Question

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

Answer 1

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.