Table 91 I4I 



CALCULATIONS INVOLVING THE RELATIONS BETWEEN THE TEMPERA- 

 TURES, PRESSURES, VOLUMES, AND WEIGHTS OF GASES 



(Abridged from S. F. Pickering, Bur. Standards Circ. 279, which see for further details.) 



Simple laws. — Any amount of gas completely fills the space in which it is confined. The 

 pressure it exerts upon the confining walls depends upon the temperature. A quantity of 

 gas can not be specified by volume only ; all three factors — volume, temperature, and pres- 

 sure — must be stated. The relations between these three factors are expressed by means of 

 the following equation, bv — KT f,-i 



in which p, v, and T represent simultaneous values of the pressure, volume, and absolute 

 temperature of any definite quantity of gas, while K is a constant, the numerical value of 

 which depends upon the quantity of gas considered and the units in which pressure, volume, 

 and temperature are measured. 



While the behavior of gases at atmospheric pressure closely approximates the equation 

 (1), the relation is not exact. The expansion of air is nearer one 272nd of its volume at 

 273.1 ° K. per degree. For most practical purposes such errors may be neglected. 



If we take_ weights of gases proportional to their molecular weights, a new relation of 

 the greatest importance develops: The value of the constant in equation (1) is the same 

 for each gas. It is customary to use as the unit of quantity, the mol, the number of grams 

 of gas equal to the molecular weight. When 1 mol is the quantity considered, the resulting 

 value of K is designated R. 



Absolute temperature Pressure Volume R 



°C + 273.1 Atmosphere Liter 0.08206 



°C -j- 273.1 mm of mercury do 62.37 



°C -j- 273.1 Gram per cm 3 do 84.79 



C C -f 273.1 Megabar do 08315 



C C -j- 2 73-i Atmosphere Cubic feet 002898 



°C -j- 273.1 mm of mercury do 2.2024 



°C + 2 73- 1 Inches of mercury do 08671 



°C + 2 73-i Pounds per in. 2 do 04259 



With the mol the unit of quantity, N the number of mols of gas, equation ( 1 ) becomes 



pv = NRT (2) 



By the use of equation (2), the above table, and a table of molecular weights, the solution 

 of any problem involving volumes, temperatures, pressures, and weights of gases is 

 very simple. 



Mixtures of gases. — Any quantity of gas fills the space in which it is confined and exerts 

 a pressure upon the confining walls. If an additional quantity is added, the pressure is 

 increased in direct proportion to the quantity added. One can regard the pressure exerted 

 by each portion of the total quantity of gas as independent of the presence of the rest. This 

 is true if the second portion of gas is different chemically from the first (Dalton's law), 

 provided the gases do not react chemically. 



Vapor pressure and the effect of vapor pressure upon the measurement of gas. — If a 

 volatile liquid is introduced, a portion evaporates and exerts a pressure on the confining 

 walls. The amount evaporated and the pressure exerted are independent of the presence of 

 any other gas. If there is enough so that not all evaporates and if time is allowed for equili- 

 brium, the pressure is independent of the volume of space and of the amount of liquid left 

 unevaporated ; but it does depend upon the temperature. For each volatile liquid there is 

 therefore a definite saturation pressure or vapor pressure corresponding to every tempera- 

 ture (see pages 223 to 232). 



When any gas is in contact with a volatile substance, the measured pressure is the 

 pressure exerted by the gas plus the vapor pressure of the volatile material. With no 

 change of temperature, this vapor pressure remains constant no matter how we change 

 the total pressure. Hence for the purposes of volume conversion the saturated gas may be 

 considered as a dry gas, the pressure of which is the partial pressure of the gas, or its 

 equivalent, the difference between the total pressure and the saturated vapor pressure of 

 the volatile material. 



Volume conversions involving high pressures. — In the measurement of gases at high 

 pressures, pressure 2,000 lbs. /in. 2 , the quantity pv is no longer constant at constant tempera- 

 ture, but varies with the pressure by amounts which differ for each gas. Consequently the 

 relation pilh/Ti = paVt/Ta is no longer true. 



In Table 92 -{ 273.1 IT \ pv is given as a function of the pressure. This quantity 

 \ 273.1/T \ pv is called the factor (F). Consider the o°C isothermals. They are taken 

 on the basis of pv at o°C and 1 atm. as unity. The factor for any pressure given by the 

 table will represent the ratio of the value of pv at this pressure to the value of Pv at 1 

 atmosphere; that is, (fiv) n /(pvh = Fn 



where Fn is the factor for n atmospheres. This relation, of course, holds for all pressures, 

 therefore, Vm = Vn \ PnFm/PmFn \ . The corrections are made as though the substance 

 behaved as a perfect gas, and the result multiplied by the ratio of the factor at the desired 

 pressure to the factor at the measured pressure. 

 Smithsonian Tables 



