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Properties of Gases. Important 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/area Units of pressure: SI unit is the pascal (Pa)

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properties of gases
Properties of Gases

Important 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/area

Units 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 torr

1 atm = 760 torr = 760 mm Hg

Exact!

measuring pressure
Measuring Pressure

Barometer

Manometer

pressure volume temperature relationships
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
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•Kmemorize!

{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 problems
Example Problems
  • 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

  • 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:

dalton s law of partial pressures
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 problem
Example Problem

A 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

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

= 0.012624 mol N2

n =

(0.0821 L atm/mol K) x (288 K)

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

kinetic theory of gases read book
Kinetic Theory of Gases -- READ BOOK

Basic 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
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
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

MB

=

MA

rateB

real gases deviations from ideal gas law
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 forces

b ≈ molecular size

2

n

P + a (V – nb) = nRT

V

sample problems
Sample Problems

Hydrogen 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?

chemistry in the atmosphere
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.