REACTIONS OF METHANE AND ETHANE WITH OXYGEN Below are the equations for the reactions of methane and ethane with oxygen, in which corrections have been made according to the specific gravity determinations shown in the preceding table: MOLECULAR VOLUME OF CARBON DIOXIDE AT DIFFERENT PARTIAL PRESSURES As the partial pressure of gases in a mixture decreases the gases more nearly conform in behavior to the gas laws; consequently, a table is included herein which shows the correct molecular volume to use for carbon dioxide at different partial pressures. The partial pressure of the carbon dioxide refers to the ratio of the volume occupied by the carbon dioxide found after the combustion to the total volume of residual gas found after the combustion; that is, if the total volume after combustion is found to be 70 c. c. and the carbon dioxide is 40 c. c. the partial pressure of the carbon dioxide will be 40X760 -434 mm., and the proper molecular volume-0.997-will be found from the table. 70 The foregoing equations refer to gases at 0° C. and 760 mm. pressure. The following table shows the correct molecular volumes for carbon dioxide at 20° C. and different partial pressures: Molecular volume of carbon dioxide corresponding to different partial pressures at 20° C. 100.. 200. 300400. 55 In compiling this table advantage was taken of the work of Rayleigh, Leduc, and Chappius on the determination of the specific gravity and coefficient of expansion of carbon dioxide. The specific gravity determinations were given by Rayleigh and Leduc for carbon dioxide at 0° C. and 760 mm. pressure. Values for 20° C. and 760 mm. pressure were determined from the coefficient of expansion of carbon dioxide between 0° C. and 20° C. A graph was plotted from two values, the deviation from the gas laws at 760 mm. pressure and at 380 mm. pressure. The coefficient of expansion of ethane between 0° and 20° C. has not been determined, consequently the same molecular volume was used at 20° C., the laboratory working temperature, as was reported by Baumé Landolt, H., and Börnstein, R., Physikalisch-chemische Tabellen. 1912, p. 148. and Perrot 56 at 0° C. The error resulting from this usage can be disregarded without introducing any appreciable error in the analyses, judging from the molecular volume of carbon dioxide, which at 20° C. differs only 0.001 from the value at 0° C. Below are the molecular volumes to be used for ethane at different partial pressures: Molecular volume of ethane corresponding to different partial pressures Although the individual paraffins in a mixture of several can not be determined exactly, the chemist will know accurately enough which value in the above column to use by accepting the value that corresponds to the percentage of ethane determined from the combustion analysis. Moreover, the partial pressure of ethane in natural gas from many places is so low that there is only slight deviation. from the gas laws. A slight error arises from the probable percentage of propane or butane in a mixture when the combustion analysis indicates methane and ethane only, but the partial pressures of the propane and butane will usually be so low that errors in molecular volume due to their presence can be disregarded. Methane conforms so closely to the gas laws that no deviation from the given molecular volume need be made for different partial pressures. The proper equations to use can be determined only from the partial pressures obtained from the analyses. To determine the approximate percentage of ethane the theoretical equations can be used. APPLICATION OF THE USE OF CORRECTED EQUATIONS TO THE ANALYSES OF NATURAL GAS AND OTHER GAS MIXTURES Although the combustion analysis does not show an accurate distribution of hydrocarbons in a natural-gas mixture, it does show the true total paraffin content. The heating value calculated from such an analysis is also correct. Determinations by the slow-combustion method show that the natural gas supplied to Pittsburgh from Appalachian fields contains about 83 per cent CH4, 16 per cent C,H,, and 1 per cent N. These proportions vary from time to time during the year. This gas is almost all methane, but contains small amounts of ethane and pro50 Landolt, H., and Börnstein, R. Work cited, p. 148. pane and some of the higher homologues. A typical analysis with the calculation from the analytical data is given herewith. CH, and C2H, are calculated from the theoretical equations as follows: Let x=methane. and y ethane. Then 2x+2.5y=total contraction. C2H6-15.1 per cent. CH. 84.1 per cent. Total paraffins-99.2 per cent. They are calculated from the corrected equation as follows: ANALYSIS OF GAS CONTAINING HIGH PERCENTAGES OF CO An interesting situation develops when a mixture containing a high percentage of carbon monoxide is analyzed. Carbon monoxide was prepared from oxalic acid and sulphuric acid in the usual way, and the gas after purifying was analyzed by the slow-combustion method. Observed data in an analysis of a mixture containing a high percentage of carbon monoxide Some air was present in the mixture. According to the equation, 2CO+02=2CO2, the CO is double the contraction, and the CO is equivalent to the CO2. The CO2 produced by the combustion should be just twice the contraction, but it will be noticed that a difference of 0.8 c. c. exists between the observed result and the theoretical; that is, 2X25.1 50.2 c. c. and 50.2 c. c.-49.4 c. c.=0.8 c. c. 2.000 CO+1.000 O,=1.992 CO,. When the correct molecular volumes are used the equation becomes 1.984 (contraction) = CO or 49.80 c. c. 49.6 c. c. 0.20 c. c., which is only slightly greater than the experimental error of the apparatus. ANALYSIS OF METHANE For methane the correction is small. CH, prepared by the method of Gladstone and Tribe 57 and containing a small quantity of air analyzed as follows: Methane reacts with oxygen according to the theoretical equation, as follows: According to these equations the percentage of CH, becomes 98.0 When calculated from the correction basis the equation which gives 98.4 CH, when calculated from the CO2. 57 Gladstone, T. H., and Tribe, Alfred. Note on the preparation of marsh gas: Jour. Chem. Soc., vol. 45, 1884, p. 154. 49530°-26-7 The difference in the percentages when calculated from the corrected and the theoretical equations is 98.498.00.4 per cent. When the results are calculated from the contraction there is a difference between the theoretical and corrected values of 98.598.30.2 per cent. ANALYSIS OF ETHANE Ethane prepared by the method of Gladstone and Tribe 58 and mixed with air gave the following analysis: 6 From the theoretical equation C2H ̧+3.502=2CO2+3H,O, the C2H in the mixture becomes 100 per cent. According to the corrected equation, C2H=99.4 per cent, or a difference of 0.6 per cent, when calculated from the CO, produced. When the calculations are made from the contraction there is a difference between the theoretical and the corrected values of 100.6-99.6-1.0 per cent. CORRECTION FOR OTHER GASES Because gases conform more nearly to the gas laws as their partial pressures become further removed from 760 mm. of mercury, certain gases that are noteworthy because they do not conform to these laws may be in a mixture and do not need to have their volumes corrected if their partial pressures are reduced much below 1 atmosphere. In the analysis of mixtures rich in combustible constituents, however, the constituents being determined make such a large proportion of the total, and so much carbon dioxide may be produced, that the correction may have to be applied in precise work. The foregoing data indicate that when the slow-combustion method of analyses is adopted the true molecular volumes should be used when necessary in calculating the results of analyses of natural gas and other mixtures which contain a high proportion of combustible gases, and that they should also be used when necessary in slow-combustion analyses of prepared combustible gases that are being examined for purity. 58 Gladstone, T. H., and Tribe, Alfred. Work cited, p. 154. |