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## Definitions

Atomic mass = the mass of a single atom

• Example: The mass of one 12C atom

Molecular mass = the mass of a single molecule

• Example: The mass of one H2O molecule

Unit mass = the mass of a single unit

• Example: The mass of one unit of NaCl

## What does an atom weigh? Atomic mass

Very little!

A single 12C atom weighs 1.9926 × 10–23 g

Definition: A single 12C atom weighs exactly 12 u

$1\text{u} = 1\text{Da} = \frac {m_{^{12}\text{C}}}{12} \approx 1.6605 \times 10^{-24}\text{g}$

### What is the mass of a proton and a neutron?

A single 12C atom weighs 12u

The 12C atom consists of 6p+ and 6n

$m_{\text{p}^+} \approx m_{\text{n}} \approx 1\text{u}$

### The average mass of a carbon atom

98.89 % of all carbon is 12C

A single 12C atom weighs 12 u

• $$m_{^{12}\text{C}} = 12\text{u}$$

1.11 % of all carbon is 13C

A single 13C atom weighs 13.0034 u

• $$m_{^{13}\text{C}} = 13.0034\text{u}$$

Suppose we have 10,000 atoms.

• 98.89 % of them will be 12C atoms: 0.9889 × 10,000 = 9,889
• 1.11 % of them will be 13C atoms: 0.0111 × 10,000 = 111

The total mass of the atoms is:

$$m_{\text{tot}} = 9,889 × m_{^{12}\text{C}} + 111 × m_{^{13}\text{C}} =$$

$$= 9,889 × 12\text{u} + 111 × 13.0034\text{u} = 120,111.38\text{u}$$

Which gives us the average mass for a carbon atom:

$m_\text{C} = \frac {120,111.38\text{u}}{10,000} = 12.011138\text{u} \approx 12.01\text{u}$

Now, what does it say in the periodic table?

The atomic mass of carbon is 12.01u.

In the periodic table: The average masses are given for all the elements (and estimated masses are given for radioactive elements).

## Molecular mass

The average mass of a single molecule of some kind.

### Example: What is the molecular mass for hydrogen gas, H2?

Solution

• The atomic mass of hydrogen, H: $$m_\text{H} = 1.008\text{u}$$
• The atomic mass of hydrogen gas, H2: $$m_{\text{H}_2} = 1.008\text{u} \times 2 = 2.016\text{u}$$

### More examples

The molecular mass for H2O?

• $$m_{\text{H}_2\text{O}} = 1.008\text{u} \times 2 + 16.00\text{u} = 18.016\text{u} \approx 18.02\text{u}$$

The molecular mass for glucose, C6H12O6?

• $$m_{\text{C}_6\text{H}_{12}\text{O}_6} = 12.01\text{u} \times 6 + 1.008\text{u} \times 12 + 16.00\text{u} \times 6 = 180.156\text{u} \approx 180.2\text{u}$$

## Formula unit and unit mass

Ionic compounds aren’t molecules.

The formula unit for table salt is “NaCl” – one sodium ion + one chloride ion.

• Thus,we cannot talk about “a molecule of NaCl”, but rather “a formula unit of NaCl”.

The formula mass is the mass of one formula unit of an ionic compound.

Example: The formula mass for NaCl

• $$m_{\text{NaCl}} = 22.99\text{u} + 35.45\text{u} = 58.44\text{u}$$

Table salt, NaCl, doesn't exist as molecules of NaCl, but rather a crystal of alternating sodium ions (magenta) and chloride ions (green).

### Example: The formula mass for copper sulfate, CuSO4

Copper sulfate (cupric sulphate) consists of:

• One copper atom
• One sulfur atom
• Four oxygen atoms

Thus, $$m_{\text{CuSO}_4} = m_\text{Cu} + m_\text{S} + m_\text{O} \times 4 =$$

$$= 63.55\text{u} + 32.07\text{u} + 16.00\text{u} \times 4 = 159.62\text{u} \approx 159.6\text{u}$$

## Let’s use the molecular mass!

Calculate the percentage of oxygen in glucose, C6H12O6.

\begin{aligned}m_{\text{C}_6\text{H}_{12}\text{O}_6} &= 180.16\text{u} \\ m_{\text{O}_6} &= 16.00\text{u} \times 6 = 96.00\text{u} \\ \text{% oxygen} &= \frac {96.00\text{u}}{180.16\text{u}} = 0.53285968 \approx 53.29 \%\end{aligned}

## Let’s use the formula mass!

Calculate the mass of silver in 0.136g of silver chloride, AgCl.

### Solution

The proportion of silver in silver chloride:

$\frac {m_\text{Ag}}{m_\text{AgCl}} = \frac {107.9\text{u}}{(107.9 + 35.45)\text{u}} = 0.752703174$

The mass of silver in 0.136g silver chloride:

$0.752703174 \times 0.136\text{g} = 0.10236763\text{g} \approx 0.102\text{g}$

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