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# Heat of combustion ($\Delta {H^ \circ }$) for ${C_{(g)}},{H_{2(g)}}$ and $C{H_{4(g)}}$ are $- 94, - 68$ and $- 213kcal$. The value of $\Delta {H^ \circ }$ for the reaction ${C_{(g)}} + 2{H_{2(g)}} \to C{H_{4(g)}}$is:A.$- 85kcal$B.$- 111kcal$C.$- 17kcal$D.$- 170kcal$

Last updated date: 04th Aug 2024
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Answer
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Hint: Combustion is defined as the process in which element reacts with air and burns.
Heat of combustion: It is the energy released in the form of heat is light. Generally it is measured in calories.

Complete step by step answer:
Let us first read about combustion and heat of combustion.
Combustion is defined as the process in which element reacts with air and burns. Burning of mole of molecules is known as combustion.
Heat of combustion: It is the energy released in the form of heat is light. Generally it is measured in calories. The heat of combustion is measured as the heat released by the combustion of one mole of the substance or molecule.
Exothermic reaction: The reactions in which energy in the form of heat and light is released after the reaction, is known as exothermic reactions. In these reactions $Q$ (symbol of energy) is written on the product side. Although, a small amount of energy is required to start a reaction but in these reactions the given energy is greater than the released energy.
Endothermic reaction: The reactions in which the energy is required to start the reaction, are known as endothermic reactions. In these reactions $Q$ (symbol of energy) is written on the reactant side.
Here the combustion of ${C_{(g)}},{H_{2(g)}}$ and $C{H_{4(g)}}$ are $- 94, - 68$ and $- 213kcal$. So reactions are as follows:
$C + {O_2} \to C{O_2},\Delta {H^ \circ } = - 94kcal$
${H_2} + \dfrac{1}{2}{O_2} \to {H_2}O,\Delta {H^ \circ } = - 68kcal$
$C{H_4} + 2{O_2} \to C{O_2} + 2{H_2}O,\Delta {H^ \circ } = - 213kcal$
Now we want to calculate the heat of combustion of reaction i.e. ${C_{(g)}} + 2{H_{2(g)}} \to C{H_{4(g)}}$
So if we multiply combustion reaction of hydrogen by two and then add combustion of carbon and combustion of hydrogen then the reaction we will get is: $C + {H_2} + 2{O_2} \to 2{H_2}O + C{O_2}$ and heat of the reaction will be $\Delta {H^ \circ } = - 94 + ( - 2 \times 68) = - 230kcal$. Now to get the required equation we have to subtract the combustion of methane reaction from the equation we get by adding combustion of carbon and combustion of hydrogen then the reaction. The reaction we get will be as: $C{H_4} + 2{O_2} \to C{O_2} + 2{H_2}O$ and $\Delta {H^ \circ } = - 230 - ( - 213)kcal = - 17kcal$.

So option C is the correct option.

Note:
Lattice energy: It is defined as the energy required to separate one mole of ionic solid into gaseous ions. The value of lattice energy is positive quantity.
Formation energy: It is defined as the energy required or released to generate molecules from the given set of molecules or ions. It has negative value but equal to the value of lattice energy.