Question

Heats of combustion of $C{{H}_{4}},{{C}_{2}}{{H}_{6}},$ and ${{C}_{2}}{{H}_{2}}$ is -212.8,-373.0,-337.0 and -310.5 kcal respectively at the same temperature. The best fuel among these gases is:
A.$C{{H}_{4}}$
B.${{C}_{2}}{{H}_{6}}$
C.${{C}_{2}}{{H}_{4}}$
D.${{C}_{2}}{{H}_{2}}$

Answer 1

Hint: The meaning of best fuel means that the fuel should have a high calorific value. So, it is preferred to find the calorific value of the fuels by using the heat of combustion values and the molar mass.

Complete answer:
In order to answer this question, let us find out what calorific value is. A fuel is said to be a good fuel if it is economical and gives good energy. Efficiency of a fuel means the output the fuel gives, compared to the input energy we have to give to burn the fuel. A fuel which is highly efficient in nature is said to have a high calorific value. Calorific value is the amount of heat that is released by a fuel, on complete combustion, when a unit weight, rather than unit volume of it is used up. So, for a fuel to be a good fuel, it has to give the maximum amount of heat by using the minimum volume or minimum weight.
Now, we are given with 4 gases, whose heat of combustion is given. So we can find the calorific value by the formula:
$Calorific\,value=\dfrac{Heat\,of\,combustion}{molar\,mass}$
So, the calorific values of the respective gases are:
$\begin{align}
  & C.{{V}_{C{{H}_{4}}}}=\dfrac{-212.8\times {{10}^{3}}}{16}=-13.3\times {{10}^{3}} \\
 & C.{{V}_{{{C}_{2}}{{H}_{6}}}}=\dfrac{-373\times {{10}^{3}}}{30}=-12.4\times {{10}^{3}} \\
 & C.{{V}_{{{C}_{2}}{{H}_{4}}}}=\dfrac{-337\times {{10}^{3}}}{28}=-12.03\times {{10}^{3}} \\
 & C.{{V}_{{{C}_{2}}{{H}_{2}}}}=\dfrac{-310.5\times {{10}^{3}}}{26}=11.92\times {{10}^{3}} \\
\end{align}$
From the given data, we find that the maximum calorific value is of methane ${{C}_{2}}{{H}_{4}}$.

Hence, it is the most efficient fuel and so our correct answer is option A.

Note:
It is to be noted that only the magnitude of the calorific value is needed to determine the efficiency of the fuel, sign is not important. Methane is used as a fuel in chemical processes carried out in industries and is transported as a refrigerated liquid(LMG).