Question

Initially, a gas of diatomic molecules is contained in a cylinder of volume V₁ at a pressure P₁ and temperature 250 K. Assuming that 25% of the molecules get dissociated causing a change in the number of moles. The pressure of the resulting gas at temperature 2000 K, when contained in a volume 2V₁ is given by P₂. The ratio P₂ / P₁ is ________.

Answer 1

• initial volume = V₁, initial pressure = P₁, initial temperature = T₁ = 250K

So, ideal gas equation $PV=nRT$ will be

$P_1{V}_1=n_{0}R{T}_1$

$P_1{V}_1=n_{0}R\left(250\right)$ ……. (1)

• Final volume (V₂) = 2V₁, final pressure = P₂, final temperature = T₂ = 2000K

So, ideal gas equation will be

$P_2{V}_2=n_{f}R{T}_2$

$P_2\left(2V_1\right)=n_{f}R\left(2000\right)$ ……. (2)

• Now, 25% of gas is dissociated. So, amount of gas remain undissociated is 75%.
• total number of moles = number of moles of diatomic molecules + number of moles of monoatomic.

total number of moles = (2 × 0.25 × no. of moles) + (0.75 × no. of moles)

• dividing eq. (1) and (2),

$\left[\frac{P_1{V}_1}{P_2\left(2V_1\right)}\right]=\left[\frac{n_{0}R\left(250\right)}{n_{f}R\left(2000\right)}\right]$

$\frac{P_1}{P_2}=\frac{1}{5}$ or $\frac{P_2}{P_1}=5$

So, the correct answer is 5.