RSPT 2305: Section 9
CALCULATION OF GAS VOLUMES AT DIFFERENT
TEMPERATURES AND PRESSURE
I. The Gas Laws
A. Boyle's Law - at constant temperature, the volume of any gas varies inversely with
the pressure to which the gas is subjected:
P1V1 = P2V2
B. Charles' Law - the volume of a gas at constant pressure increases proportionately to
the absolute temperature. If V1 and V2 are volumes of the same mass of gas at
absolute temperature, T1 and T2 then:
V1 = T1
V2
T2
C. Dalton's Law - The pressure exerted by each component in a gaseous mixture is
dependent of other gases in the mixture, and the total pressure of the mixture is
equal to the sum of the separate pressures which each gas would exert if it occupied
the whole volume.
PCO2 + PO2 + PN2 + PH2O = PB
D. Partial Pressure of Water Vapor - the warmer a liquid, the greater the vapor
pressure. Water vapor in a gas at 37oC maintains a partial pressure of 47 torr,
regardless of changes of PB.
II. Applying these laws, then, a volume of gas collected at one temperature and pressure can
be converted to the volume which it would occupy at another temperature and pressure.
A. ATPS to BTPS - to correct a volume of gas collected at room (ambient) temp. and
pressure saturated with water vapor (ATPS) to the volume that it would occupy at
body temp. (BTPS), the following equation is used:
VBTPS = VATPS x (273 + 37) x
PB - PH2O at TA
273 + TA
PB - 47
The factors for correcting a volume from ATPS to BTPS are given on page 3, and
were calculated using this equation.
B. ATPS to STPD - in some instances, a gas volume is corrected to the volume it
would occupy at standard temp. and pressure, dry (0oC, 760 torr). For correcting
ATPS to STPD, the following equation is used:
VSTPD = VATPS x (273 + 0) x PB - PH2O at TA
273 + TA
760
C. BTPS to STPD - to correct a volume from BTPS to STPD, the following equation is
used:
VSTPD = VBTPS x (273 + 0) x PB - 47
273 + 37
760
D. In correcting a volume of gas, saturated, to the volume it would occupy, dry, at the
same temp. and pressure, the following equation should be used to determine the
correction factor:
Section 9; Calculation of Gas Volumes
2
VDRY = VSAT x (PB - PH2O at ambient temp)
PB
Table 1
Water Vapor Pressure
Gas Temp (oC)
PH2O (torr)
20..................................................17.5
21..................................................18.7
22..................................................19.8
23..................................................21.1
24..................................................22.4
25..................................................23.8
26..................................................25.2
27..................................................26.7
28..................................................28.3
29..................................................30.0
30..................................................31.8
31..................................................33.7
32..................................................35.7
33..................................................37.7
34..................................................39.9
35..................................................42.2
36..................................................44.6
37..................................................47.0
Section 9; Calculation of Gas Volumes
E. Factors to Convert Gas Volumes from Room Temperature Saturated (ATPS) to
Volume Occupied at 37o C, Saturated (BTPS)
Table 2
Conversion Factors ATPS TO BTPS - Amarillo, Texas
Ambient Temperature (oC)
Conversion Factor
20.....................................................1.108
21.....................................................1.101
22.....................................................1.097
23.....................................................1.091
24.....................................................1.086
25.....................................................1.080
26.....................................................1.073
27.....................................................1.067
28.....................................................1.062
29.....................................................1.055
30.....................................................1.049
31.....................................................1.042
32.....................................................1.034
33.....................................................1.028
34.....................................................1.020
35.....................................................1.014
36.....................................................1.007
37.....................................................1.000
Note: These factors have been calculated for a PB of 665 torr. Since the factors
change very little from 675 to 655 torr, it is not necessary to correct for
small changes in PB. However, if the PB varies greatly from 665 torr, the
formula on page 1 (II, A) should be used to obtain the correct conversion
factor.
3