GASESAP CHEMISTRY CHAPTER 5

MEASUREMENT OF GASES• To specify the state of a gaseous substance, we have the values of

four variables: V, n, T, P

• Volume: the volume of a gas is the volume of it’s container - a gas expands to fill the volume of its container

• Amount: given in moles– if given grams, change into moles (mass over formula weight)

• Temperature: expressed in Kelvin – Celsius temperature + 273.15 = Kelvin (can’t have negatives or zeroes)

• Pressure: force per unit area– may be measured in mm Hg, Torr, atmospheres (atm), or kilopascals (kPa)

• 1 atm = 760 mmHg (or Torr) = 101.325 kPa

• Conversions may need to be done • Example 5L.1

GAS LAWS• Volume is proportional to amount (number of moles). –

Avogadro’s Law

• V = kn n1 = n2

V1 V2

• Volume is directly proportional to Kelvin temperature. – Charles’ Law

• V = kT V1 = V2

T1 T2

• Volume is inversely proportional to pressure. – Boyle’s Law

• V = k P1V1 = P2V2

P

IDEAL GAS LAW• A single equation has been derived which relates volume to

amount, temperature, and pressure. PV = nRT (Ideal Gas Law)

• The gas constant, R, can be calculated from experimental values in P, V, n and T. One mole of gas occupies a volume of 22.4 L at 0o C and 1.00 atm.

• R = PV = (1.00 atm)(22.4 L) = 0.0821 L atm

nRT (1 mol)(273.15K) mol K

• Another value of R (in energy terms) is 8.31 J___

mol K

• From the ideal gas law various relationships can be derived using a 1 to denote initial and 2 to denote the final state – Examples 5L.2-3

MOLAR MASS AND DENSITY• It is sometimes convenient to rewrite the Ideal Gas Law in a different form,

expressing the amount in grams rather than in moles. Substituting for n in the Ideal Gas Law we obtain: n = mass in grams so PV = mRT

molar mass M

• The Ideal Gas Law in this form is useful for calculating the following:

• 1. The molar mass (M) of a gas knowing the mass (g) of a given volume (V) at a certain temperature (T) and pressure (P). The equation is M = mRT

PV

• 2. The density (d) of a gas of known molar mass (M) at a given temperature (T) and pressure (P). The equation is

d = m M = mRT d = MP

V PV RT

• Examples 5L.4-5

STOICHIOMETRY OF GASEOUS REACTIONS

• Use the Ideal Gas Law

• Also may use molar volume – at STP 1 mole of gas will occupy 22.4 L

• Examples 5L.6-7

• The law of combining volumes states: The volumes of different gases involved in a reaction, if measured at the same temperature and pressure, are in the same ratio as the coefficients in the balanced equation.

• Example 5L.8

GAS MIXTURES

•Dalton’s Law of Partial Pressures: the total pressure of a gas mixture is the total pressure of the components of the mixture. Add them together to get total.

PT = P1 + P2 + P3

WET GASES: PARTIAL PRESSURE OF WATER

•PT = PG + PH2O

•PG = PT - PH2O

•Use Dalton’s Law to find P of dry gas (use table of water vapor pressures on p. 486)•Use Ideal Gas Law to find moles•Example 5L.9

PARTIAL PRESSURE AND MOLE FRACTION

• The mole fraction of A in the mixture is : XA = nA OR PA

nTOTAL PTOTAL

• The partial pressure of a gas in a mixture is equal to its mole fraction multiplied by the total pressure.

PA = XA PTOTAL

• Example 5L.10-11

KINETIC THEORY OF GASES

• Postulates of the Kinetic Theory

• 1. Gases consist of particles (atoms or molecules) in continuous random motion.

• 2. Collisions between gas particles are elastic.

• 3. The volume occupied by the particles is negligibly small compared to the container.

• 4. Attractive forces between particles have a negligible effect on their behavior.

• 5. The average kinetic energy of a gas particle is directly proportional to the absolute temperature. At a given temperature, all gases have the same average kinetic energy.

AVERAGE SPEED OF GAS PARTICLES

• The average speed of a gas molecule can be calculated by

urms = 3RT

M

• The average speed of a molecule is

• directly proportional to square root of Kelvin temperature

• inversely proportional to square root of the molar mass

• Example 5L.12

EFFUSION OF GASES

• Diffusion is spreading of a gas from area of high concentration to low concentration

• Effusion is flow of gases through pores or pinholes

• Rate depends on pressure of gas and relative speeds of different gases

• Rate of effusion of A = MB

• Rate of effusion of B MA

• The relationship between the rate of effusion of two gases and their molar masses is inversely proportional to the square root of the molar mass

GRAHAM’S LAW

• Graham's Law states at a given temperature and pressure, the rate of effusion of a gas is inversely proportional to the square root of the molar mass

• The relationship between rate and time is inverse

• Example 5L.13

END OF CHAPTER 5STUDY FOR TEST!