.MCAD 303010000 1 0 50 0 .CMD PLOTFORMAT 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 0 0 NO-TRACE-STRING 0 2 1 0 NO-TRACE-STRING 0 3 2 0 NO-TRACE-STRING 0 4 3 0 NO-TRACE-STRING 0 1 4 0 NO-TRACE-STRING 0 2 5 0 NO-TRACE-STRING 0 3 6 0 NO-TRACE-STRING 0 4 0 0 NO-TRACE-STRING 0 1 1 0 NO-TRACE-STRING 0 2 2 0 NO-TRACE-STRING 0 3 3 0 NO-TRACE-STRING 0 4 4 0 NO-TRACE-STRING 0 1 5 0 NO-TRACE-STRING 0 2 6 0 NO-TRACE-STRING 0 3 0 0 NO-TRACE-STRING 0 4 1 0 NO-TRACE-STRING 0 1 21 15 0 3 .CMD FORMAT rd=d ct=10 im=i et=3 zt=15 pr=3 mass length time charge temperature tr=0 vm=0 .CMD SET ORIGIN 0 .CMD SET TOL 0.001000000000000 .CMD SET PRNCOLWIDTH 8 .CMD SET PRNPRECISION 4 .CMD PRINT_SETUP 1.200000 0.000000 1.000000 1.000000 0 .CMD HEADER_FOOTER 1 1 *empty* *empty* *empty* 0 1 *empty* *empty* *empty* .CMD HEADER_FOOTER_FONT fontID=14 family=Arial points=10 bold=0 italic=0 underline=0 .CMD HEADER_FOOTER_FONT fontID=15 family=Arial points=10 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE_NAME fontID=0 name=Variables .CMD DEFINE_FONTSTYLE_NAME fontID=1 name=Constants .CMD DEFINE_FONTSTYLE_NAME fontID=2 name=Text .CMD DEFINE_FONTSTYLE_NAME fontID=4 name=User^1 .CMD DEFINE_FONTSTYLE_NAME fontID=5 name=User^2 .CMD DEFINE_FONTSTYLE_NAME fontID=6 name=User^3 .CMD DEFINE_FONTSTYLE_NAME fontID=7 name=User^4 .CMD DEFINE_FONTSTYLE_NAME fontID=8 name=User^5 .CMD DEFINE_FONTSTYLE_NAME fontID=9 name=User^6 .CMD DEFINE_FONTSTYLE_NAME fontID=10 name=User^7 .CMD DEFINE_FONTSTYLE fontID=0 family=Times^New^Roman points=12 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE fontID=1 family=Times^New^Roman points=12 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE fontID=2 family=Times^New^Roman points=12 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE fontID=4 family=MS^Sans^Serif points=10 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE fontID=5 family=Courier points=10 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE fontID=6 family=System points=10 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE fontID=7 family=Script points=10 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE fontID=8 family=Terminal points=10 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE fontID=9 family=Modern points=10 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE fontID=10 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 .CMD UNITS U=1 .CMD DIMENSIONS_ANALYSIS 0 0 .TXT 3 1 24 0 Cg a41.700000,73.000000,52 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} } {\plain {\b \fs28 Mass-Spectroscopic Analysis of a Mixture}} } .TXT 4 8 25 0 Cg a50.500000,53.600000,83 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} } {\plain {\i \fs24 Zoran Zdravkovski, Institute of Chemistry, Skopje, Macedoni}{\i \fs24 a}} } .TXT 3 -8 27 0 Cg a80.600000,80.900000,1491 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} } {\plain { 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:\par \par }{\i H = r}{\fs16 \dn8 \i 1}{\i s}{\fs16 \dn8 \i 1}{\i p}{\fs16 \dn8 \i 1}{\i + r}{\fs16 \dn8 \i 2}{\i s}{\fs16 \dn8 \i 2}{\i p}{\fs16 \dn8 \i 2}{\i + r}{\fs16 \dn8 \i 3}{\i s}{\fs16 \dn8 \i 3}{\i p}{\fs16 \dn8 \i 3}{\i + . . . + r}{\fs16 \dn8 \i n}{\i s}{\fs16 \dn8 \i n}{\i p}{\fs16 \dn8 \i n}{\par where \par }{\i H}{ - the height of the peak\par }{\i p}{ - the partial pressure of a component in the mixture\par }{\i 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}{\i \par s}{ - the sensitivity factor for a given component; determined from the mass spectra of the individual components.\par When the }{\i r}{ and }{\i 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 }{\i \b n}{ component mixture, }{\i \b n}{ equations are necessary, or only }{\b \i n}{ peaks of all the avilable peaks are needed. \par }} } .TXT 42 0 49 0 Cg a45.400000,81.900000,63 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} } {\plain { This will be illustrated on a three component mixture: }} } .TXT 3 25 1 0 Cg a8.000000,10.900000,24 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} } {\plain {Relative intensities}} } .TXT 4 34 2 0 Cg a7.400000,11.200000,10 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} } {\plain {Unknown}} } .TXT 2 -56 3 0 Cg a2.800000,56.000000,6 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} } {\plain {m/z}} } .TXT 