AS Chemistry 9701: Relative Atomic Mass from Mass Spectrometry Data

A newly isolated element is given the temporary label Q while it is investigated. A sample of Q is analysed in a mass spectrometer. The mass spectrum contains three peaks, at $m/z = 24$ , $m/z = 25$ and $m/z = 26$ , with relative peak heights of $20.0$ , $2.0$ and $3.0$ units respectively. No other isotopes of Q are present in a measurable amount.

(a) Calculate the percentage abundance of each of the three isotopes of Q. [2]

(b) Calculate the relative atomic mass, $A_r$ , of this sample of Q, giving your answer to three significant figures. [2]

(c) Explain why all three isotopes of Q react identically with a given reagent, yet a sample enriched in the $m/z = 26$ isotope would have a measurably higher density than a sample enriched in the $m/z = 24$ isotope. [2]

Part (a): Percentage abundance from peak heights

The percentage abundance of each isotope is its peak height as a fraction of the total of all the peak heights, not the number of peaks.

Total peak height: $20.0 + 2.0 + 3.0 = 25.0$

Percentage abundance of each isotope: $\%(m/z=24) = \frac{20.0}{25.0}\times 100 = 80.0\%$ $\%(m/z=25) = \frac{2.0}{25.0}\times 100 = 8.0\%$ $\%(m/z=26) = \frac{3.0}{25.0}\times 100 = 12.0\%$

Check: $80.0 + 8.0 + 12.0 = 100.0\%$ . ✓

Part (b): Relative atomic mass

Relative atomic mass is a weighted mean, found by multiplying each isotope’s mass number by its percentage abundance, summing these, and dividing by 100:

$A_r = \frac{(24\times 80.0) + (25\times 8.0) + (26\times 12.0)}{100}$

$A_r = \frac{1920 + 200 + 312}{100} = \frac{2432}{100} = 24.32$

To three significant figures: $A_r = 24.3$

Part (c): Same chemistry, different physical properties

All three isotopes of Q have the same number of protons and the same number of electrons, so they have identical electron configurations. Chemical reactivity is governed almost entirely by electron arrangement (particularly the outer-shell electrons), so all three isotopes undergo exactly the same reactions with a given reagent, at the same rate under the same conditions.

However, the isotopes have different numbers of neutrons, so they have different masses (mass numbers 24, 25 and 26). Physical properties that depend on mass (such as density, rate of diffusion, or precise melting/boiling point) differ slightly between isotopes. A sample enriched in the heavier $m/z=26$ isotope packs more mass into the same number of atoms (and essentially the same atomic volume, since nuclear charge and electron arrangement are unchanged), so it has a measurably higher density than a sample enriched in the lighter $m/z=24$ isotope.

Final answers

(a) $80.0\%$ ( $m/z=24$ ), $8.0\%$ ( $m/z=25$ ), $12.0\%$ ( $m/z=26$ )
(b) $A_r = \boxed{24.3}$
(c) Identical proton/electron arrangement $\Rightarrow$ identical chemistry; different neutron number $\Rightarrow$ different mass $\Rightarrow$ different density.