Question

Enthalpy of combustion of carbon to $C{O_2}$ is $ - 393.5\;kJ$ per mole. Calculate the heat released upon formation of $35.2g\;C{O_2}$ from carbon and dioxygen gas.

Answer 1

Hint: We know that the enthalpy of combustion of carbon also represents the enthalpy of formation of carbon dioxide. For the given question, first find the number of moles of carbon dioxide corresponding to the given mass and then estimate the value of heat released with the help of given enthalpy of formation of $C{O_2}$ for one mole.

Complete answer:
Enthalpy of combustion: It is defined as the change in enthalpy when one mole of a covalent compound is completely burnt in the presence of dioxygen gas to form respective products in the gaseous phase.
Reaction for combustion of carbon to $C{O_2}$ will be as follows:
$C(s) + {O_2}(g) \to C{O_2}(g)\;\;\;\;\;\Delta H = - 393.5kJmo{l^{ - 1}}$
Enthalpy of formation: It is the amount of heat released or absorbed when exactly one mole of a compound is formed from its elements in their most stable state. The reaction for formation of carbon dioxide can be represented as follows:
$C(s) + {O_2}(g) \to C{O_2}(g)$
Thus, we can conclude that the enthalpy of formation of one mole of carbon dioxide is $ - 393.5kJmo{l^{ - 1}}$.
Now, the given mass of carbon dioxide $ = 35.2g$
Molar mass of $C{O_2} = 44g$
Number of moles corresponding to the given mass of $C{O_2} = \dfrac{{{\text{given mass}}}}{{{\text{molar mass}}}}$
$ \Rightarrow n = \dfrac{{35.2}}{{44}}$
$ \Rightarrow n = 0.8\;{\text{moles}}$
As per given data, the heat released on the formation of $1$ mole of $C{O_2} = - 393.5kJmo{l^{ - 1}}$
Therefore, the amount of heat released on the formation of $0.8$ moles of $C{O_2} = 0.8 \times ( - 393.5)$
$ \Rightarrow - 314.8kJmo{l^{ - 1}}$
Hence, the heat released upon formation of $35.2g\;C{O_2}$ from carbon and dioxygen gas is $ - 314.8kJmo{l^{ - 1}}$.

Note:
Remember that the value of enthalpy of formation and enthalpy of combustion can be same only in the case when one mole of reactant burns to form one mole of the product. The negative sign in the enthalpy indicates the heat is released i.e the reaction is exothermic in nature.