Chapter 9 - The Gaseous State

I. Nature of Gases - Properties

• Gases are compressible.
• Gases have low densities. (typically 2 x 10-3 g/mL)
• Gases Mix Thoroughly.
• Gases fill a Container Uniformly.
• A Gas exerts Pressure Uniformly on all sides of a container.

II. Kinetic Molecular Theory

1. a gas is composed of very small particles widely spaced. a gas is composed mostly of empty space.
2. the molecules of a gas are in rapid, random motion, colliding with each other and the sides of the container. Pressure is a result of these collisions.
3. All collisions involving gas molecules are elastic (inelastic - ball bouncing gets lower and lower each time).
4. gas molecules have negligible attractive (or repulsive) forces between them.
5. The temperature of a gas is related to the average kinetic energy of the gas molecules. (At the same temp. diff. gases have the same average KE).

 

III. Relative velocity of gas molecules

KE = ½mv²
where, m = mass and v = velocity

• Looking at # 5 above:
  • KE(gas 1 ) = ½m₁v₁²
  • KE(gas 2) = ½m₂v₂²
  • KE(gas 1 ) = KE (gas 2)

Þ

• DIFFUSION - mixing of gas molecules
• EFFUSION - moving through an open hole
• GRAHAM’S LAW - the rates of diffusion of gases are inversely proportional to the square roots of their molar masses. (i.e. the lighter the molecule the faster the velocity).

Example:

Relative velocities of Neon and Oxygen.

IV. Pressure - the force applied per unit area

P(pressure) =

• One Atmosphere (1 atm) - the average pressure of the atmosphere at sea level (standard for pressure).

1.00 atm = 76.0 cm Hg = 760 mm Hg = 760 torr
(1 torr = 1 mm Hg; named in honor of Torricelli)
Table 9-1 lists units of pressure equivalent to 1 atm.

V. Boyle's Law

• (Relationship between volume and pressure) - there is an inverse relationship between the pressure exerted on a quantity of gas and its volume if the temperature is held constant.

proportionality constant k

Examples:

VI. Charle's Law

• ( relationship between volume and temperature)the VOLUME of a gas is DIRECTLY proportional to the TEMPERATURE in Kelvin (T) at constant pressure.

Examples:

VII. Absolute Zero

• the lowest possible temperature known - temp. at which now translational motion (everything is solid).
• T(K) = t( ° C) + 273K

VIII. Gay-Lussac’s Law

• (relates pressure and temperature) the PRESSURE is DIRECTLY proportional to the Kelvin TEMPERATURE at constant volume.

P a T or P = kT

Examples:

IX. Avogadro’s Law

• (relates volume to number of moles) equal volumes of gases at the same pressure and temperature contain equal number of moles.

V a n or V = kn

Examples:

X. The Ideal Gas Law

• Combine Boyle’s Law, Avogadro’s Law, and Charles’ Law

• Into one general relationship

V a

• Using the gas constant it becomes:

V = nRT/P or PV = nRT

Examples:

XI. Standard Temperature and pressure (STP)

• Standard temperature: O° C or 273K
• Standard pressure: 760 torr or 1 atm

 

XII. Dalton’s Law of Partial Pressures

• the total pressure of a gas in a system is the sum of the partial pressures of each component gas.

P_T = P₁ + P₂ + P₃ + ....

Example:

XII. Molar volume

• the volume of one mole gas at STP = 22.4 L
• PV = nRT with P = 1 atm, V = ?, n = 1,
• R = 0.08206 L-atm/mol-K, and T = 273
• Plug in and solve for V: V = 22.4 L/mol

Examples:

XIII. Density of a gas

• at STP: V = 22.4 L/mol
• d = molar mass/ molar volume

XIV. Stoichiometry

• Add volumes of gas to our list of stoichiometry

example:

What volume of CO₂ is produced at STP when 22.3 g of C₂H₆ is reacted with excess oxygen?

What volume is produced when the Pressure is 560 torr and the T = 298 K?