Question

What will be the heat of formation of methane, if the heat of combustion of carbon is $-xkJ$, the heat of formation of water is $-ykJ$ and the heat of combustion of methane is $zkJ$?
(A) $(-x-y+z)kJ$
(B) $(-z-x+2y)kJ$
(C) $(-x-2y-z)kJ$
(D) $(-x-2y+z)kJ$

Answer 1

Hint: To solve this question first we have to write all the equations involved in the formation of methane. The heat released when a sample is burned in the presence of air in its standard form to form a stable compound in its standard state is known as the heat of combustion.

Complete step by step solution:
In this question, we have to find the value of heat of formation of methane
Given in the question:
The heat of combustion of carbon= $-xkJ$
The heat of formation of water = $-ykJ$
The heat of combustion of methane= $zkJ$= $-zkJ$, the value of heat of combustion is always negative.
Now write the reaction:
Combustion of carbon: carbon reacts with oxygen and produces carbon dioxide.
\[C+{{O}_{2}}\to C{{O}_{2}}\] And given value = $-xkJ$
Formation of water: dihydrogen reacts with oxygen and produces water.
\[{{H}_{2}}+\dfrac{1}{2}{{O}_{2}}\to {{H}_{2}}O\]And given value= $-ykJ$
Combustion of methane: methane reacts with oxygen and produces carbon dioxide and water.
\[C{{H}_{4}}+2{{O}_{2}}\to C{{O}_{2}}+2{{H}_{2}}O\] And given value= -$zkJ$
The required equation is for formation of methane:
\[C+2{{H}_{2}}\to C{{H}_{4}}\]
To get the value of heat of formation of methane we have to add the value of heat of combustion of carbon = $-xkJ$ to two times the value of heat of formation of water = $-ykJ$ and subtract the heat of combustion of methane= -$zkJ$
Heat of formation of methane = \[Heat\text{ }of\text{ }combustion\text{ }of\text{ }carbon+2(Heat\text{ }of\text{ }formation\text{ }of\text{ }water)\text{ -}Heat\text{ }of\text{ }combustion\text{ }of\text{ }methane\]
$\implies$ \[-x+(-2y)-(-z)=(-x-2y+z)kJ\]

Hence the correct option is (C).

Note: The heat of formation is the amount of heat absorbed or evolved when 1 mole of a compound is formed from its constituent elements and each element is present in its normal physical state. The normal physical state can be solid, liquids or gases.