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Question: Heats of combustion of \(C{{H}_{4}},{{C}_{2}}{{H}_{6}},\) and \({{C}_{2}}{{H}_{2}}\) is -212.8,-373....

Heats of combustion of CH4,C2H6,C{{H}_{4}},{{C}_{2}}{{H}_{6}}, and C2H2{{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.CH4C{{H}_{4}}
B.C2H6{{C}_{2}}{{H}_{6}}
C.C2H4{{C}_{2}}{{H}_{4}}
D.C2H2{{C}_{2}}{{H}_{2}}

Explanation

Solution

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=Heat of combustionmolar massCalorific\,value=\dfrac{Heat\,of\,combustion}{molar\,mass}
So, the calorific values of the respective gases are:
C.VCH4=−212.8×10316=−13.3×103 C.VC2H6=−373×10330=−12.4×103 C.VC2H4=−337×10328=−12.03×103 C.VC2H2=−310.5×10326=11.92×103 \begin{aligned} & 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{aligned}
From the given data, we find that the maximum calorific value is of methane C2H4{{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).