2.1.1 (d) Mass Spectrometry and Relative Isotopic/Atomic Masses

Syllabus

The use of mass spectrometry in:

the determination of relative isotopic masses and relative abundances of the isotope,
calculation of the relative atomic mass of an element from the relative abundances of its isotopes

{a) Knowledge of the mass spectrometer not required. (b) Limited to ions with single charges.}

What does this mean?

The Spectrometer

You won't have to answer many questions about the workings of a Mass Spectrometer, though you need to know the stages of the process that happens inside it.

Basically, a substance is injected as a gas.

It passes an "electron gun" which fires fast moving electrons at it.

As far as we are concerned it is enough to think of these "knocking" electrons off the atoms in the sample by repulsion.

This ionisation creates positive ions - cations.

X + e^- --> X⁺ + 2e^-

^{(In the equation above the first electron is from the electron-gun.)}

^Acceleration^{- the cations are}^accelerated^{by increasingly positive plates with a hole in the centre that most pass through. they emerge moving quickly and parallel to the sides of the spectrometer}

^Deflection^{- a variable electromagnet then causes the path of the ions to change. As far as the OCR is concerned}^{all the ions are 1+}^{(not actually true).}

^{So the amount of deflection is determined by the mass of the ion. Strictly, they are deflected according to their Mass/Charge ration (M/Z ratio)}

^{The bigger the mass}^{the more momentum the ion has and}^{the harder it is to deflect}^{. This allows the ions to be sorted by their mass.}

^Detection^{. The ions are then detected electrically - we don't have to worry about how.}

Relative Atomic Mass

^{If we inject a normal sample of an element then it should contain}^all^the^isotopes^{that exist naturally.}

^{The Mass Spectrometer then sorts them by mass, measures the different mass, and also measures their}^{relative abundances}^{- how common each is.}

^{On A level papers these are either displayed on a graph or given in a table of data and used to calculate the}^{Relative Atomic Mass.}

In this case we would calculate the Relative Atomic Mass as below:

(79 x 24) + (10 x 25) + (11 x 26) = 24.34

100

We multiply the mass of an isotope by its abundance and divide by 100 because the abundances total 100

To calculate the Relative Atomic Mass of Chlorine from the chart right

(3 x 35) + (1 x 37) = 35.5

100

In this case we divided by 4 because the total of the abundances is 4

To find the Relative Atomic Mass of Lithium from this data

(6.02 x 7.5) + (7.02 x 92.5) = 6.945

100

Video

Calculating a relative abundance.

It's not impossible that you could be given the Relative Atomic Mass as well as data about some isotopes and then be asked to calculate an abundance of another isotope or its mass.

Eg1.

Neon has a relative atomic mass of 20.18

The relative abundance of ²⁰Ne is 90.92%

The relative abundance of ²¹Ne is 0.26%

Calculate the mass of the only other isotope.

Answer:

The abundance of the remaining isotope is 100 - 90.92 - 0.26 = 8.82%

If the mass of the remaining isotope is X then:

(90.92 x 20) + (0.26 x 21) + (8.82 x X) = 20.18

100

(1818.4) + (5.46) + (8.82X) = 20.18

100

1823.86 + (8.82X) = 20.18 x 100

8.82X = 2018 - 1823.86

8.82X = 194.14

X = 194.14 = 22.01 So the other isotope is ²²Ne

8.82

Eg2

There are two isotopes of Copper: ⁶³Cu and ⁶⁵Cu.

The relative atomic mass of Copper is 63.62. Calculate the relative abundances of the two isotopes.

Since the relative atomic mass is closer to 63 we'll say the abundance of ⁶³Cu = X

This makes the abundance of ⁶⁵Cu = (100 - X)

{63 x X} + {65 x (100 - X)} = 63.62

100

63X + 6500 - 65X = 6362

-2X = 6362 - 6500

-2X = -138

X = -138/-2 = 69

So the abundance of ⁶³Cu = 69% and the abundance of ⁶⁵Cu = 100 - 69 = 31%

VIDEOS

Exam style questions

(1) The mass spectrum of a sample of Chromium shows four peaks. Use the data below to calculate the relative atomic mass of Chromium in the sample. Give your answer to two decimal places.

.......................................................................................................................................................................

....................................................................................................................................................................(2)

2. The table below gives the relative abundance of each isotope in a mass spectrum of a sample of Magnesium.

Use the data above to calculate the relative atomic mass of this sample of magnesium.

Give your answer to one decimal place.

.......................................................................................................................................................................

..................................................................................................................................................................(2)

3. When a pure, gaseous sample of element X is introduced into a mass spectrometer, four mononuclear, singly-charged ions are detected, as shown in the spectrum below.

(i) Use data from the spectrum above to calculate the relative atomic mass of X.

.......................................................................................................................................................................

(ii) Identify the element X.

................................................................................................................................................................(4)

Answers

1.

Ar = (50 × 0.043) + (52 × 0.838) + (53 × 0.095) + (54 × 0.024) (1)

52.06 OR 52.05 (1)

Mark consequentially on transcription, or addition of %, error

2.

(d) Ar = (24 × 0.735) + (25 × 0.101) + (26 × 0.164) 1

= 24.4 1

(mark M2 conseq on transcription error or incorrect addition of %)

3.

(f) (i) (1 x 82) + (1 x 83) + (6 x 84) + (2 x 86) 1

10 1

= 84×1 (1)

(ignore units)

(iv) Kr (1)

(allow consequential marks)

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