At a total pressure of 1.0 atm, N2O4(g) is 20\% dissociated at 300 K and 50\% dissociated at 350 K (equilibrium N2O4(g) 2NO2(g)). Assuming Delta H is constant and R = 8.314 J mol^-1 K^-1, find Delta H in kJ/mol to the nearest integer.

JEE Advanced levelNumerical answerDifficulty 3 of 3ce215

At a total pressure of $1.0 atm$ , $N X_{2} O X_{4} (g)$ is 20\% dissociated at $300 K$ and 50\% dissociated at $350 K$ (equilibrium $N X_{2} O X_{4} (g) 2 NO X_{2} (g)$ ). Assuming $Δ H$ is constant and $R = 8.314 J mo l^{- 1} K^{- 1}$ , find $Δ H$ in kJ/mol to the nearest integer.

Numerical answer type, answer in kJ/mol, tolerance 0.5.

K_{p} = 4 α^{2} P / (1 - α^{2})

K_{p 1} = 0.1667

K_{p 2} = 1.3333

atm.

Δ H = R ln (K_{p 2} / K_{p 1}) / (1/300 - 1/350) = 8.314 \times 2.0794/0.000476 = 36.31

kJ/mol, i.e. 36.