Relative Mass (VCE SSCE Chemistry): Revision Notes

Relative Mass

Introduction to relative mass in chemistry

Chemists working in diverse fields such as environmental monitoring, pharmaceuticals, and fuel production regularly perform chemical reactions. Being able to measure specific amounts of reactants quickly and accurately is crucial because the quantity of products formed depends on the amount of reactants used.

Individual atoms and molecules are far too small to be counted, even in groups of thousands or millions. Instead, chemists rely on knowledge of atomic and molecular masses to measure out the quantities they need for reactions.

The mass of a single atom is incredibly tiny. For example, one carbon atom has a mass of approximately $2 \times 10^{-23}$ g. A single glucose molecule, which contains 6 carbon atoms, 12 hydrogen atoms, and 6 oxygen atoms bonded together, has an actual mass of $3 \times 10^{-22}$ g. A teaspoon of glucose contains approximately $1.4 \times 10^{22}$ glucose molecules.

To overcome this problem, chemists use more convenient measures called relative masses to determine quantities in samples.

Understanding relative masses

In chemistry, we typically work with relative masses rather than actual masses. A relative mass is determined by comparison to a standard mass, making calculations more manageable.

The carbon-12 standard

The standard against which all relative masses in chemistry are compared is the common isotope of carbon, carbon-12 (represented as $^{12}$C). This isotope is assigned an exact mass value of 12 units. All other atomic and molecular masses are expressed relative to this standard.

Relative isotopic mass

Each individual isotope of an element has its own relative isotopic mass. This is defined as the mass of an atom of that isotope compared to the mass of a carbon-12 atom, which is taken as exactly 12 units.

Comparing isotopes to carbon-12

The table below shows how the masses of various isotopes compare to carbon-12:

Isotopes and their different masses

Recall that isotopes are atoms of the same element that contain different numbers of neutrons in their nucleus. They have the same atomic number but different mass numbers.

Chlorine provides a good example of isotopes. The element chlorine exists as two isotopes:

• $^{35}$Cl, which contains 17 protons and 18 neutrons
• $^{37}$Cl, which contains 17 protons and 20 neutrons

The isotopes have different masses because they contain different numbers of neutrons. Remember that an atom's mass is mainly determined by the number of protons and neutrons in the nucleus, since electrons have relatively insignificant mass.

Relative isotopic abundance

Naturally occurring chlorine consists of a mixture of the two isotopes shown above. Of all chlorine atoms that exist in nature, 75.80% are the lighter isotope ($^{35}$Cl) and 24.20% are the heavier isotope ($^{37}$Cl). This composition remains virtually the same regardless of the source of the chlorine sample.

The percentage of an isotope found in the natural environment is called its relative isotopic abundance. Most elements, like chlorine, exist as a mixture of two or more isotopes in nature.

Examples of isotopic composition

The table below shows the isotopic composition of some common elements:

Element	Isotopes	Relative isotopic mass	Relative isotopic abundance (%)
hydrogen	$^1$H	1.008	99.986
	$^2$H	2.014	0.014
	$^3$H	3.016	0.0001
oxygen	$^{16}$O	15.995	99.76
	$^{17}$O	16.999	0.04
	$^{18}$O	17.999	0.20
silver	$^{107}$Ag	106.9	51.8
	$^{109}$Ag	108.9	48.2

Notice that some isotopes are much more abundant than others. For example, hydrogen-1 makes up 99.986% of all naturally occurring hydrogen atoms, while silver's two isotopes are present in nearly equal amounts.

Mass spectrometry

The relative isotopic masses of elements and their isotopic abundances are determined using an instrument called a mass spectrometer, which was invented by Francis Aston in 1919.

How a mass spectrometer works

A mass spectrometer is a laboratory instrument used to:

• Detect different isotopes of an element
• Determine the relative mass of each isotope
• Measure the abundance of each isotope

Inside a mass spectrometer:

1. A sample of an element is introduced into an ionisation chamber
2. The sample is ionised (atoms are converted to ions by electron bombardment)
3. The ions are accelerated through charged plates that create an electric field
4. The ions pass through a magnetic field, which deflects them according to their mass-to-charge ratio
5. Ions with different masses are deflected by different amounts
6. A detector measures the ion current for each mass-to-charge ratio
7. The results are displayed as a mass spectrum

Applications of mass spectrometry

Mass spectrometry has many practical applications beyond simply identifying isotopes. Scientists can use this technique to determine the relative abundance of isotopes in tissues from living or once-living organisms, providing insights into the organism's life history.

Interpreting a mass spectrum

A mass spectrum is a graph that displays the results from a mass spectrometer. Understanding how to read this graph is essential for determining isotopic composition.

Mass spectrum of chlorine

The mass spectrum of chlorine shows two distinct peaks:

Relative atomic mass

Most elements consist of a mixture of isotopes, each with a different relative mass. For calculations, it is convenient to know the average relative mass of an atom in the mixture of isotopes.

Definition and formula

The average relative mass of an element is called the relative atomic mass, given the symbol $A_r$. The relative atomic mass of an element is the weighted average of the relative masses of the isotopes of the element on the $^{12}$C scale.

The formula for calculating relative atomic mass is:

$A_r = \frac{(\text{relative isotopic mass} \times \% \text{ abundance}) + (\text{relative isotopic mass} \times \% \text{ abundance})}{100}$

For elements with more than two isotopes, additional terms are added to the numerator following the same pattern.

Why use a weighted average?

Calculating relative atomic mass

To calculate the relative atomic mass from isotopic data, you need to consider both the mass and abundance of each isotope.

Most periodic tables include the relative atomic mass of each element, calculated by taking into account the relative abundances of all natural isotopes.

Practice calculation: boron

Boron has two isotopes with the following data:

Isotope	Relative isotopic mass	Relative abundance (%)
$^{10}$B	10.013	19.91
$^{11}$B	11.009	80.09

Calculating percentage abundances

Sometimes you know the relative atomic mass and the relative isotopic masses, but need to find the percentage abundances of the isotopes. This requires solving an algebraic equation.

Using significant figures in calculations

When performing calculations involving relative masses, remember that the accuracy of your answer is limited by the least accurate piece of information used.