Chapter 5 Gas Laws

1. Characteristics of Gases

2. Gas Laws

Pressure and it's Measurement

The Ideal Gas Law

Molar Mass and Gas Densities

Volumes of Gases in Chemical Reactions

Gas Mixtures and Partial Pressures

3. Kinetic-Molecular Theory

Kinetic Theory of an Ideal Gas

Molecular Effusion and Diffusion

Deviations from Ideal Behavior.

1. Characteristics of Gases

• Gases have indefinite shape and indefinite volume.
• Gases will expand to fill a container.
• Gases are highly compressible.
• Gases form solutions. That is, mixtures of gases are homogeneous.

2. Gas Laws

Pressure and it's Measurement

Review temperature conversions. Gas laws are based upon the absolute temperature scale, Kelvin.

Pressure- the force a substance exerts per unit of surface area.

Units of Pressure

See barometer and manometer diagrams.

Example: The gauge on a cylinder of compressed oxygen reads 1500 psi. Express this pressure in atm, torr, kPa, and mmHg.

The gas laws relate temperature (K), volume, pressure, and number of moles of matter present in the gaseous state. For our purposes, we will assume the gases we use are ideal and the laws apply to any gas.

Boyle's Law-T and n (moles of gas) are constant P= constant •(1/V)

Charles Law- P and n are constant V= constant •T

These two laws together give us the Combined Gas Law

Avagadro's Law- P and T are constant

Relates moles of gas to volume. The same no. of moles of any gas at the same T and P, occupy the same volume

Two gases are put into two separate piston containers where the volume will expand or contract. The gases are both at 20ºC and 1 atm pressure and you have two moles of gas 1 and four moles of gas 2. What is the relationship between the volumes of the two gases?

Gay-Lussac's Law- n and V are constant

Standard Temperature and Pressure (STP)

• Standard Temperature is 0ºC or 273K
• Standard Pressure is 760 torr or 1.000 atm.
• At STP, one mole of any gas occupies 22.4 L

Examples

1. A 1.5 L sample of gas was collected at a pressure of 1.8 atm. What volume will it have when the pressure is reduced to 1.0 atm?
   
   
   
   
   
   
2. A toy balloon is filled to volume of 5.0 L with helium gas at 25ºC. The balloon is then left in a closed car where the temperature increases to 75ºC. What is the volume of the balloon now?
   
   
   
   
   
   
3. Calculate the final volume of the balloon if the atmospheric pressure changes from 0.97 atm to 1.04 atm at a temperature of 25ºC and an initial volume of 5.0 L.
   
   
   
   
   
   
4. A sample of gas has a volume of 1.75 liters at 25ºC and 754 mmHg. At what temperature will it have a volume of 1.25 liters and a pressure of 725 mmHg?

The Ideal Gas Law

Example: A 2.50L flask was used to collect a 5.65 g sample of propane gas. (formula?). After the sample was collected, the gas pressure was found to be 741 mmHg. What is the temperature of the propane in the tank?

Molar Mass and Gas Densities

• Densities of gases are in g/L
• Molar masses are in g/mol

Examples:

1. Calculate the molar mass of a gas if it's density is 2.4 g/L at STP. mass= 2.4 g, V= 1 L
   
   
   
   
   
   
   
2. The density of dimethyl ether vapor is 0.940 g/L @25ºC and 380 torr. Estimate the molar mass of methyl ether. See diagram in text.
   
   
   
   
   
   

Volumes of Gases in Chemical Reactions

Back to stoichiometry. As long as the T, P and V are specified, we can use gas laws in combination with stoichiometry to do calculations! Write the balanced equations for the reactions.

Examples:

1. Solid mercury(II) oxide decomposes into liquid mercury and oxygen gas when heated. How many grams of mercury(II) oxide will produce 750 mL of oxygen gas measured at 30ºC and 0.975 atm?
   
   
   
   
   
   
2. What volume of hydrogen gas is produced in the reaction of 1.33 g of zinc metal and 300 mL of 2.33 M H₂SO₄? The gas is collected at 1.12 atm and 25ºC. Diagram in text.
   
   
   
   
   
   
3. The "air" that fills the air-bags installed in automobiles is actually nitrogen produced by the explosive decomposition of sodium azide, NaN₃ (s). Assuming the other product to be sodium metal, what volume of gas is released (at 25ºC and 1 atm from decomposition of 1.88 g of sodium azide?
   
   
   
   
   
   

Gas Mixtures and Partial Pressures

Dalton's Law of Partial Pressures- the total pressure exerted by a mixture of gases is equal to sum of the pressures of each gas (partial pressure).
P_t= P_a + P_b + P_c + ...

A table of the vapor pressure of H₂O at various temperatures is in the text. What is humidity?

Examples:

1. A sample of air is collected when the atmospheric pressure is 765 torr. If air is 78.1% N₂, 21.0% O₂, what is the % of the third major component Ar, and what are the partial pressures of each gas?
   
   
   
   

2. A sample of oxygen collected over water has a volume of 600 mL at 30ºC and a barometric pressure of 752 torr. Calculate the volume of dry oxygen at Standard Temperature and Pressure. STP is 0ºC, 1 atm.

3. Kinetic-Molecular Theory

Kinetic Theory of an Ideal Gas

KMT is the model used by scientists to explain the behavior of matter is its various states.

Postulates of the Kinetic Molecular Theory

1. Matter is composed of tiny particles whose volume is negligible.
2. The particles are in constant motion and therefore possess kinetic energy (KE= ¹/₂ mv² ). They travel in straight lines in all directions.
3. The force of attraction between molecules is negligible.
4. The particles transfer energy from one to another during collisions in which no net energy is lost from the system.
5. The average particle speed increases as the temperature increases. (KE proportional to temperature)

Molecular Effusion and Diffusion

Derived from the kinetic energy of two gases at the same T.

Graham's Law relates the rate of effusion or diffusion of two gases to the masses of the molecules.

Example: Helium gas is found to diffuse approximately three times as fast as an unknown gas. How do the masses of helium and the unknown gas molecules compare? (i.e. what is the molar mass of the unknown).

Deviations from Ideal Behavior.

Assumptions of the Ideal Gas Law: PV=nRT

• space between gas particles is large, so...
  • actual volume of gas particles is insignificant.
  • any attractive forces become insignificant.
• this is true when...
  • P is low

    very few particles, come into contact.

  • T is high

    KE > PE so the energy of motion overcomes any attractive forces

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van der Waal's Equation

P = nRT/(V-nb) – n²a/V² or

(P + n²a/V²) (V - nb) = nRT

These equations correct for a non-ideal gas with experimentally determined constants, a and b.

Example: Using both the ideal gas law and van der Waal's equation, calculate the pressure expected for 10.0 mol of He in a 1.00 L container at 25ºC. a=0.0346 L²atm/mol², b=0.0238 L/mol

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UpdatedSept. 20, 2003. Questions or comments on this Web site should go to Robin Terjeson.