(©2004, François G. Amar, All rights reserved)
 

Summary for Weeks 14 & 15

Reading:

For these two weeks: Chapter 10 ; quiz on Wednesday, December 8.

A look ahead:

Help session in 316 Aubert on Sunday the 12th at 4 PM

Final exam in Period A2, 10:30-12:30, Monday, December 13 in 316 Aubert

1 PM

 

Homework problems:

Beginning of Chapter 10: 4, 5, 9, 12, 15, 19, 20, 25, 29, 31, 35

End of Chapter 10: 41, 44, 47, 48, 51, 53, 55, 57, 59

The following homeworkproblems will not be covered on the Final

61, 66, 67, 69, 72

Key concepts and equations:

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

P_tot = P₁+P₂+P₃+^{. . .} = S P_i Dalton's law of partial pressures

P_i = n_iRT/V partial pressure of component i

P_tot = n_totRT/V where n_tot = S n_i

X_i= n_i/n _tot =P_i/P_tot mole fraction

The following concepts will not be covered on the Final 

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)

 

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