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Difficulty: HardStandard Enthalpy Changes and Hess's Law

The standard enthalpy of formation of gaseous water (H2O(g)\text{H}_2\text{O}(g)) at 298 K298\text{ K} is equal to the sum of the standard enthalpy of combustion of hydrogen gas (H2(g)\text{H}_2(g)) and the standard enthalpy of vaporization of liquid water (H2O(l)\text{H}_2\text{O}(l)).

Answer: Answer

Answer

The statement is true because adding the thermochemical equation for the combustion of hydrogen (which forms liquid water) to the equation for the vaporization of liquid water yields the formation equation for gaseous water from its constituent elements.
The statement accurately reflects Hess's law by combining the reaction for hydrogen combustion to form liquid water with the phase transformation of liquid water into water vapor.

Step-by-Step Solution

1
Write the thermochemical equation for the standard enthalpy of combustion of hydrogen gas.
H2(g)+12O2(g)→H2O(l)ΔH1∘=ΔHc∘[H2(g)]\text{H}_2(g) + \frac{1}{2}\text{O}_2(g) \rightarrow \text{H}_2\text{O}(l) \quad \Delta H_1^\circ = \Delta H_c^\circ[\text{H}_2(g)]
By definition, standard combustion of hydrogen produces water in its standard state at 298 K298\text{ K}, which is liquid water.
2
Write the thermochemical equation for the standard enthalpy of vaporization of water.
H2O(l)→H2O(g)ΔH2∘=ΔHvap∘[H2O(l)]\text{H}_2\text{O}(l) \rightarrow \text{H}_2\text{O}(g) \quad \Delta H_2^\circ = \Delta H_{\text{vap}}^\circ[\text{H}_2\text{O}(l)]
Vaporization represents the phase change of one mole of liquid water into gaseous water.
3
Apply Hess's law to combine Step 1 and Step 2.
H2(g)+12O2(g)+H2O(l)→H2O(l)+H2O(g)\text{H}_2(g) + \frac{1}{2}\text{O}_2(g) + \text{H}_2\text{O}(l) \rightarrow \text{H}_2\text{O}(l) + \text{H}_2\text{O}(g), which simplifies to H2(g)+12O2(g)→H2O(g)\text{H}_2(g) + \frac{1}{2}\text{O}_2(g) \rightarrow \text{H}_2\text{O}(g) with ΔH∘=ΔH1∘+ΔH2∘\Delta H^\circ = \Delta H_1^\circ + \Delta H_2^\circ.
Summing the two equations cancels out liquid water, leaving the formation reaction of gaseous water from its elemental gases.

Key Concept

Hess's Law and Thermochemical Cycles involving Standard States
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Topics

Standard Enthalpy Changes and Hess's Law