Gas Laws Chapter 5

PressureForce per unit areaMeasured in

Atmospheres (atm)Mm of Hg = TorrPascals or kiloPascals (Pa or kPa)

Conversions1 mm = 1 torr1 atm = 760 mm1 atm = 101 325 Pa1 atm = 101.325 kPa

Example Problem

Convert 4.39 atm to torr, Pa, and kPa.

Example Problem

Convert 369 mm to atm and kPa.

Example Problem

Convert 109 821 Pa to kPa, atm, and torr.

Boyle’s LawPressure and volume vary inversely

PV = k or P1V1 = P2V2

Sample ProblemAs part of the training for high

altitude flight, pilots and flight crews are placed in a hypobaric chamber where the pressure is dropped to approximately .250 atm to simulate the thinner atmosphere at altitude. If a person’s stomach has a 30.0 ml gas bubble when they enter the chamber, what will be the new volume of the bubble at “altitude”?

In your Scientist’s Notebook:

The pressure of water increases as depth increases. If you immerse a balloon containing 1.25 L of air in 10.0 meters of water, the new pressure is 1.10 atm. What will be the volume of the balloon?

Charles LawTemperature and volume are directly proportional

V/T = K or V1/T1 = V2/T2

Example Problem

A 10.0 ml canister of compressed carbon dioxide at room temperature (25* C) is allowed to expand into a balloon with a volume of 3.00 liters. Assuming the pressure remained constant, what is the new temperature?

In your Scientist’s Notebook:

A balloon contains 534 ml of gas at 22.0o C. If the temperature increases to 44o C, what is the new volume of the balloon?

Gay-Lussac’s Law

Temperature and pressure vary directly

P/T = K orP1/T1 = P2/T2

Example Problem

The pressure inside your basketball is only 2.20 atm., and it has lost its bounce. You put it in the sun to warm its temperature from 19.2o C to 27o C. Assuming very insignificant volume change, what is the new pressure?

In your Scientist’s Notebook

When you leave for school on a chilly morning (5.00oC), the pressure in your car tires is 29.6 psi. What is the pressure after you have driven to school and friction with the road increased the temperature to 28.0oC?

Combined Gas Law

All three of the preceding laws can be combined into one equation:

P1V1 P2V2

T1 T2

=

Example Problem

A weather balloon at the surface (25o C and 760 torr) has a volume of 425 L. What is the volume at 25 000 feet where the pressure is 245 torr and the temperature is -35o C?

In your Scientist’s Notebook:

A whale releases 34.5 ml of air under water where pressure is 4.32 atm. The volume of the air bubble at the surface is 170. ml. The temperature and pressure at the surface are 28.0*C and 1.00 atm. What was the temperature under the water?

Avogadro’s LawVolume is directly proportional to the # of moles of gas

V/n = K orV1/n1 = V2/n2

Combined or Ideal Gas LawPV = nRTR = 0.08206 L atm/K mol

Example Problem:

What mass of oxygen gas occupies 34.5 L at 1.5 atm and 27* C?

In your Scientist’s Notebook:

What mass of carbon dioxide is needed to fill a 3.0 L fire extinguisher at 25.0* C with a pressure of 5.64 atm?

Example Problem

The density of a gas at 1.50 atm and 27* C is found to be 1.95 g/L. What is the molar mass of the gas?

In your Scientist’s Notebook:What is the atomic mass of an

elemental gas that has a density of .178 g/L at 0.00* C and 1.00 atm?

What is the gas?

Example

What is the volume of 1.00 mole of a gas at 0* C and 1.00 atm pressure?

Example Problem

What is the volume of 2.00 moles of a gas at 0* C and 1.00 atm?

STPStandard Temperature and Pressure

0* C or 273 K1.000 atm

Molar Volume1 mole of any gas at STP

has a volume of

22.414 L

Example Problem

What is the density of oxygen at STP?

In your Scientist’s Notebook:The density of an elemental gas at STP is 3.16 g/L. What is the gas?

Dalton’s LawThe total pressure of a mixture of gases is equal to the sum of the partial pressures of all gases present.

Ptotal = P1 + P2 + P3 . . .

Example Problem

Air is a mixture of gases in the following percentages: N2--78.1% ; O2—20.9%; Ar--0.93%; CO2—0.035%. At 760. torr, what is the partial pressure of each gas?

Example Problem

Oxygen was collected over water at a temperature of 22* C and a pressure of 754 torr. If water’s vapor pressure at this temperature is 21 torr, what is the partial pressure of the oxygen?

Kinetic Molecular TheoryA model that explains the

behavior of individual gas particles

Oversimplifies the true nature of gases for ease of understanding

Ideal Gases1. Particles have no volume2. Rapid, random motion &

collisions with the walls of the container cause pressure

3. No attraction between particles so collisions are perfectly elastic

4. Kinetic energy is directly proportional to Kelvin temperature

Ideal GasesHypothetical—none really exist

Conditions approach ideal as temperature increases and pressure decreases.

Deviations from Ideal

“Concentrated” gases hit the sides of a container slightly less often—lower P

Gases with attraction for each other have lower pressure and lower energy

Volume of particles becomes significant at small overall volumes

How Does KMT Account for:

Boyle’s Law (V & P)—less volume should produce more collisions so pressure increases (and vice versa)

Gay-Lussac’s Law (P & T)—at increased temperature, particles collide with greater energy producing higher pressure

How Does KMT Account for:

Charles’s Law (V & T)—at higher temperature, particles collide with greater energy & can expand a flexible container

Avogadro’s Law—individual particles have no volume or attractions—should all occupy the same molar volume

Meaning of Temperature

Temperature = average kinetic energy of particles

The relationship between temperature and energy:(KE)avg = 3/2 RT

R = 8.3145 J/K mol

What is the average kinetic energy of He particles at 67oC?

(KE)avg = 3/2 RT

What is the average kinetic energy of Ne particles at 67oC?

What is the average kinetic energy of Cl2 particles at 67oC?

Velocity of Gas Particles

Since kinetic energy depends only on temperature, how does mass affect the motion of the particles?

KE = ½ mv2 and KE = 3/2 RT Since kinetic energy must remain

the same, velocity must decrease as mass increases.

Root Mean Square Velocity

R = 8.3145 J/K mol T = Kelvin Temperature

M = mass of 1 mole of particles in kgSince a joule = kg m2/s2, units

cancel leaving m/s (velocity)

Calculate the root mean square velocity of atoms in helium gas at 25oC.

Graham’s LawDiffusion—the mixing of gases

Effusion—passage of gas molecules through a small opening

Graham’s LawAt equal temperatures, the rate of effusion is inversely proportional to the square root of the molar mass

Graham’s Law Equation

Rate of effusion1 M2

Rate of effusion 2 M1

=

Example Problem

How much faster will H2 effuse than O2?

Example Problem

Samples of hydrogen gas and chlorine gas are placed at opposite ends of a tube that is 1.00 m long. At what distance from the hydrogen end will the reaction which forms HCl occur?

In your Scientist’s Notebook:

A vial of ammonia (NH3) and chlorine gas are opened simultaneously. You detect the odor of ammonia in 15 seconds. How long will it be before you detect the chlorine?