Mass to moles relationship

Linking a measurable mass to an amount of particles

Individual atoms, molecules and formula units are far too small to count directly in an ordinary laboratory. Chemists therefore count them in moles. Every mole contains the same number of specified particles, but one mole of different substances can have a different mass because their particles have different masses.

The chemical formula provides the link. Add the relative atomic masses, $A_r$, of all the atoms in the formula to obtain the relative formula mass, $M_r$. For example, using $A_r(\mathrm{C})=12$ and $A_r(\mathrm{H})=1$:

$M_r(\mathrm{C_2H_4})=(2\times12)+(4\times1)=28$

$M_r$ is a relative value and has no unit. However, one mole of ethene has a mass of $28\text{ g}$. More generally, the mass of one mole in grams is numerically equal to the substance's relative formula mass.

Finding the number of moles from a mass

The required relationship is

$n=\frac{m}{M_r}$

where $n$ is the amount in moles, $m$ is the mass in grams and $M_r$ is the relative formula mass.

This division asks, in effect, “How many one-mole masses fit into the mass of this sample?” A $1.4\text{ kg}$ sample of ethene must first be converted to $1400\text{ g}$. Since $M_r(\mathrm{C_2H_4})=28$:

$n=\frac{1400}{28}=50\text{ mol}$

For a fixed substance, $M_r$ does not change. The number of moles is therefore directly proportional to mass: doubling the mass doubles the amount in moles.

A reliable method is to:

1. identify the formula of the substance;
2. calculate its $M_r$ from the periodic table;
3. convert the given mass to grams if necessary;
4. divide the mass by $M_r$;
5. give the answer in mol.

For a single element, the same calculation uses its relative atomic mass, $A_r$. For molecular elements such as $\mathrm{O_2}$, use the mass of the whole molecule, so $M_r(\mathrm{O_2})=2\times16=32$.

Finding mass from a number of moles

The relationship also works in reverse. Rearranging it gives

$m=nM_r$

To find a mass, multiply the number of moles by the relative formula mass. Carbon monoxide has

$M_r(\mathrm{CO})=12+16=28$

so $3\text{ mol}$ of carbon monoxide has a mass

$m=3\times28=84\text{ g}$

This shows the central connection: $M_r$ tells you the mass in grams corresponding to one mole, allowing conversion in either direction between a laboratory measurement of mass and an amount of substance.

Using the mass of the correct substance

Sometimes the mass given is not entirely the substance being considered. If a sample is a mixture or is impure, first determine the mass of the required substance. For instance, a $9\text{ g}$ object that is $60\%$ gold contains $5.4\text{ g}$ of gold. That gold mass—not the full $9\text{ g}$—is then divided by $A_r(\mathrm{Au})$ to find the amount of gold.

Always keep the chemical identity attached to each value. The same mass of two substances usually represents different numbers of moles because their relative formula masses differ.

Core relationship

$n=\frac{m}{M_r}$

• $$: amount in mol