Question

The standard molar heat of formation of ethane, carbon dioxide and liquid water are $-21.1kcal,-94.1kcal$ and $-68.3kcal$ respectively. Calculate the standard molar heat of combustion of ethane.

Answer 1

Hint: We can solve the question by the information given above in this question. It is asked for the standard molar heat of combustion of ethane after which carbon dioxide and water are released. Write the balanced chemical equation firstly and then write the molar enthalpy for reaction. Molar enthalpy of reaction is written as the difference of enthalpies of products minus for the reactants.

Complete step by step answer:
As we have ethane and its combustion is done, it means ethane is reacting with full supply of oxygen after which we get product as carbon dioxide and water. The products are obtained the same when any hydrocarbon is burned in full presence of oxygen. We have to write the complete balanced equation for above reaction,
${{C}_{2}}{{H}_{6}}+\dfrac{7}{2}{{O}_{2}}\to 2C{{O}_{2}}+3{{H}_{2}}O$
Here, for this balanced chemical reaction we can write the molar enthalpy of reaction as,
$\Delta {{H}_{C}}=\left[ 2\Delta {{H}_{f(C{{O}_{2}})}}+3\Delta {{H}_{f({{H}_{2}}O)}} \right]-\left[ \Delta {{H}_{f({{C}_{2}}{{H}_{6}})}}+\dfrac{7}{2}\Delta {{H}_{f({{O}_{2}})}} \right]$
On putting the values of enthalpies given above we can easily calculate the value of standard molar heat of combustion of ethane.
$\Delta {{H}_{C}}=\left[ 2(-94.1)+3\left( -68.3 \right) \right]-\left[ \left( -21.1 \right)+\dfrac{7}{2}\left( 0 \right) \right]$
\[\Rightarrow \Delta {{H}_{C}}=\left[ \left( -188.2 \right)+\left( -204.9 \right) \right]-\left[ -42.2 \right]\]
\[\Rightarrow \Delta {{H}_{C}}=350.9kcal\cdot mo{{l}^{-1}}\]
Therefore, As the standard molar enthalpy is \[350.9kcal\cdot mo{{l}^{-1}}\]

Note: The standard molar enthalpy of any reaction is written as the sum of enthalpy of product subtracting the sum of enthalpy of the reactant. In the above expression we wrote the molar enthalpy of oxygen as zero, this is because the molar enthalpy of molecules which are in their reference state is always written as zero.