General Chemistry I

Chapter 10


Characteristics of Gases

n    No definite shape or volume

n    vapors

n    co-exist with a liquid or solid

n    mixtures always homogeneous

n    molecules act independently


n    force per unit area (psi)

n    atmospheric pressure - due to gases in the atmosphere

n    Standard atmospheric pressure - 1atm

n    14.7 psi

n    29.92 in Hg

n    760 torr

n   760 mm Hg

n    101.325 kPa

n   101,325 Pa

n   1.013 B (bar)

n   1013 mB


n    Previous is a list of conversion factors

n    760 torr = 1 atm

n    14.7 psi = 1013.25 mB

n    Examples!

Problems:  1-13 odd

Gas Laws

n    Boyle's Law

n    Relationship between Pressure and Volume

n    As one increases, the other decreases

n    For a sample of gas at a constant T:  PV = k

n   k will vary with temperature and the amount of gas!

n      More useful: P1V1 = P2V2

n    Charles' Law

n    As temperature increases, volume increases

n    Not as ‘clean’ mathematically in Boyle’s time

Kelvin Temperature Scale

n     Charles Law shows limiting temperature

n    Temperature below this value would give negative value

n    All Volume/Temperature plots intercept at the same point

n     Absolute Zero

n    no temperature can be colder than this value

n    when kelvins used, equations simplify greatly!

Gas Laws

n    Charles’ Law

n    For a given sample of gas; V/T = k

n   P is constant

n   T must be in an absolute scale

n   kelvins

n    P/T relationship

n    For a given sample of gas; P/T = k

n   V is constant

n   T must be in an absolute  scale

n    Combined Gas Law

n    For a sample of gas: 

n    P1V1 / T1  =  P2V2 / T2

n    Combines Boyle’s, Charles’ and the P/T relationships into a single equation.

n    Second most important gas law!

n    Avogadro's Law

n    For a gas under equal pressure and temperature conditions, equal volumes of the gas contain equal numbers of molecules

n    Volumes directly related to #molecules / moles.

Problems:  15 – 19 odd

Ideal Gas Law

n    Combines all variables into a single equation

n    PV/nT = R

n    PV = nRT

n    R - Ideal Gas Constant

n    0.08206 L atm mol-1 K-1

n    8.314 L kPa mol-1 K-1

n      62.36 L torr mol-1 K-1

n    STP

n    Standard Temperature and Pressure

n    273.15 K and 101.325 kPa

n   OOC and 1 atm

n   Allows a convenient way to report gas volumes.

n    Molar volume - 22.41 L @ STP

n    Comes from Avagadro’s Law

n    Some slight variation for some 'real' gases

Problems:  21 - 33 odd

Molar Mass Determinations

n    Molar Mass (MW) = grams/mole

n    rearrange   n=g/MW

n    substitute into ideal gas law - PV = (g/MW)RT

n    Rearrange -  MW - gRT/PV

n    Independent method for determining molecular weight

n    Use in conjunction with empirical formula to determine molecular formula


n     Units are typically g/L for a gas

n    since gas densities are much lower, these values give more ‘reasonable’ numbers.

n     Density will change with change in P, V, T

n     substitute n = g/MW into ideal gas equation

n    rearranging gives g/V = P(MW) / RT

n    When V = L, term is a density term

n    Units for V determined by units for R

Problems:  35 - 45 odd

Mixtures of Gases

n     Partial Pressures

n    Pressure exerted by a gas independent of any other gases that may be present

n     PT = EPi

Mole Fractions

n    Fraction of what you are interested in to total number of moles present

n    mole fractions (P)

n    Assume a 2 component system (A and B)

n     PA =  molesA / (molesA + molesB)

n    For a mixture of gases

n      PT * Pi = Pi

Volumes of Gases in Chemical Reactions

n    Collection over water

n    Mixture of gases

n    Appendix B - partial pressures of water

Problems:  47 - 55 odd

Kinetic - Molecular Theory

n     5 postulates

n    Large # of molecules in continuous, random motion.

n    gas molecule volume <<< volume contained in.

n    Intermolecular forces negligible.

n    Energy transferred in collisions, but the average kinetic energy constant with constant temp. (perfectly elastic collisions.)

n    Average kinetic energy proportional to absolute T.

Kinetic - Molecular Theory

n    Explain gas laws

n   Boyle's - lower volume & increase frequency of same energy collisions.

n   P/T - increase T and increase energy & frequency of collisions

n   Charles' - for P to remain constant must decrease frequency of higher energy collisions.

Graham's Law

n    Relates speed of molecule to molecular weight

n    Derived from KM theory postulates.

n    Used to predict both molecular speed and relative rate of diffusion

n    Oak Ridge, TN

n    Molecular speed >> Rate of diffusion

n    mean free path is typically 100 nm @ typical pressures

Problems:  57 - 65 odd

Deviations from Ideal Behavior

n    Molecular volume greater than 0

n    molecular interaction forces greater than 0

n    van der Walls equation

n    Introduces terms into the ideal gas equation (a and b)  to compensate for differences in molecular volume


van der Walls equation

n    a - correct for IM forces

n    b - correct for molecular volume

n   a & b determined experimentally

Problems:  67 - 73 odd

Learning Goals

n    Describe the general characteristics of gases as compared to other states of matter, and list the ways in which gases are distinct.

n    Define atmosphere, torr, and pascal (the most important units in which pressure is expressed) and describe how a barometer and manometer work.

n    Describe how a gas responds to changes in pressure, volume, temperature, and quantity of gas.

n    Use the ideal gas equation to solve for one variable given the other three, or information from which the other variables can be calculated.

n    Use the gas laws, including the combined gas law, to calculate how one variable of a gas responds to changes in one or more of the other variables.

n    Calculate the molar mass of a gas, given the mass or density under specified conditions of temperature and pressure.

n     Calculate the partial pressure of any gas in a mixture, given the composition of that mixture.

n     Calculate the mole fraction in a mixture, given its partial pressure and the total pressure of the system.

n     Describe how the distribution of speeds and the average speeds for gas molecules changes with changes in temperature.

n    Describe how the relative rates of effusion and diffusion of two gases depend on their molar masses.

n    Cite the conditions of P and T under which real gases most closely approximate ideal-gas behavior.