The equilibrium constant of a gas-phase reaction is 0.020 at 400 K and 0.090 at 450 K. Taking R = 8.314 J mol^-1 K^-1 and Delta H independent of temperature, find Delta H in kJ/mol to the nearest integer.

JEE Main levelNumerical answerDifficulty 2 of 3ce192

The equilibrium constant of a gas-phase reaction is $0.020$ at $400 K$ and $0.090$ at $450 K$ . Taking $R = 8.314 J mo l^{- 1} K^{- 1}$ and $Δ H$ independent of temperature, find $Δ H$ in $kJ/mol$ to the nearest integer.

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

ln (K_{2} / K_{1}) = (Δ H / R) (1/ T_{1} - 1/ T_{2})

ln (0.090/0.020) = 1.5041

and

1/400 - 1/450 = 0.000278

Δ H = 8.314 \times 1.5041/0.000278 = 45018 J/mol = 45.02

kJ/mol, i.e. 45.