# Atomic Mass & Molecular Mass

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### Atomic Mass

Atomic mass is the mass of an atom. Different atom has different mass (because they have different number of neutrons, protons). The masses of the atoms are not measured directly. (You can’t put an atom on a mass balance to weigh it) Hence, we have to compare the atomic mass of an element with another element. (Hence, the name relative atomic mass)

• The mass of $\frac{1}{12}$ of one atom of carbon-12 was used as the standard. The mass of all the other elements are compared with the mass of $\frac{1}{12}$ of one atom of carbon.
• We take the mass of one atom of carbon to be 12 units $\rightarrow$ $\frac{1}{12}$ of one atom of carbon is 1 unit.

Recall that there are the existence of isotopes (different neutron number but same proton number). This will result in different mass for different isotopes of the same element. Hence, we will need to take the existence of the isotopes into account for the computation of the relative atomic mass. One example calculation will be shown below.

Definition: Relative atomic mass is the average mass of the atoms of the various isotopes of the element compared with one twelfth the mass of an atom of carbon-12.

The relative atomic mass is calculated using:

$$\text{Rel. Atomic Mass} = \frac{\text{Mass of 1 atom of element}}{\frac{1}{12} \, \text{mass of 1 atom of carbon} 12}$$

You can think of relative atomic mass from another angle: Relative atomic mass of an atom is the number of times the atom is heavier than one twelfth of a carbon-12 atom.

Calculating mass of 1 atom of element when the element has isotopes

Certain isotopes of an element is more abundant than others. Hence, we will have to take the abundance of the different isotopes into account for the calculation of relative atomic mass. Consider chlorine for the calculation. Chlorine has two isotopes – 75% is chlorine-35 and 25% is chlorine-37.

• The relative atomic mass of chlorine-35 and chlorine-37 is 35 and 37 units respectively.
• Relative atomic mass of chlorine will then be: \begin{aligned}(0.75 \times 35) + (0.25 \times 37) &= 26.25 + 9.25 \\ &= 35.5 \end{aligned}

### Relative Molecular Mass

The relative molecular mass ($\text{M}_{r}$) is the average mass of one molecule of the substance compared with one twelfth the mass of a carbon-12 atom.

$$\text{Rel. Mol. Mass} = \frac{\text{Mass of 1 molecule of sub.}}{\frac{1}{12} \, \text{mass of 1 atom of carbon} 12}$$

Example on how to calculate relative molecular mass from chemical formula

Consider the formula $\text{C}_{14}\text{H}_{9}\text{Cl}_{5}$.

• Contains 14 C and 1 C has a mass of 12 units. We have: $12 \times 14 = 168$
• Contains 9 H and 1 H has a mass of 1 unit. We have: $9 \times 1 = 9$
• Contains 5 Cl and 1 Cl has a mass of 35.5 units. We have: $35.5 \times 5 = 177.5$
• Hence, Relative molecular mass, \begin{aligned}\text{M}_{r} &= 168 + 9 + 177.5 \\ &= 354.5 \end{aligned} 