Question

The heat of combustion for C, ${{H}_{2}}$​ and $C{{H}_{4}}$ are −349 kJ/mol, −241.8 kJ/mol and −906.7 kJ/mol respectively. The heat of formation in kJ/mol of $C{{H}_{4}}$​is:
(A) 174.1 kJ/mol
(B) 274.1 kJ/mol
(C) 374.1 kJ/mol
(D) 74.1 kJ/mol

Answer 1

Hint: As we know that heat of formation is also known as standard heat of formation or enthalpy of formation and it is the amount of heat evolved or absorbed when one mole of a compound is formed from its constituent elements where each substance on reactant side has to in its normal physical state.

Complete answer:
Let us discuss about heat of formation followed by calculating the same for methane as follows:-
-Heat of formation: It is the amount of heat evolved when one mole of a compound is formed from its constituent elements where each substance on the reactant side has to be in its normal physical state (whether gas, liquid, or solid).
-Heat of combustion: It is the total energy released as heat when a substance or a compound undergoes complete combustion with oxygen under standard conditions of pressure.
-We are provided the heat of combustion for C, ${{H}_{2}}$​ and $C{{H}_{4}}$ which will be accounted as the heat of reaction ($\Delta {{H}_{r}}$) of their combustion as shown below:-
$C(s)+{{O}_{2}}(g)\to C{{O}_{2}}\left( g \right)~;~\Delta {{H}_{r}}=-349~kJ/mol\text{ }..........\left( i \right)$
${{H}_{2}}(g)+\dfrac{1}{2}{{O}_{2}}(g)\to {{H}_{2}}O\left( l \right)~;~\Delta {{H}_{r}}=-241.8~kJ/mol\text{ }~..........\left( ii \right)$
$C{{H}_{4}}(g)+2{{O}_{2}}(g)\to C{{O}_{2}}\left( g \right)+2{{H}_{2}}O\left( l \right)~;~\Delta {{H}_{r}}=-906.7~kJ/mol\text{ }.........\left( iii \right)$
-Now methane is formed by carbon and hydrogen gas as follows:-
$C\left( s \right)+2{{H}_{2}}\left( g \right)\to C{{H}_{4}}\left( g \right)$
Heat of reaction for the above equation is calculated by $\left( i \right)+2\times \left( ii \right)-\left( iii \right)$as follows:-
$\Delta {{H}_{r}}$= [−349 + 2(−241.8) + 906.7] kJ/mol = 74.1 kJ/mol
As we know that heat of formation is equal to the heat of reaction when one mole of a compound is formed from its constituent elements where each substance on reactant side has to be in its normal physical state.

Therefore, the heat of formation of ​$C{{H}_{4}}$ is (D) 74.1 kJ/mol.

Note:
-Remember that the compounds or reactants which are in their original physical state (or the state in which they actually exist in nature) have zero heat of formation.
-Also perform calculations along with units for better results.