Mass-Spectroscopic Analysis of Mixtures

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The mass-spectroscopic analysis of mixtures of gases is based on the fact that a given component contributes to a given peak independently of the other components. In other words these contributions are additive, and the total peak height is the sum of all contributions from the components that form an ion that gives such a mass to charge ratio. Generally for any peak, the height is given by the expression:

where
H - the height of the peak
p - the partial pressure of a component in the mixture
r - the relative intensity of the ion resulting from a given component; the values are obtained from the mass spectra of pure samples of the components of the unknown mixture, and
s - the sensitivity factor for a given component; determined from the mass spectra of the individual components

When the r and s values have been determined, the analysis of an unknown mixture can be performed by forming a set of simulatenous equations from the peak heights. For an n component mixture, n equations are necessary, or only n peaks of all the avilable peaks are needed.

This will be illustrated on a three component mixture:

m/zr(A) r(B)r(C)H(mixture)
1556.4215.23 1.8939.16
262.531.9861.0833.72
279.274.5361.95 39.05
290.252.0500.10
3121.52012.8718.62
4415.41 16.7232.5132.72
4570.0528.01 73.1189.05
4647.638.3710081.72
4721.452.954.0515.35
5815.276.45011.37
7268.95 51.21061.10
731001000100

The sensitivity factor for the components are as follows: s(A) = 0.240, s(B) = 0.422 and s(C) = 0.160.

Such a set of linear equations can be solved in Mathcad in a Given/Find block Since this is a three component mixture, only three peaks are necessary, and the choice of the peaks is very important. It is best to choose the ones with high intensity or/and the ones with high relative intensities of the components. However, it is much better to take into accoutn all peaks. This can be done by using well established methods of matrix algebra: .
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