Gases and gas laws

Chapter 12

1. Understand basic characteristics of gases.2. Know the definition of pressure and measurement units commonly used

with pressure3. Know what a barometer measures.4. Know the relationships described by Boyle’s Law, Charles’ Law, and

Avogadro’s Law.5. Know the ideal gas equation and it’s derivation.6. Understand gas density and using molar masses in the ideal gas

equation.7. Understand Dalton’s law of partial pressures and its applications.8. Know the basic principles of the kinetic theory of gases and how this

explains gas behavior described by the ideal gas laws.9. Know the terms effusion and diffusion; know Graham’s law of effusion.10. Understand gas interactions that cause deviations from ideal gas law

behavior.

Key concepts

Common characteristics of gases (uniquely different from liquids or solids)

• All gas mixtures are homogeneous mixtures.

• Gases expand to fill the container they occupy– the volume of EACH GAS in a mixture of gases in a

container = volume of the container.

• The actual space occupied by the gas molecules is small relative to the total volume.

Pressure

• Force applied per unit area

P = F/A

• The same force may result in much different pressures…

Pressure units

• pounds per square inch (psi) • inches of mercury (in Hg) • mm Hg• Pascals (SI units)• torr (from Torricelli, inventor of the barometer)

– 1 torr = 1 mm Hg• standard atmospheric pressure

– 760 torr = 1 atmosphere (atm); typical pressure at sea level.

• conversions:– 1 atm = 760 torr = 1.01325 105 Pa = 14.7 psi

The barometer

• Mercury barometer:– atmospheric pressure

force applied on Hg the change in height of mercury column.

http://www.usatoday.com/weather/wbaromtr.htm

Basic Gas Laws

• Relationships between gas pressure, temperature, volume, and amount (moles).

• Now, let’s have some fun….

Boyle’s Law

• Boyle’s law relates to changes in pressure and volume.

• At constant temperature, the change in pressure is ________ proportional to the change in volume.

Charles’ Law

• Charles’ Law relates changes in volume and temperature

• At constant pressure, the change in volume is _______ proportional to the change in temperature

Avogadro’s Law

• Identical volumes of a gas at the same temperature and pressure have the same number of gas particles.

Summary

• P 1/V (constant n and T) (Boyle)

• V T (constant n and P) (Charles)

• V n (constant T and P) (Avogadro)

• Combined, we get….

PV=nRT; the ideal gas equation

• Gases that can have their temperature, volume, and pressure characteristics completely described by this equation are called ideal gases.

• R = the gas constant. It’s units vary depending on the units of P, V, and T.

• If • P is in atm, • V is in L, • T is in K, • STP = standard temperature and pressure. Defined as

1 atm and 0 C (273.15 K).• What is the molar volume of a gas at STP?

Kmol

atmLR

08206.0

Using ideal gas equation to represent gas laws.

1. Boyle’s Law.– PV = nRT– P and V will change, but n, R and T are

constant.

2. Charles’ Law

• PV = nRT

• V and T will change, but n, R, and P are constant.

3. P, V, and T all change, but n is constant– PV = nRT

More applications of the ideal gas equation.

• Obtaining the density of a gas: – from PV = nRT…

• d = PM/RT (where M is the molar mass)

volumes of gases in chemical reactions.

• air bags.– 2 NaN3(s) 2 Na (s) + 3 N2 (g)

– air bag volume: 36 L; pressure 1.15 atm; temperature 26.0 C. How much NaN3, in g, needed?

• 2 KClO3 (s) 2 KCl (s) + 3 O2 (g)

• volume of O2 produced when 1.50 g KClO3 decomposes?

Gas mixtures and partial pressures

• Dalton’s Law of partial pressures:– from PV = nRT….

• Ptotal = P1 + P2 + P3 + ….

• collecting gases over water—the gas is not alone….

Kinetic molecular theory of gases.

• An explanation of what happens at the molecular level that causes the observations in the ideal gas laws.

1.Gases consist of large numbers of molecules in continuous random motion.

2.The volume of all the molecules of gas is negligible compared to the total volume (i.e., each gas molecule is basically an infintessimally small dot).

3.Attractive and repulsive forces between molecules are negligible.

4. Energy transitions between molecules are perfectly elastic. The average kinetic energy of the molecules will not change over time as long as the temperature stays constant.

5. The absolute temperature is proportional to the average kinetic energy of the gas. At any given temperature all gases in the mixture have the same average kinetic energy.

• KE = ½ mu2. u = the root mean square (rms) speed of the gas. (root mean square is an averaging technique, though it is not the same as the average)

The kinetic theory explains the gas law

Important observations:• volume increases at constant temperature

(Boyle’s law). Molecules must travel further to reach the wall of a larger container. Thus, collisions against the container wall are less frequent, the pressure therefore drops.

• Temperature increases at constant volume (Charles’ Law). when temperature (and kinetic energy) increase, the speed of the molecules increases. Faster molecules collide with the container walls more often, so pressure increases.

Effusion and diffusion

• effusion –

• diffusion –

• Lighter molecules move faster than heavier molecules

MRT

u3

Graham’s Law of effusion

• the rate of effusion is twice as fast for r1 if M1 is 4 times lighter than M2.

12

1

M

M2r

r

Diffusion vs. effusion

• Diffusion is complicated by the presence of other molecules. The mean free path is a determining factor.

• Mean free path –

Real gases

• Assumptions in kinetic theory of gases not always valid.– Molecules are not

infinitely small– Attractive and

repulsive forces are not negligible.

– Collisions are not always elastic.

Deviations from ideality

• for one mole of an ideal gas (n=1). PV/RT always = 1.

• For ANY amount of ideal gas, PV/nRT = 1

• However, for real gases, PV/nRT doesn’t always = 1.

• Ideal gas equation is better in some regions than in others.

1

RT

VP

nRT

PV

Deviations more likely to occur at…

• low temperature: Molecules moving slower, intermolecular forces become a greater factor (especially near liquid/gas interface).

• Higher pressure: Molecule size becomes an greater factor; interfering with travel of molecules.

• Corrections to ideal gas equation are made to take this into account.– Van der Waal’s equation is one example