Question

Standard Molar Enthalpy of Formation of ${\mathrm{CO}}_2$ Is equal to

Answer 1

Step 1: Understand the term "Standard Molar Enthalpy of Formation"

The standard reaction enthalpy for the creation of the chemical from its elements (atoms or molecules) in their most stable reference states at the given temperature ($298.15\mathrm{K}$) and pressure ($1\mathrm{bar}$) is the enthalpy of formation.

Or in other words, the standard molar enthalpy of formation of a compound is defined as the enthalpy of formation of $1.0$ mol of the pure compound in its stable state from the pure elements in their stable states at $\mathrm{P}=1.0$ bar at a constant temperature.

The enthalpy of combustion is the heat released when a given amount of a combustible pure substance is burned (in oxygen) to form incombustible products (e.g., water and carbon dioxide).

Step 2: Analyse the reaction for the formation of ${\mathrm{CO}}_2$

For one mole of Carbon dioxide (${\mathrm{CO}}_2$)

$\underset{\mathrm{Oxygen}}{{\mathrm{O}}_2\left(\mathrm{g}\right)}+\underset{\mathrm{Graphite}}{\mathrm{C}\left(\mathrm{s}\right)}\rightleftharpoons \underset{\mathrm{Carbon}\mathrm{dioxide}}{{\mathrm{CO}}_2\left(\mathrm{g}\right)}$

Thus, one mole of Oxygen reacts with one mole of Graphite to form one mole of Carbon dioxide.

Step 3: Determine enthalpy of formation.

Enthalpy of formation can be determined by

$△{\mathrm{H}}_{\mathrm{reaction}}^0=\mathrm{\Sigma }△{\mathrm{H}}_{\mathrm{f}\left(\mathrm{product}\right)}^0-\mathrm{\Sigma }△{\mathrm{H}}_{\mathrm{f}\left(\mathrm{reactant}\right)}$

So, according to the reaction

$△{\mathrm{H}}_{\mathrm{reaction}}^0=△{\mathrm{H}}_{\mathrm{f}}^0\left({\mathrm{CO}}_2\right(\mathrm{g}))-[△{\mathrm{H}}_{\mathrm{f}}^0({\mathrm{O}}_2\left(\mathrm{g}\right))+△{\mathrm{H}}_{\mathrm{f}}^0(\mathrm{C}\left(\mathrm{graphite}\right)\left)\right]$

${\mathrm{O}}_2\left(\mathrm{g}\right)$ exists in its most basic stable form, with a standard enthalpy of production of zero.

Thus, the enthalpy of Carbon dioxide generation will be equal to the usual molar enthalpy of Carbon burning (Graphite).

Hence, the standard molar enthalpy of the formation of Carbon dioxide is equal to the standard molar enthalpy of combustion of Carbon (Graphite).