Converting grams to moles (and back): 3 worked examples

To find the number of moles ($n$) in a given mass ($m$) of a substance, we use the formula:
$n = \frac{m}{M}$
where $M$ is the molar mass of the substance.
Given:
Mass ($m$) = $36.0\text{ g}$
Molar mass ($M$) = $18.02\text{ g/mol}$

Substitute the values into the formula:
$n = \frac{36.0\text{ g}}{18.02\text{ g/mol}}$
$n \approx 1.99777...\text{ mol}$

Rounding to three significant figures (matching the precision of the given mass), we get:
$n \approx 2.00\text{ mol}$

To find the number of moles in a substance, we use the formula:
$n = \frac{m}{M}$
where $n$ is the number of moles, $m$ is the mass of the substance in grams, and $M$ is the molar mass of the substance in grams per mole.

Given:
Mass ($m$) = $11.0$ g
Molar mass ($M$) = $44.01$ g/mol

Substitute these values into the formula:
$n = \frac{11.0 \text{ g}}{44.01 \text{ g/mol}}$

$n \approx 0.249943$ mol

Rounding to three significant figures (matching the precision of the given $11.0$ g), we get $0.250$ mol.

To find the mass of a substance when the number of moles and the molar mass are known, we use the formula:
$\text{mass} = \text{moles} \times \text{molar mass}$

Given:
$\text{moles} = 0.750 \text{ mol}$
$\text{molar mass} = 58.44 \text{ g/mol}$

Substitute the values into the formula:
$\text{mass} = 0.750 \text{ mol} \times 58.44 \text{ g/mol}$
$\text{mass} = 43.83 \text{ g}$