Chemistry » Quantitative Aspects of Chemical Change » Atomic Mass And The Mole

# Molar Mass

## Molar Mass

### Definition: Molar mass

Molar mass ($$M$$) is the mass of 1 mole of a chemical substance. The unit for molar mass is grams per mole or $$\text{g·mol^{-1}}$$.

You will remember that when the mass, in grams, of an element is equal to its relative atomic mass, the sample contains one mole of that element. This mass is called the molar mass of that element.

#### Fact:

You may sometimes see the molar mass written as $$M_{m}$$. We will use $$M$$ in this book, but you should be aware of the alternate notation.

It is worth remembering the following: On the periodic table, the relative atomic mass that is shown can be interpreted in two ways.

1. The mass (in grams) of a single, average atom of that element relative to the mass of an atom of carbon.

2. The average atomic mass of all the isotopes of that element. This use is the relative atomic mass.

3. The mass of one mole of the element. This third use is the molar mass of the element.

 Element Relative atomic mass (u) Molar mass ($$\text{g·mol^{-1}}$$) Mass of one mole of the element (g) Magnesium $$\text{24.3}$$ $$\text{24.3}$$ $$\text{24.3}$$ Lithium $$\text{6.94}$$ $$\text{6.94}$$ $$\text{6.94}$$ Oxygen $$\text{16.0}$$ $$\text{16.0}$$ $$\text{16.0}$$ Nitrogen $$\text{14.0}$$ $$\text{14.0}$$ $$\text{14.0}$$ Iron $$\text{55.8}$$ $$\text{55.8}$$ $$\text{55.8}$$

Table: The relationship between relative atomic mass, molar mass and the mass of one mole for a number of elements.

## Example:

### Question

Calculate the number of moles of iron (Fe) in an $$\text{11.7}$$ $$\text{g}$$ sample.

### Step 1: Find the molar mass of iron

If we look at the periodic table, we see that the molar mass of iron is $$\text{55.8}$$ $$\text{g·mol^{-1}}$$. This means that 1 mole of iron will have a mass of $$\text{55.8}$$ $$\text{g}$$.

### Step 2: Find the mass of iron

If 1 mole of iron has a mass of $$\text{55.8}$$ $$\text{g}$$, then: the number of moles of iron in $$\text{111.7}$$ $$\text{g}$$ must be:

\begin{align*} n & = \frac{\text{111.7}\text{ g}}{\text{55.8}\text{ g·mol$^{-1}$}} \\ & = \frac{\text{111.7}\text{ g·mol}}{\text{55.8}\text{ g}} \\ & = \text{2}\text{ mol} \end{align*}

There are 2 moles of iron in the sample.

## Example:

### Question

You have a sample that contains 5 moles of zinc.

1. What is the mass of the zinc in the sample?

2. How many atoms of zinc are in the sample?

### Step 1: Find the molar mass of zinc

Molar mass of zinc is $$\text{65.4}$$ $$\text{g·mol^{-1}}$$, meaning that 1 mole of zinc has a mass of $$\text{65.4}$$ $$\text{g}$$.

### Step 2: Find the mass

If 1 mole of zinc has a mass of $$\text{65.4}$$ $$\text{g}$$, then 5 moles of zinc has a mass of: $$\text{65.4}\text{ g} \times \text{5}\text{ mol} = \text{327}\text{ g}$$ (answer to a)

### Step 3: Find the number of atoms

$$\text{5}\text{ mol} \times \text{6.022} \times \text{10}^{\text{23}}\text{ atoms·mol^{-1}} = \text{3.011} \times \text{10}^{\text{23}}\text{ atoms}$$ (answer to b)