Question

The heat of combustion of carbon is $ - 393.5\;kJmo{l^{ - 1}}$. The heat released upon the formation of $35.2g$ of $C{O_2}$ from carbon and oxygen gas is:
(A) $ + 315\,kJ$
(B) $ - 31.5\;kJ$
(C) $ - 315\,kJ$
(D) $ + 31.5\;kJ$

Answer 1

Hint: As we know that heat of combustion or change in enthalpy of combustion is the amount of heat released when $1$ mole of compound undergoes complete combustion reaction in the presence of oxygen or we can say that the amount of heat required to form a compound upon burning its elements.

Complete Step by step answer: As we know that heat of combustion or change in enthalpy is that amount of heat which is released when $1$ mole of compound undergoes a complete combustion reaction in the presence of oxygen or we can say that change in enthalpy that takes place when $1$ mole of product is formed from its elements which are present in their standard state in the most stable allotropic form which we normally call the heat of formation.
We are given the heat of combustion of carbon, so let us first write the equation for combustion of carbon and oxygen to form carbon dioxide.
$C + {O_2} \to C{O_2}$, ${\Delta _f}H = - 393.5\;kJ\;mo{l^{ - 1}}$
The heat of formation of carbon or heat of formation of carbon dioxide is $ - 393.5\;kJmo{l^{ - 1}}$. We know that $1$ mole of carbon reacts with $1$ mole of oxygen to form $1$ mole of carbon dioxide or we can say that $22g$ of carbon dioxide reacts with $32g$of oxygen to form $44g$ of carbon dioxide.
So, heat of formation of $44g$ of carbon dioxide is ${\Delta _f}H = - 393.5\;kJ\;mo{l^{ - 1}}$now we can calculate the heat released upon formation of $35.2g$which will be:
${\Delta _f}H = \dfrac{{ - 393.5 \times 35.2}}{{44}}$
 $\Rightarrow {\Delta _f}H = - 315\;kJmo{l^{ - 1}}$

Therefore, the correct answer is (C).

Note: Combustion reactions mostly take place at high temperatures and the energy produced during such reactions is converted to heat or light energy which can be used to heat water, cook food, electricity generation and even can be used to provide the power to vehicles.