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Chapter 5. Gases. Overview. Gas Laws Gas Pressure and its measurement Empirical gas laws Ideal gas laws Stoichiometry and gases Gas Mixtures; Law of partial pressures Kinetic and Molecular Theory Kinetic theory of an Ideal gas Molecular speeds: diffusion and effusion Real gases.

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overview
Overview
  • Gas Laws
    • Gas Pressure and its measurement
    • Empirical gas laws
    • Ideal gas laws
    • Stoichiometry and gases
    • Gas Mixtures; Law of partial pressures
  • Kinetic and Molecular Theory
    • Kinetic theory of an Ideal gas
    • Molecular speeds: diffusion and effusion
    • Real gases
gases and gas pressure
Gases and Gas Pressure
  • They form homogeneous solutions. All gases dissolve in each other.
    • Gases are compressible.
    • Large molar volume.
  • Barometer usually mercury column in tube; mm Hg is a measure of pressure.
  • Manometer tube of liquid connected to enclosed container makes it possible to measure pressure inside the container.
  • Pressure
    • One of the most important of the measured quantities for gases
    • defined as the force/area P = f/area.
    • Pressure has traditionally been measured in units relating to the height of the Hg and is thus expressed as mm Hg = 1 Torr.
gas pressure
Gas Pressure
  • Pressure is directly proportional to the height of the column in a barometer or manometer.
  • Mercury often used but other low density liquids are used for low pressure changes:

P = dHgghHg = doilghoil or dHghHg = doilhoil.

  • E.g. Water is sometimes used to determine pressure; determine the height of water if the barometer pressure was 750 mmHg. The density of Hg = 13.596 g/cm3 and 1.00 g/cm3 respectively.
  • Solution:
the gas laws
The Gas Laws
  • Boyle's Law: For a fixed amount of gas and constant temperature, PV = constant.
  • Charles's Law: at constant pressure the volume is linearly proportional to temperature. V/T = constant
  • Avagadro’s law for a fixed pressure and temperature, the volume of a gas is directly proportional to the number of moles of that gas. V/n = k = constant.

E.g. 1 The volume of some amount of a gas was 1.00 L when the pressure was 10.0 atm; what would the volume be if the pressure decreased to 1.00 atm?

E.g. 2 A gas occupied a volume of 6.54 L at 25°C what would its volume be at 100°C?

E.g. 3 The volume of 0.555 mol of some gas was 100.0 L; what would be the volume of 15.0 mol of the same gas at the same T and P?

the ideal gas equation
The Ideal Gas Equation
  • Ideal gas law the functional relationship between the pressure, volume, temperature and moles of a gas. PV = nRT; all gases are ideal at low pressure.
  • PV =nRT. Each of the individual laws is contained in this equation.
  • Boyle's Law: PV = k1 = nRT.
  • Charles's Law:
  • Avagadro’s law:
  • When any of the other three quantities in the ideal gas law have been determined the last one can be calculated.

E.g. Calculate the pressure inside a TV picture tube, if it's volume is 5.00 liters, it's temperature is 23.0C and it contains 0.0100 mg of nitrogen.

further applications of ideal gas equation
Further Applications of Ideal-Gas Equation
  • The density of a gas the density of a gas can be related to the pressure from the ideal gas law using the definition of density: d = mass/vol.

E.g. Estimate the density of air at 20.0C and 1.00 atm by supposing that air is predominantly N2.

E.g. From the results above determine the density of He.

  • Rearrangement permits the determination of molecular mass of a gas from a measure of the density at a known temperature and pressure.

E.g. A certain gas was found to have a density of 0.480 g/L at 260C and 103 Torr. Determine the FM of the compound.

stoichiometric relationships with gases
Stoichiometric Relationships with Gases
  • When gases are involved in a reaction, das properties must be combined with stoichiometric relationships.

E.g. Determine the volume of gas evolved at 273.15 K and 1.00 atm if 1.00 kg of each reactant were used. Assume complete reaction (i.e. 100% yield)

CaO(s) + 3C(s)  CaC2(s) + CO(g).

