Question

The heat of combustion of carbon is $C{O_{2(g)}}$ is -393.5KJ/mol. The heat released upon formation of 35.2 g of $C{O_{2(g)}}$ from carbon and oxygen gas is:
A. -630 KJ
B. -3.15 KJ
C. -315 KJ
D. +315 KJ

Answer 1

Hint: We know that heat of formation of elements in their standard states is zero. A chemical reaction involves a lot of enthalpy changes such as in exothermic reaction enthalpy change has a negative sign whereas endothermic reaction has an enthalpy change of positive sign.

Complete step by step answer:
Heat of combustion is the enthalpy change when one mole of a substance is burnt in oxygen whereas heat of formation is the enthalpy change when one mole of a given compound is formed from its elements. In this case we know that carbon dioxide is formed from carbon and oxygen.
Let us write the balanced equation to the reaction occurring above,
${C_{(s)}} + {O_{2(g)}} \to C{O_{2(g)}}$
Hence from the above equation we understand that one mole of carbon and oxygen is burnt to form one mole of carbon dioxide. We are given the heat of combustion of carbon as -393.5KJ/mol. From Avogadro’s law it is known that equal volumes of all gases contain equal numbers of molecules under similar conditions. Now since one mole of molecules of all gases contain the same number (6.022$ \times {10^{23}}$ ) of molecules, therefore they occupy the same volume under similar pressure and temperature. The mass of one mole of atoms is exactly equal to the atomic mass in grams of that element. Therefore we can say that 44g which is the molecular mass of carbon dioxide and is also one mole of carbon dioxide has the heat of formation as -393.5 KJ/mol. Therefore,
\[\Delta {{\rm H}_f}(44gC{O_2}) = - 393.5KJ/mol\]
\[\Delta {{\rm H}_f}(35.2gC{O_2}) = \dfrac{{ - 393.5 \times 35.2}}{{44}} = - 315KJ/mol\]

Hence the correct option is C.

Note: Thermochemistry deals with the transfer of heat between a chemical system and its surroundings when a change of phase or chemical reaction takes place within the system.