2.2. Atomic Mass, Molecular Mass, and Unit Mass

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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:

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