The standard enthalpy of formation of gaseous H2 O at 298.15...

The standard enthalpy of formation of gaseous $\mathrm{H}_{2} \mathrm{O}$ at $298.15 \mathrm{K}$ is $-241.82 \mathrm{kJmol}^{-1}$. Using the ideas contained in Figure $7-16,$ estimate its value at $100.0^{\circ} \mathrm{C}$ given the following values of the molar heat capacities at constant pressure: $\mathrm{H}_{2} \mathrm{O}(\mathrm{g}): 33.58 \mathrm{JK}^{-1} \mathrm{mol}^{-1}$ $\mathrm{H}_{2}(\mathrm{g}): 28.84 \mathrm{JK}^{-1} \mathrm{mol}^{-1} ; \quad \mathrm{O}_{2}(\mathrm{g}): 29.37 \mathrm{JK}^{-1} \mathrm{mol}^{-1}$ Assume the heat capacities are independent of temperature.

The standard enthalpy of formation of gaseous $\mathrm{H}_{2} \mathrm{O}$ at $298.15 \mathrm{K}$ is $-241.82 \mathrm{kJmol}^{-1}$. Using the ideas contained in Figure $7-16,$ estimate its value at $100.0^{\circ} \mathrm{C}$ given the following values of the molar heat capacities at constant pressure: $\mathrm{H}_{2} \mathrm{O}(\mathrm{g}): 33.58 \mathrm{JK}^{-1} \mathrm{mol}^{-1}$
$\mathrm{H}_{2}(\mathrm{g}): 28.84 \mathrm{JK}^{-1} \mathrm{mol}^{-1} ; \quad \mathrm{O}_{2}(\mathrm{g}): 29.37 \mathrm{JK}^{-1} \mathrm{mol}^{-1}$
Assume the heat capacities are independent of temperature.

Key Concepts

Standard Enthalpy of Formation

This term refers to the heat change that occurs when one mole of a compound is formed from its elements in their standard states under standard conditions. It provides a baseline energy value for compounds that can be used to calculate reaction enthalpies using thermochemical cycles or Hess's Law.

Molar Heat Capacity at Constant Pressure

Molar heat capacity at constant pressure, often denoted as Cp, is the amount of energy required to raise the temperature of one mole of a substance by one Kelvin at constant pressure. It is essential in determining how the enthalpy of a substance changes with temperature and is often assumed to be constant over moderate temperature ranges.

Temperature Dependence of Reaction Enthalpies

Reaction enthalpies are temperature dependent, and the change in enthalpy with temperature can be calculated by integrating the heat capacities of the reactants and products over the temperature range of interest. This approach allows for the estimation of reaction enthalpies at temperatures different from the standard 298.15 K.

Kirchhoff's Law

Kirchhoff's Law in thermodynamics relates the change in the heat of reaction with temperature to the difference in molar heat capacities between products and reactants. It provides a method to adjust standard reaction enthalpies calculated at one temperature to another temperature by accounting for the temperature-dependent contributions of heat capacities.

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