Question

When hydrogen is burnt in chlorine $2000$cals of heat is liberated during the formation of $3.65\,{\text{g}}$ of HCl, ${{\Delta H}}$ of formation of HCl is
A. $2$Kcal
B. $ - 20$Kcal
C. $ + 20$Kcal
D. $ - 2$Kcal

Answer 1

Hint: Enthalpy of formation is the heat change when one mole of substance forms from its constituting elements at the given temperature and pressure. We will determine the number of moles of HCl. Then by comparing the heat change for the given moles with one mole we can calculate the enthalpy of formation of HCl.

Complete step-by-step solution :One mole of hydrogen chloride forms from hydrogen gas and chlorine gas.

The formation of HCl is shown as follows:

${{\text{H}}_{\text{2}}}{\text{(g)}}\,{\text{ + }}\,{\text{C}}{{\text{l}}_{\text{2}}}{\text{(g)}}\, \to \,{\text{HCl(g)}}$

We will use the mole formula to determine the number of moles of hydrogen chloride as follows:
${\text {mole}}\, {\text {=}}\, \dfrac{{{\text{mass}}}}{{{\text{molar}}\,{\text{mass}}}}$
The molar mass of hydrogen chloride is $36.5$ g/mol.
We will substitute $36.5$ g/mol for molar mass and $3.65\,{\text{g}}$for mass.
${\text {mole}}\, {\text {=}}\, \dfrac{{3.65}}{{{\text{36}}{\text{.5}}}}$
${\text {mole}}\, {\text {= 0}} {\text{.1}}$
So, by the formation of $0.1$ mole of hydrogen chloride $2000$ cals of heat is liberated so, by the formation of one mole of hydrogen the amount of heat liberated will be,
Heat is liberated so the sign will be negative.
$0.1$mole = $ - 2000$cals
$1$mole = $ - 20000$cals
We will convert the heat liberated from cals to kilocals as follows:
${\text {1000}}\, {\text{cal}}\, {\text {=}}\, {\text{1}}\, {\text{K}}{\text{.cal}}$
$\Rightarrow - \, {\text{20000}}\, {\text{cal}}\, {\text {=}}\, \, - \,{\text{20}}\,{\text{K}}{\text{.cal}}$
So, $\therefore { {\Delta H}} $ of formation of HCl is$ - \,{\text{20}}\,{\text{K}}{\text{cal}}$.

Therefore, option (B) $ - 20$Kcal, is correct.

Note:Standard enthalpy of formation is the heat change when one mole of substance forms in its standard state from its constituting elements at the standard temperature and pressure. Standard enthalpy of formation is measured in kJ/mol or K.cal/mol. Hydrogen and chlorine is found in a gaseous state, so, there is no change in enthalpy during the formation of gaseous hydrogen and chlorine. Standard enthalpy of formation is also different in different phases. The standard enthalpy of formation is zero for an element in its natural state.