0 20 4 0 Cg a1.400000,40.000000,4 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} } {\plain {A}} } .TXT 0 7 5 0 Cg a1.300000,33.600000,4 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} } {\plain {B}} } .TXT 0 7 6 0 Cg a1.300000,28.000000,4 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} } {\plain {C}} } .TXT 1 23 7 0 Cg a5.900000,8.800000,10 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} } {\plain {mixture}} } .EQN 21 -58 8 0 ({12,1}737258474645443129272615) .EQN 0 14 9 0 {0:r}NAME:({12,3}0004.05100.0073.1132.5112.87061.9561.081.89100.0051.216.452.958.3728.0116.7202.054.531.9815.23100.0068.9515.2721.4547.6370.0515.4121.520.259.272.5356.42) .EQN 0 39 10 0 {0:H}NAME:({12,1}100.0061.1011.3715.3581.7289.0532.7218.620.1039.0533.7239.16) .TXT 25 -54 48 0 Cg a37.900000,80.900000,51 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} } {\plain {The sensitivity of each component is also given:}} } .EQN 0 41 31 0 {0:sA}NAME:0.240 .EQN 0 15 32 0 {0:sB}NAME:0.422 .EQN 0 14 33 0 {0:sC}NAME:0.160 .TXT 13 -70 50 0 Cg a51.600000,80.900000,80 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} } {\plain { The set of linear equations are defined in a }{\i \b Given/Find}{ block:}} } .TXT 9 6 46 0 Cg a23.400000,76.900000,35 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} } {\plain {initialization of the variables:}} } .EQN 0 38 37 0 {0:pA}NAME:1 .EQN 0 9 38 0 {0:pB}NAME:1 .EQN 0 10 39 0 {0:pC}NAME:1 .EQN 5 -60 35 0 {0:Given}NAME .TXT 4 2 34 0 Cg a11.400000,79.900000,17 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} } {\plain {peak at 45 m/z}} } .EQN 0 24 36 0 89.0570.05*{0:sA}NAME*{0:pA}NAME+28.01*{0:sB}NAME*{0:pB}NAME+73.11*{0:sC}NAME*{0:pC}NAME .TXT 4 -24 43 0 Cg a11.400000,79.900000,17 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} } {\plain {peak at 46 m/z}} } .EQN 0 24 40 0 81.7247.63*{0:sA}NAME*{0:pA}NAME+8.37*{0:sB}NAME*{0:pB}NAME+100.0*{0:sC}NAME*{0:pC}NAME .TXT 4 -24 45 0 Cg a11.400000,79.900000,17 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} } {\plain {peak at 73 m/z}} } .EQN 0 24 41 0 100100*{0:sA}NAME*{0:pA}NAME+100*{0:sB}NAME*{0:pB}NAME+0*{0:sC}NAME*{0:pC}NAME .EQN 8 -1 42 0 {0:Find}NAME({0:pA}NAME,{0:pB}NAME,{0:pC}NAME)={0}?_n_u_l_l_ .TXT 9 -26 47 0 Cg a80.000000,80.900000,289 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} } {\plain { Apparently, the choice of the peaks will influence the result and it is better to pick the ones with high relative intensities of the components. However, it is even better to take into account all peaks. This can be done by}{ using well established methods of matrix algebra: }} } .TXT 9 -1 11 0 Cg a53.400000,58.400000,72 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} } {\plain {The }{sensitivity of each component is defined in another vector-row:}} } .EQN 3 17 12 0 {0:s}NAME:({1,3}0.1600.4220.240) .EQN 1 33 13 0 {0:i}NAME:0;{0:last}NAME(({0:s}NAME){51}) .TXT 4 -49 14 0 Cg a56.000000,57.600000,76 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} } {\plain {The product of the partial pressure and the sensitivity is obtained from:}} } .EQN 6 2 15 0 {0:sp}NAME:((({0:r}NAME){51}*{0:r}NAME))^(-1)*({0:r}NAME){51}*{0:H}NAME .EQN 1 41 16 0 {0:sp}NAME={0}?_n_u_l_l_ .TXT 7 -43 17 0 Cg a50.300000,56.000000,69 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} } {\plain {The partial pressure is caluclated by dividing by the sensitivity:}} } .EQN 7 3 18 0 ({0:p}NAME)[({0:i}NAME):(({0:sp}NAME)[({0:i}NAME))/(((({0:s}NAME){51}))[({0:i}NAME)) .EQN 0 40 19 0 {0:p}NAME={0}?_n_u_l_l_ .TXT 9 -42 20 0 Cg a31.000000,56.800000,44 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} } {\plain {Finally, the mole fraction is calculated:}} } .EQN 8 2 21 0 ({0:x}NAME)[({0:i}NAME):(({0:p}NAME)[({0:i}NAME))/({0:i}NAME$({0:p}NAME)[({0:i}NAME)) .EQN 0 40 22 0 {0:x}NAME={18993}?{0:%}NAME .TXT 17 -43 26 0 Cg a70.300000,71.000000,334 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} } {\plain {\b References}{:\par \par 1. Z. Zdravkovski, Mathcad in Chemistry Calculations, }{\i J. Chem. Ed.}{ }{\b 1991}{, }{\i 68}{, A95 and }{\b 1992}{, }{\i 69}{, A240.\par \par 2. T. R. Dickson, The Computer and Chemistry, W. H. Freeman, San Francisco, 1968 .\par \par 3. P. W. Atkins, Physical Chemistry, W. H. Freeman, New York, 4th Ed., 1990.\par \par }} }