calculate the pressure of C at \( t = 30 \, \text{sec} \).
From the given, the pressure of B and C combined at \( t = 30 \, \text{sec} \) is 300 torr. Since 1 mole of C is formed for every 2 moles of A that react, the pressure of C at \( t = 30 \, \text{sec} \) is: \[ P_C = \frac{300 \, \text{torr}}{3} = 20 \, \text{torr} \]