Properties of GasesImportant properties of a Gas

Quantity n = moles

Volume V = container size (usually L or mL)

Temperature T ≈ average kinetic energy of molecules (must be in K for all “gas

laws”)

Pressure P = force/areaUnits of pressure: SI unit is the pascal (Pa)

• 1 atm = 101,325 Pa (not commonly used) = 14.7 psi

More important:

1 mm Hg = 1 torr1 atm = 760 torr = 760 mm Hg

Exact!

Measuring Pressure

Barometer

Manometer

Pressure - Volume - Temperature Relationships

• Boyle’s Law (at constant T and n)V ∝ 1/P or PV = constant

• Charles’ Law (at constant P and n)V ∝ T or V/T = constant

• Gay-Lussac’s Law (at constant V and n)P ∝ T or P/T = constant

• Combined Gas Law (for constant n)PV/T = constant or

(remember that T must be in units of K -- practice problems in book!)

P1V1 P2V2

T1 T2

=

Ideal Gas Law• Avogadro’s Principle

– At constant P and T, V ∝ n– i.e. at constant T and P, equal volumes of gases contain

equal numbers of moles

• The Ideal Gas Equation

PV = nRT

where R = “universal gas constant”= 0.0821 L•atm/mole•K memorize!

{useful in many different kinds of calculations involving gases!}

• Standard Molar Volume– At Standard Temperature and Pressure (0 °C and 1 atm), 1

mole of any gas occupies 22.4 L (i.e. 22.4 L/mol)

Example Problems1. At STP, the density of a certain gas is 4.29 g/L. What is the

molecular mass of the gas?(4.29 g/L) x (22.4 L/mol) = 96.1 g/mol

2. Acetylene (welding gas), C2H2, is produced by hydrolysis of calcium carbide.

CaC2(s) + 2 H2O --> Ca(OH)2(s) + C2H2(g)

Starting with 50.0 g of CaC2, what is the theoretical yield of acetylene in liters, collected at 24 °C and a pressure of 745 torr?1st find yield in moles:

Now use ideal gas law to find volume of C2H2:

PV = nRT V =nRT

P

V =(0.780 mol) x (0.0821 L atm /mole K) x (297 K)

(745 torr) x (1 atm/760 torr)= 19.4 L

50.0 g CaC2 x1 mole CaC2

64.1 g CaC2

x1 mole C2H2

1 mole CaC2

= 0.780 mol C2H2

Dalton’s Law of Partial Pressures• For a mixture of gases: Ptotal = Pa + Pb + Pc + …

• Mole fraction: Xa = moles a/total moles = Pa/Ptotal

• Gases are often prepared and collected over water:Ptotal = Pgas + Pwater

where Pwater = vapor pressure of water (depends on temperature)

e.g. at 25 °C, Pwater = 23.8 torr

at 50 °C, Pwater = 92.5 torr

Example ProblemA sample of N2 gas was prepared and collected over water

at 15 °C. The total pressure of the gas was 745 torr in a volume of 310 mL. Calculate the mass of N2 in grams. (vapor pressure of water at 15 °C = 12.8 torr)

Answer: Ptotal = Pgas + Pwater

745 torr = Pgas + 12.8 torr

Pgas = 732 torr

PV = nRT n =RTPV

mass N2 = (0.012624 mol N2) x (28.014 g N2/mol N2) = 0.354 g N2

n = (732 torr) x (1 atm/760 torr) x (0.310 L)

(0.0821 L atm/mol K) x (288 K)= 0.012624 mol N2

Kinetic Theory of Gases -- READ BOOKBasic Postulate -- A gas consists of a very large number of

very small particles, in constant random motion, that undergo perfectly elastic collisions with each other and the container walls.

There is a distribution of kinetic energies of the particles. Temp ∝ average KE

The kinetic theory “explains” the gas laws, pressure, etc. based on motion and kinetic energy of gas molecules.

e.g. Boyle’s Law (P ∝ 1/V) ~ at constant Temp (same average KE)If volume of container is reduced, there are more gas particles per unit volume, thus, more collisions with the container walls per unit area.

higher pressure

Temperature & Molecular Velocities• Kinetic molecular theory states that all particles have the same

average kinetic energy at a given temperature.

KE = ½mv2

• If m is smaller, v is bigger! i.e. small particles move faster.

Quantitatively,

where urms = root mean square velocity (a kind of average),

M = formula mass (in kg/mol!),

and R = universal gas constant, but in J/mol∙K rather than L∙atm/mol∙K!

R = 8.314 J/mol∙K = 0.0821 L∙atm/mol∙K

urms =3RT

M

Graham’s Law of Effusion• diffusion “mixing” of gases throughout a given

volume• effusion “leaking” of a gas through a small opening• mean free path average distance between collisions

Graham’s Law: effusion rate ∝ 1/√ M where M = formula mass

So, effusion rates of two gases can be compared as a proportion:

e.g. He (FM = 4.0 g/mol) effuses 2 times faster than CH4 (FM = 16.0)

rateA

rateB

=MB

MA

Real Gases -- Deviations from Ideal Gas Law

For real gases, small corrections can be made to account for:– Actual volume of the gas particles themselves, and– intermolecular attractive forces

One common approach is to use the Van der Waals’ Equation:

Don’t memorize!

where a and b are empirical parameters that are dependent on the specific gas (e.g. Table 5.5)

a ≈ intermolecular attractive forcesb ≈ molecular size

2

P + a (V – nb) = nRTnV

Sample ProblemsHydrogen gas is produced when metals such as aluminum

are treated with acids. Calculate the volume (in mL) of 0.500 M HCl solution that is required to produce a total gas pressure of 725 torr in a 2.50-L vessel if the hydrogen gas (H2) is collected over water at 25 °C. (The vapor pressure of water at 25 °C is 24 torr.)

2 Al(s) + 6 HCl(aq) --> 2 AlCl3(s) + 3 H2(g)

A gas mixture contains 25.0 g of CH4, 15.0 g of CO and 10.0 g of H2. If the total pressure of the mixture is 1.00 atm, what is the partial pressure of CH4 in torr?

Sample ProblemsHydrogen gas is produced when metals such as aluminum

are treated with acids. Calculate the volume (in mL) of 0.500 M HCl solution that is required to produce a total gas pressure of 725 torr in a 2.50-L vessel if the hydrogen gas (H2) is collected over water at 25 °C. (The vapor pressure of water at 25 °C is 24 torr.)

2 Al(s) + 6 HCl(aq) --> 2 AlCl3 + 3 H2(g)

Answer: 377 mL

A gas mixture contains 25.0 g of CH4, 15.0 g of CO and 10.0 g of H2. If the total pressure of the mixture is 1.00 atm, what is the partial pressure of CH4 in torr?

Answer: 168 torr

Chemistry in the Atmosphere• Air Pollutants

– SOx

• e.g 2 SO2(g) + O2(g) + 2 H2O(g) 2 H2SO4(aq) acid rain

– NOx

• e.g. 4 NO2(g) + O2(g) + 2 H2O(g) 4 HNO3(aq) acid rain

– O3 (ozone)

– CO– solid particles

• Ozone Layer– Stratospheric ozone ≠ ground-level ozone– CFC’s produce Cl, and

• O3(g) + UV light O2(g) + O(g)

• Cl(g) + O3(g) ClO(g) + O2(g)

• ClO(g) + O(g) Cl(g) + O2(g)

– Freons are being replaced by other less harmful refrigerants.