Identifying an element from ionisation energies and a mass spectrum
An unknown element X is investigated in two ways. A mass spectrum shows three peaks at m/z 24, 25 and 26 with relative abundances 79.0%, 10.0% and 11.0%. A separate experiment measures successive ionisation energies of X in kJ mol−1: 738, 1451, 7733, 10540, 13630, 18020, 21710, 25660, 31630, 35460, 169988 and 189368. The sample is a silvery metal that burns in oxygen with a brilliant white flame, and the oxide formed is used in refractory linings. A student claims the large jump in ionisation energy proves X is in Group 2, but another student argues the jump only shows that two electrons are removed from the same shell. The periodic table gives the relative atomic mass of X as 24.31. The teacher asks you to use both sets of data, not just the periodic table position, to decide the identity and bonding of X and its oxide.
1. Calculate the relative atomic mass of X from the mass spectrum and use it, together with the ionisation-energy pattern, to identify X. Show your working.
Read the worked answer
Relative atomic mass from the mass spectrum
Use the weighted mean of the isotope masses:
Ar = (24 × 0.790) + (25 × 0.100) + (26 × 0.110) Ar = 18.96 + 2.50 + 2.86 = 24.32
This agrees with the periodic-table value of 24.31 to within rounding.
Ionisation-energy pattern
The first two ionisation energies are relatively low and close together (738 and 1451 kJ mol−1). The third is 7733 kJ mol−1, about five times larger than the second. This shows that the first two electrons are removed from the same outer shell, while the third is removed from a much less shielded inner shell. Therefore X has two valence electrons and is in Group 2.
Combining the evidence
Group 2, Ar ≈ 24.3 and three stable isotopes at m/z 24, 25 and 26 together identify X as magnesium, Z = 12. The mass spectrum alone gives the atomic mass but not the group; the ionisation energies alone give the group but not the identity. Both are needed.
2. Explain why the third ionisation energy of X is much larger than the second, and why X forms an ionic oxide with formula XO rather than X2O3.
Read the worked answer
The second electron is removed from the outer 3s shell. This electron is relatively far from the nucleus and is shielded by the inner shells, so the effective nuclear charge attracting it is moderate. The third electron must be removed from the n = 2 shell, which is much closer to the nucleus and much less shielded. The electrostatic attraction is therefore far stronger, so the third ionisation energy is much larger.
Magnesium has the configuration 1s2 2s2 2p6 3s2. Losing two electrons gives the stable Mg2+ ion with the neon configuration. Forming Mg3+ would mean removing an electron from the stable n = 2 core, which requires an energy far beyond that available in normal ionic compound formation. Oxygen accepts two electrons to give O2−. The charges balance in a 1:1 ratio, so the oxide is MgO, not Mg2O3. An X2O3 formula would require X3+ ions, which is inconsistent with the very high third ionisation energy.
3. The oxide of X has a melting point of 2852 °C and conducts electricity only when molten. Explain these observations in terms of structure and bonding, and state one industrial consequence of the high melting point given in the setup.
Read the worked answer
The oxide is a giant ionic lattice of Mg2+ and O2− ions. Each ion is surrounded by ions of opposite charge, and the lattice is held together by strong electrostatic attractions in all directions. Melting requires enough energy to overcome these attractions throughout the lattice, so the melting point is very high.
In the solid state, the ions are fixed in their lattice positions and cannot move, so there are no mobile charge carriers and the solid does not conduct electricity. When molten, the lattice breaks down and the ions become mobile. These mobile ions can carry current, so the molten oxide conducts.
One industrial consequence is that the oxide can be used as a refractory lining in furnaces: it retains its structure at very high temperatures and does not conduct electricity while solid, which is useful in applications where electrical insulation is also required.