AQA A-Level Chemistry

Particles in the atom

An atom has a small, dense nucleus made of protons and neutrons, with electrons in the space around it. The model has changed over time: Dalton pictured solid indivisible spheres, Thomson found electrons and described a positive sphere with electrons embedded in it, Rutherford's scattering experiment showed that the positive charge and nearly all the mass sit in a tiny nucleus, and Bohr and later quantum models placed the electrons in shells and orbitals of fixed energy.

The atomic (proton) number, $Z$, is the number of protons in the nucleus and fixes which element it is. The mass number, $A$, is the number of protons plus neutrons. An atom is neutral, so it has as many electrons as protons; an ion has gained or lost electrons.

Counting particles

For an ion of element X with mass number $A$, atomic number $Z$ and charge $n$:

• protons $= Z$
• neutrons $= A - Z$
• electrons $= Z - n$ for a positive ion of charge $n+$, and $Z + n$ for a negative ion of charge $n-$

For $\ce{^{27}Al^{3+}}$ (atomic number 13) there are 13 protons, 14 neutrons and $13 - 3 = 10$ electrons. For $\ce{^{32}S^{2-}}$ (atomic number 16) there are 16 protons, 16 neutrons and 18 electrons.

Isotopes

Isotopes are atoms of the same element with the same number of protons but different numbers of neutrons, so they have different mass numbers. Their chemical properties are the same, because chemical behaviour is governed by the electrons and so by the proton number. Physical properties that depend on mass, such as density and the rate of diffusion, differ slightly.

Chlorine has two common isotopes, $\ce{^{35}Cl}$ (18 neutrons) and $\ce{^{37}Cl}$ (20 neutrons). Both have 17 protons and 17 electrons in the neutral atom.

Relative masses

The relative isotopic mass is the mass of an atom of an isotope compared with one twelfth of the mass of an atom of carbon-12. The relative atomic mass, $A_r$, is the weighted mean mass of an atom of an element compared with one twelfth of the mass of an atom of carbon-12, where the mean is taken over the naturally occurring isotopes. The relative molecular mass, $M_r$, is the mean mass of a molecule compared with one twelfth of the mass of an atom of carbon-12. For ionic compounds the term relative formula mass is used, because there are no separate molecules. All three are ratios, so they have no units.

Relative atomic mass from isotopic abundance

The abundances can be percentages or relative intensities from a mass spectrum, because the denominator divides out the total.

A sample of magnesium contains 78.6% $\ce{^{24}Mg}$, 10.1% $\ce{^{25}Mg}$ and 11.3% $\ce{^{26}Mg}$.

The answer is given to three significant figures, matching the data. It lies close to 24 because the lightest isotope is by far the most abundant.

A common exercise runs the other way. Boron has two isotopes, $\ce{^{10}B}$ and $\ce{^{11}B}$, and $A_r = 10.81$. If the abundance of $\ce{^{10}B}$ is $x$ per cent then

so boron is 19% $\ce{^{10}B}$ and 81% $\ce{^{11}B}$.

Time of flight mass spectrometry

A mass spectrometer measures the mass-to-charge ratio, $m/z$, of ions and the relative amount of each. In a time of flight (TOF) instrument the stages are:

1. Ionisation: The sample is vaporised and ionised, either by electron impact (a beam of high-energy electrons knocks an electron off each atom or molecule, giving $\ce{X+}$) or by electrospray (the sample is dissolved and sprayed through a needle at high voltage, so each molecule picks up a proton and becomes $\ce{XH+}$).
2. Acceleration: The positive ions are accelerated by an electric field so that every ion has the same kinetic energy.
3. Ion drift: The ions pass through a flight tube with no field. Because the kinetic energy $\frac{1}{2}mv^2$ is the same for all ions, lighter ions travel faster and reach the detector sooner.
4. Detection: The ions hit a detector, which records the time of arrival and produces a current proportional to the number of ions arriving.
5. Data analysis: A computer converts the flight times into $m/z$ values and plots a mass spectrum, in which the height of each peak shows the relative abundance of that ion.

The flight time $t$ over a distance $d$ comes from $v = d/t$ and $\text{KE} = \frac{1}{2}mv^2$, giving $t^2 = \frac{m d^2}{2\,\text{KE}}$, so $t$ increases with the square root of the mass. The instrument must be under a vacuum so that the ions do not collide with air molecules.

Reading a spectrum

For an element, each peak is an isotope with a charge of 1+, so the $m/z$ value is the relative isotopic mass and the peak height gives the abundance. The spectrum of an element can therefore be used to work out its $A_r$ with the weighted mean above, and the pattern of peaks helps to identify the element.

Chlorine gas, $\ce{Cl2}$, gives more peaks than the atoms alone. The molecular ions are $\ce{^{35}Cl-^{35}Cl+}$ at 70, $\ce{^{35}Cl-^{37}Cl+}$ at 72 and $\ce{^{37}Cl-^{37}Cl+}$ at 74, alongside atomic ions at 35 and 37.

For a compound, the peak at the highest $m/z$ is the molecular ion peak, and its $m/z$ equals the relative molecular mass $M_r$ of the compound. Fragmentation peaks at lower values are dealt with in the note on organic analysis.