Question

The heat of formation of $C{O_2}$ is $ - 96\;K\;cal$. The amount of carbon which on burning will evolve $1000\;KCal$ is:
(A) $12.63g$
(B) $17.95g$
(C) $125.0g$
(D) $1.263g$

Answer 1

Hint: As we know that the heat of formation is the change in enthalpy that takes place when one mole of product is formed from its element which are present in their standard state in its most stable allotropic form. And the amount of any substance is given by the product of its moles and molecular mass.

Complete step-by-step solution:As we already discussed that the heat of formation or enthalpy of formation is that amount of heat which is released when a product is formed from its elements. Similarly, we know that the carbon dioxide in gaseous state is formed when carbon in solid form reacts with oxygen in gaseous form. We can show this with the help of a chemical equation as given below:
$C(s) + {O_2}(g) \to C{O_2}(g)\;\;\Delta {H_f} = - 96\;Kcal$
Now, we are given that the amount of heat evolved while burning carbon is $ - 1000\;KCal$.
Thus, we can say that the moles of carbon which is burnt will be given as the ratio of amount of heat evolved during burning of carbon to the enthalpy of formation of carbon dioxide. After solving we will get:
$moles = \dfrac{{\Delta H}}{{\Delta {H_f}}} = \dfrac{{ - 1000}}{{ - 96}}mol$
$moles = \dfrac{{125}}{{12}}mol$
Now we can calculate the mass of the carbon which will be evolved on burning of $1000\;KCal$. We know that the moles of any substance are given as the ratio of the mass of substance to the molecular mass of that particular substance.
Thus, the mass of the carbon will be:
$moles = \dfrac{{mass}}{{molecular\;mass}}$
$\Rightarrow mass = moles \times molecular\;mass$
$\Rightarrow mass = \dfrac{{125}}{{12}} \times 12$
$\therefore mass = 125.0g$

Therefore, the correct answer is (C).

Note:Always remember that the number of moles is given by the ratio of the mass of a particular substance to the molecular or atomic mass of that substance and enthalpy of formation of any product is given when the elements of that product are burnt in their elemental form.