Question

How do you convert $\text{kJ/g}$ to $\text{kJ/mol}$?

Answer 1

Hint: For the conversion of unit of energy from kilojoules per gram ($\text{kJ/g}$) to kilojoules per moles ($\text{kJ/mol}$), we have to know about the molecular formula of the specie which is present in the given system to calculate the molecular weight of that species.

Complete step by step solution:
For the conversion of any species from grams to mole we have to know about the molecular weight of that species because the quantities moles ($\text{mol}$) and grams ($\text{g}$) related to each other in the following manner:
     $$\text{n = }\frac{\text{W}}{\text{M}}$$
Where, $\text{n}$ = moles of species (in $\text{mol}$)
$\text{W}$= Given weight of the species in grams ($\text{g}$)
$\text{M}$ = Molecular or molar mass of the given species in grams per mole ($\text{g/mol}$)
Whenever we have to convert any quantity from the $\text{kJ/g}$ unit to $\text{kJ/mol}$ unit, first we will convert the quantity from grams to moles, by dividing the given mass of that species by molecular mass.
For example: When$\text{1g}$of $\text{NaCl}$ undergoes combustion, $\text{5kJ/g}$ of heat are being given off. Then in this condition for the conversion of value of heat from kilojoules per gram ($\text{kJ/g}$) to kilojoules per mole ($\text{kJ/mol}$), we will multiple the value of heat to the molecular mass of Sodium chloride ($\text{NaCl}$) as follow:
Molecular mass of $\text{NaCl}$ = $\text{23 + 35 = 58g/mol}$
$\text{5}\frac{\text{kJ}}{\text{g}}\text{ times 58}\frac{\text{g}}{\text{mol}}\text{ = 290}\frac{\text{kJ}}{\text{mol}}$
So we get $290$ kilojoules per mole ($\text{kJ/mol}$).

Note: Here some of you may think that how the unit converts into mole by multiplying given heat to molar mass, so the reason is that grams from numerical & denominator gets canceled and only moles will remain.