ΔH at another temperature (Kirchhoff)

Worked example

ΔH = 45.0 kJ mol⁻¹ at 298 K and ΔCₚ = 29.0 J K⁻¹ mol⁻¹ (assumed constant). Find ΔH at 875 K.

1. 1. Kirchhoff's law: solve for ΔH(T₂)

   $\Delta H(T_2) = \Delta H(T_1) + \Delta C_p\,(T_2 - T_1)$

   = 61.73 kJ mol⁻¹

Answer: ΔH(T₂) = 61.7 kJ mol⁻¹

Method

ΔH(T₂) = ΔH(T₁) + ΔCₚ(T₂ − T₁). ΔCₚ is in J, ΔH in kJ: watch the factor of 1000.

Common mistakes

• ΔCₚ multiplies the temperature change (T₂ − T₁), not T₂ itself.

Formulas used

• Kirchhoff's law

  $\Delta H(T_2) = \Delta H(T_1) + \Delta C_p\,(T_2 - T_1)$

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