The standard enthalpy of formation (\Delta H_f^\circ) of carbon dioxide gas (\text{CO}_2(g… — JAMB UTME

The standard enthalpy of formation ( $\Delta H_f^\circ$ ) of carbon dioxide gas ( $\text{CO}_2(g)$ ) is numerically identical to the standard enthalpy of combustion ( $\Delta H_c^\circ$ ) of diamond under standard thermochemical conditions ( $298\text{ K}$ and $1\text{ atm}$ ).

Answer: Answer

Answer

False

The standard enthalpy of formation (

\Delta H_f^\circ

) of a compound is defined as the enthalpy change when one mole of the substance is formed from its constituent elements in their reference standard states. For carbon at

298\text{ K}

and

1\text{ atm}

, the reference standard state is graphite. Consequently,

\Delta H_f^\circ[\text{CO}_2(g)]

represents the reaction of graphite with oxygen. In contrast, the combustion of diamond involves

\text{C}(s, \text{diamond})

. Because conversion of graphite to diamond is endothermic (

\Delta H_f^\circ[\text{diamond}] \approx +1.9\text{ kJ mol}^{-1}

), the combustion of diamond produces more heat than the formation of

\text{CO}_2(g)

from graphite. Thus, the two values are not numerically identical.

Step-by-Step Solution

Define the reaction equation for the standard enthalpy of formation (

\Delta H_f^\circ

) of

\text{CO}_2(g)

\text{C}(s, \text{graphite}) + \text{O}_2(g) \rightarrow \text{CO}_2(g) \quad \Delta H_1^\circ = \Delta H_f^\circ[\text{CO}_2(g)]

By international convention (IUPAC), the standard enthalpy of formation requires elements to be in their most stable allotropic form at

298\text{ K}

and

1\text{ atm}

, which is graphite for carbon.

Define the reaction equation for the standard enthalpy of combustion (

\Delta H_c^\circ

) of diamond.

\text{C}(s, \text{diamond}) + \text{O}_2(g) \rightarrow \text{CO}_2(g) \quad \Delta H_2^\circ = \Delta H_c^\circ[\text{diamond}]

The standard enthalpy of combustion of diamond measures the enthalpy change when 1 mole of diamond completely reacts with oxygen.

Apply Hess's law to relate

\Delta H_1^\circ

and

\Delta H_2^\circ

\Delta H_c^\circ[\text{diamond}] = \Delta H_f^\circ[\text{CO}_2(g)] - \Delta H_f^\circ[\text{diamond}]

Since diamond is less stable than graphite (

\Delta H_f^\circ[\text{diamond}] \approx +1.9\text{ kJ mol}^{-1}

\Delta H_2^\circ \neq \Delta H_1^\circ

Key Concept

Standard State Conventions and Allotropy in Hess's Law

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