Question

Calorific value of ${{H}_{2}}$gas is x $KJ/gm$. What is the heat of formation of ${{H}_{2}}O$?
A. x KJ
B. 2x KJ
C. $\dfrac{x}{2}$KJ
D. 18x KJ

Answer 1

Hint: Calorific value is the amount of heat energy present in food or fuel which is further determined by complete combustion of specified quantity at constant pressure in normal conditions. It is also known as calorific power.

Complete step by step solution: We know that by the combustion process water vapors are generated and with the help of some special techniques heat is recovered during these combustion processes. If the heat contained in the water vapor has a possibility to be recovered then it is said that the process has high calorific value and if heat contained in the water vapor can-not be recovered then the solution has low calorific value.
Now we know that the calorific value of a fuel is the same as that of the heat of combustion.
Given calorific value of ${{H}_{2}}$gas is x \[{{H}_{2}}+\dfrac{1}{2}{{O}_{2}}\to {{H}_{2}}O\]$KJ/gm$
Now we know that molar mass of ${{H}_{2}}$gas is 2 gm
Therefore calorific value of ${{H}_{2}}$gas per mole = $\dfrac{x}{2}$ $KJ/mol$
Hence the heat of combustion of ${{H}_{2}}$is $\dfrac{x}{2}$ $KJ/mol$
Combustion of ${{H}_{2}}$ can be represented by the reaction:
\[{{H}_{2}}+\dfrac{1}{2}{{O}_{2}}\to {{H}_{2}}O\]
Hence from the above reaction we conclude that heat of formation of ${{H}_{2}}O$is the same as that of heat of combustion of ${{H}_{2}}$gas.
Hence the heat of formation of ${{H}_{2}}O$is $\dfrac{x}{2}$ $KJ/mol$.

Thus option C is the correct answer.

Note: The efficiency of any food or fuel also depends upon its calorific value. Its calorific value is high then efficiency is also high and if calorific value is low then efficiency is also low and in short we can say that calorific value is directly proportional with the efficiency.