## 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/z* | *r*(A) |
*r*(B) | *r*(C) | *H*(mixture) |

15 | 56.42 | 15.23 |
1.89 | 39.16 |

26 | 2.53 | 1.98 | 61.08 | 33.72 |

27 | 9.27 | 4.53 | 61.95 |
39.05 |

29 | 0.25 | 2.05 | 0 | 0.10 |

31 | 21.52 | 0 | 12.87 | 18.62 |

44 | 15.41 |
16.72 | 32.51 | 32.72 |

45 | 70.05 | 28.01 |
73.11 | 89.05 |

46 | 47.63 | 8.37 | 100 | 81.72 |

47 | 21.45 | 2.95 | 4.05 | 15.35 |

58 | 15.27 | 6.45 | 0 | 11.37 |

72 | 68.95 |
51.21 | 0 | 61.10 |

73 | 100 | 100 | 0 | 100 |

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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