  • Strategy:
    • Determine the number of moles of each reactant to which this mass corresponds.
    • Use stoichiometry to tell us the corresponding number of moles of CO produced.
    • Determine the volume of the gas from the ideal gas law.
partial pressure and dalton s law
Partial Pressure and Dalton’s Law
  • Dalton's Law = the sum of the partial pressures of the gases in a mixture = the total pressure or P = PA + PB + PC + ...where Pi = the partial pressure of component i.
  • Dalton found that gases obeying the ideal gas law in the pure form will continue to act ideally when mixed together with other ideal gases.
  • The individual partial pressures are used to determine the amount of that gas in the mixture, not the total pressure, PA = nART/V.
  • Since they are in the same container T and V will be the same for all gases.

E.g. 1.00 g of air consists of approximately 0.76 g nitrogen and 0.24 g oxygen. Calculate the partial pressures and the total pressure when this sample occupies a 1.00 L vessel at 20.0C.

    • Solution:
      • Determine the number of moles of each gas.
      • Using the ideal gas law determine the pressure of each and sum to determine the total pressure.
partial pressure and dalton s law2
Partial Pressure and Dalton’s Law2
  • Mole fraction another quantity commonly determined for gas mixtures. It is defined the number of moles of one substance relative to the total number of moles in the mixture or
  • X can be calculated from
    • moles of each gas in the mixture or
    • the pressures of each gas

E.g. determine the mole fraction of N2 in the above example.

  • Collection of a gaseous product over water is another example of Dalton's Law. Subtract the vapor pressure of water to find the pressure of the gaseous product.

E.g. Suppose KClO3 was decomposed according to

2 KClO3(s)+  2KCl(s) + 3O2(g).

PT = 755.2 Torr and 370.0 mL of gas was collected over water at 20.0C. Determine the number of moles of O2 if the vapor pressure of water is 17.5 torr at this temperature.

the behavior of real gases
The Behavior of Real Gases
  • The molar volume is not constant as is expected for ideal gases.
  • These deviations due to an attraction between some molecules.
  • Finite molar molecular volume.
  • For compounds that deviate from ideality the van der Waals equation is used:

where a and b are constants that are characteristic of the gas.

  • Applicable at high pressures and low temperatures.
the kinetic theory molecular theory of gases
The Kinetic Theory – Molecular Theory of Gases
  • Microscopic view of gases is called the kinetic theory of gases and assumes that
    • Gas is collection of molecules (atoms) in continuous random motion.
    • The molecules are infinitely small point-like particles that move in straight lines until they collide with something.
    • Gas molecules do not influence each other except during collision.
    • All collisions are elastic; the total kinetic energy is constant at constant T.
    • Average kinetic energy is proportional to T.
the kinetic theory molecular theory of gases13
The Kinetic Theory – Molecular Theory of Gases
  • Theory leads to a description of bulk properties i.e. observable properties.
  • The average kinetic energy of the molecule is

where NA = Avagadro’s number.

  • Average kinetic energy of moving particles can also be obtained from

where u = average velocity

  • All speeds are possible giving really a distribution of speeds.
  • Combine 1 & 2 to get a relationship between the velocity, temperature and molecular mass.
  • Express M in kg/mol and R = 8.3145 J/mol*K.

E.g. determine average velocity of He at 300 K.

E.g.2 predict the ratio of the speeds of some gas if the temperature increased from 300 K to 450 K.

graham s law diffusion and effusion of gases
Graham’s Law: Diffusion and Effusion of Gases
  • Diffusion the process whereby a gas spreads out through another gas to occupy the space with uniform partial pressure.
  • Effusion the process in which a gas flows through a small hole in a container.
  • Graham’s law of Effusion the rate of effusion of gas molecules through a hole is inversely proportional to the square root of the molecular mass of the gas at constant temperature and pressure.

E.g. determine the molecular mass of an unknown compound if it effused through a small orifice if it effused 3.55 times slower than CH4.

E.g. A compound with a molecular mass of 32.0 g/mol effused through a small opening in 35 s; determine the effusion time for the same amount of a compound with a molecular mass of 16.0.