Calculating Moles and Mass
An equation to calculate moles and mass
We can calculate molar mass as follows: \(\text{molar mass } (M) = \frac{\text{ mass (g)}}{\text{mole (mol)}}\)
This can be rearranged to give the number of moles:
\[n = \frac{n}{M}\]
The following diagram may help to remember the relationship between these three variables. You need to imagine that the horizontal line is like a division sign and that the vertical line is like a multiplication sign. So, for example, if you want to calculate \(M\), then the remaining two letters in the triangle are \(m\) and \(n\) and \(m\) is above \(n\) with a division sign between them. Your calculation will then be \(M = \frac{m}{n}\)
Tip:
Remember that when you use the equation \(n=\frac{m}{M}\), the mass is always in grams (g) and molar mass is in grams per mol (\(\text{g·mol$^{-1}$}\)). Always write the units next to any number you use in a formula or sum.
Example:
Question
Calculate the number of moles of copper there are in a sample that with a mass of \(\text{127}\) \(\text{g}\).
Step 1: Write down the equation
\[n = \frac{m}{M}\]Step 2: Find the moles
\begin{align*} n & = \frac{\text{127}\text{ g}}{\text{63.5}\text{ g·mol$^{-1}$}} \\ & = \text{2}\text{ mol} \end{align*}There are 2 moles of copper in the sample.
Example:
Question
Calculate the number of atoms there are in a sample of aluminium that with a mass of \(\text{81}\) \(\text{g}\).
Step 1: Find the number of moles
\begin{align*} n & = \frac{m}{M} \\ & = \frac{\text{81}\text{ g}}{\text{27.0}\text{ g·mol$^{-1}$}} \\ & = \text{3}\text{ mol} \end{align*}Step 2: Find the number of atoms
Number of atoms in \(\text{3}\) \(\text{mol}\) aluminium \(= 3 \times \text{6.022} \times \text{10}^{\text{23}}\)
There are \(\text{1.8069} \times \text{10}^{\text{24}}\) aluminium atoms in a sample of \(\text{81}\) \(\text{g}\).
This lesson is part of:
Quantitative Aspects of Chemical Change