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Mass spectrometry 

​​In a nutshell

The mass spectrometer is an instrument used when determining the relative atomic mass of elements. It identifies the atomic mass of the isotopes of an element and their relative abundance. This data can be used to determine the relative atomic mass. Below are the equations that you will use need to calculate atomic and molecular masses from mass spectra.​

Equations

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What is a mass spectrometer?  

The mass spectrometer is an instrument that is used to determine relative atomic mass ($$A_r$$​). The basic principle of a mass spectrometer is generating ions from a sample and separating these according to the atomic mass of the isotopes. 

The relative atomic masses are determined using a scale where  $$^{12}$$​Carbon ($$^{12}C$$​) is defined as exactly ​$$12$$. It is the only element which has an isotope with an exact whole number. The equations for relative atomic mass ($$A_r$$) and relative molecular mass ($$M_r$$​) are compared to the mass of one atom of $$^{12}C$$.    

$$A_r = \frac{average\thickspace mass \thickspace of \thickspace one \thickspace atom}{\frac{1}{12} \ mass \thickspace of \thickspace one \thickspace atom \thickspace of \thickspace ^{12}C}$$

$$M_r = \frac{average\thickspace mass \thickspace of \thickspace molecule}{\frac{1}{12} \ mass \thickspace of \thickspace one \thickspace atom \thickspace of \thickspace ^{12}C}$$

Interpreting simple mass spectra

The spectra from a mass spectrometer will show you the number of isotopes an element has and their abundance. 

The height of the peak obtained on the spectrum will show the relative abundance of each isotope as a percentage. The horizontal axis shows the mass-to-charge ratio, for a singly charged ion this is equal to the relative atomic mass. A common example is chlorine ($$Cl$$), shown in the graph below.

Example

The mass spectrum shows that chlorine has two isotopes, one occurring with a mass/charge ratio of $$35$$​ ( $$^{35}Cl$$ )and one with a mass charge/ratio of $$37$$​ ($$^{37}Cl$$). The two isotopes occur in a $$3:1$$ ratio, that is $$75\% \thickspace ^{35}Cl$$ isotopes and $$25\% \thickspace ^{37}Cl$$ isotopes. So for every three $$^{35}Cl$$ there is one $$^{37}Cl$$.

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High resolution vs low resolution

The graph above is an example of low resolution mass spectrometry because it shows the relative atomic masses to one decimal place. High resolution mass spectrometry can determine relative atomic mass to five decimal places. This is particularly useful for differentiating between molecules which appear to have the same mass when rounded to the nearest whole number.

Calculating relative atomic mass

The relative atomic mass ($$A_r$$) takes into account the atomic mass of each isotope and the abundance of this isotope. The equation below can be used to calculate $$A_r$$ from spectra.​

​$$A_r = \frac{isotope \thickspace mass \thickspace \times \thickspace isotope \thickspace abundance }{100}$$

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Example

Take the example of this spectrum for zirconium - it has five isotopes: 

Using the formula above, the relative atomic mass for zirconium can be calculated:  

​$$A_r = \frac{isotope \thickspace mass \thickspace \times \thickspace isotope \thickspace abundance }{100} \\$$

​$$A_r = \frac{ (90 \thickspace \times \thickspace 51.5)+(91 \thickspace \times \thickspace 11.2) + (92 \thickspace \times \thickspace 17.1) + (94 \thickspace \times \thickspace 17.4) + (96 \thickspace \times \thickspace 2.8) }{100}$$

​$$\underline {A_r = 91.3}$$​​

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Mass spectra for molecular compounds

So far we have described how to use mass spectra to identify elements, it can also be used to identify molecules. Similar to when elements are put through the mass spectrometer, a molecule is bombarded with electrons to produce a molecular ion ($$M^{+}$$). 

Example

To identify the molecular mass you look for the peak with the second to largest mass/charge ratio. This peak represents $$M^{+}$$. To the right of this peak is a small peak known as $$M+1$$, this is due to the presence of $$^{13}C$$ isotope in the sample. 

Molecular fragments

When the sample is bombarded with electrons, some of the molecules break up into fragments (the other peaks you see on the spectrum). This fragmentation pattern can be used to work out what the molecule is and its structure. Below are examples of common fragments and the molecular mass (peak) you'll see on the graph if they are present.  

This information can be pieced together to identify the structure of the molecule.