Pressure of Gases
pressure definition and units:
1 atm = 760 torr = 101.325 kPa = 1.01325x105 Pa
1 bar = 105 Pa so 1 atm = 1.01325 bar
measuring pressure
manometers -- open ended and closed ended
Gas Laws
V~T or V/T = constant (Charles law and the Kelvin temperature scale)
V~1/P or PV = constant (Boyle's law)
V~n or V/n = constant (Avogadro's law)
PV=nRT (ideal gas law, section 10.4)
Temperature units
In the gas law formulas, the Kelvin temperature must be used:
T (K) = t (°C) + 273.15
(that is, add 273.15 to the Celsius temperature to get the absolute temperature)
The Gas Constant
The units of the gas constant, R, must be consistent with the units of the pressure, volume, temperature and amount of stuff (moles) used in the problem
Some numerical values of R with their units are:
R = 0.08206 L-atm/mol-K
R = 62.37 L-torr/mol-K
R = 8.3145 Pa-m3/mol-K
since 1 Pa-m 3 = 1 J , this is the same as
R = 8.3145 J/mol-K
Quantitative Use of the Gas Laws
n=PV/RT
rearranging the ideal gas law gives another way to find out the number of moles of a substance from PVT information. This can be used "below the line" in stoichiometry problems, limiting reagent problems and the like.
d=P(MW)/RT or MW = dRT/P
expresses the density in terms of gas pressure and temperature and molecular weight
P2V2/T 2 = P1V1/T 1
the basis for a variety of problems using ratios.
STP or standard temperature and pressure:
T=273.15 K or 0 °C and P=1 atm
at STP, 1 mole of gas occupies a volume of V= 22.4 L
Gas Mixtures
Ptot = P1+P2+P3+. . . = S Pi Dalton's law of partial pressures
Pi = niRT/V partial pressure of component i
Ptot = ntotRT/V where ntot = S ni
Xi= ni/n tot =Pi/Ptot mole fraction
Kinetic Molecular Theory
According to Richard Feynman in his Lectures in Physics, Volume I (p1-2):
"If in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generation of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis (or the atomic fact, or whatever you wish to call it) that all things are made of atoms--little particles that move around in perpetual motion, attarcting each other when they are a little distance apart, but repelling upon being squeezed into one another."
See page 373 of BLB for a few more sentences summarizing the kinetic molecular theory.
Molecules have a distribution of speeds which is well characterized and has a well understood average value
rms speed of gas molecules is u=[3RT/(MW)]1/2
average energy of gas molecule is e = mu2/2
Molecular Effusion and Diffusion
effusion is the process of gas molecules escaping through a pinhole (leak)
rate of effusion is = amount of stuff per unit time [moles/s] or [g/hr] or [molecules/s] etc
rate1/rate2 = r1/r2 = (MW2/MW1)1/2 Graham's Law of effusion
r1/r2 = (u1/u2)1/2
diffusion is the spread of molecules by random collisions through space or a volume containing another substance
Barometric formula
(the change of Pressure with altitude)
Real gases
Deviations from the ideal gas law --van der Waals equation of state:
at small V and T, this equation predicts a P vs V curve that is"unphysical" where liquid condensation occurs (gas-->liquid phase transition). An equation such as this one with only two parameters is not adequate to handle a discontinuity in the density.
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