For N2(g) + 3H2(g) -> 2NH3(g), Delta H deg_298 = -92.2 kJ. Molar heat capacities C_P (assumed constant, J mol^-1K^-1): N2 29.1, H2 28.8, NH3 35.1. Using Kirchhoff's law, calculate Delta H deg at 500 K in kJ (two decimals, with sign).

JEE Advanced levelNumerical answerDifficulty 3 of 3td030

For $N X_{2} (g) + 3 H X_{2} (g) 2 NH X_{3} (g)$ , $Δ H_{298}^{\circ} = - 92.2 kJ$ . Molar heat capacities $C_{P}$ (assumed constant, $J mo l^{- 1} K^{- 1}$ ): $N X_{2}$ 29.1, $H X_{2}$ 28.8, $NH X_{3}$ 35.1. Using Kirchhoff's law, calculate $Δ H^{\circ}$ at $500 K$ in $kJ$ (two decimals, with sign).

Numerical answer type, answer in kJ, tolerance 0.02.

Δ C_{P} = 2 (35.1) - 29.1 - 3 (28.8) = - 45.3 J K^{- 1}

Δ H_{500} = Δ H_{298} + Δ C_{P} (500 - 298) = - 92200 + (- 45.3) (202) = - 101350.6 J = - 101.35 kJ