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 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 ________.

Solution

Physics sir · 3 steps

Each broken molecule gives two atoms, so count the new moles first, then let PV = nRT do the rest.

1. Count new moles. Start with n moles of diatomic gas. If 25% dissociate, 0.75n moles stay as molecules, and the other 0.25n moles split into 2 × 0.25n = 0.5n moles of atoms. The total is 0.75n + 0.5n = 1.25n.
2. Ideal gas twice. Initially P₁ V₁ = nR(250). Finally P₂ (2V₁) = (1.25n)R(2000). Divide the second equation by the first so that n, R and V₁ cancel.

   P₂/P₁ = 1.25n/n × 2000/250 × V₁/2V₁ = 1.25 × 8 × 1/2

3. So. P₂/P₁ = 10/2 = 5, so the answer is 5.

The common slip: 4. Treating the dissociated part as still 0.25n moles keeps the total at n and gives 4. Each dissociated molecule makes two atoms, so that part becomes 0.5n moles.

The idea to keep. Pressure depends on the number of particles, not their type. When molecules break up, add up the new moles first: one diatomic mole becomes two moles of atoms.

Answer from the NTA final answer key. Solution by PrepWiser.