Gases and their Laws

Pressure (P)

Force/Area = N/cm3

Force/Small Area = Greater Pressure

Force/Large Area = Less Pressure

1 atm of atmospheric pressure at sea level

= 10.1 N/cm3

Measuring PressureAir pressure is measured using a

barometer

Two of the most common barometers

are the mercury barometer and the

aneroid barometer

Units of PressureUnit Symbol Conversions

Pascal Pa 1 Pa = 1 N/m2

Millimeter of Mercury mm Hg 760 mm Hg = 1 atm

Torr torr 1 torr = 1 mm Hg

Atmosphere atm *See below

Pounds per square inch psi 14.700 psi = 1 atm

Normal atmospheric pressure:

1 atm = 760 mm Hg (torr) = 101.3 kPa

Dalton’s Law of Partial Pressure

The total pressure of a mixture of

nonreacting gases is equal to

the sum of the partial pressures

of the individual gases

Ptotal = P1 + P2 + P3 + and so on…

Dalton’s Law of Partial Pressure

Dalton found that the total pressure of mixed

gases is equal to the sum of their individual

pressures (provided the gases do not react).

Ptotal = Poxygen + Pnitrogen

+

1 L oxygen

50 kPa

1 L nitrogen

100 kPa

1 L mixed gas

150 kPa

=

Note: all of these volumes are the same

Practice Problems with

Dalton’s Law1. Calculate the partial pressure in millimeters of

mercury exerted by the four main gases in the

air at 760 mm Hg. The gases abundance by

volume is as follows 78.08% N2, 20.95% O2,

0.934% Ar, and 0.035% CO2

2. A student has stored 100.0 mL of neon gas

over water on a day when the temperature is

27.0°C. If the barometer in the room reads

743.3 mm Hg, what is the pressure of the neon

gas in its container? (Water vapor pressure =

26.7 mm Hg)

Boyle’s Law: Pressure-Volume

If pressure increases volume decreases

If pressure decreases volume increases

Inverse relationship between pressure

and volume (PV = k)

P1V1 = P2V2

(At constant temperature)

Practice Problems with

Boyle’s Law1. The piston of an internal combustion engine

compresses 450.0 mL of gas. The final

pressure is 15 times greater than the initial

pressure. What is the final volume of the

gas, assuming constant temperature?

2. A helium-filled balloon contains 125 mL of

gas at a pressure of 0.974 atm. What

volume will the gas occupy at standard

pressure?

The study of gases in early 1800's in France concerned hot air balloons popularity and wanting to improve the performance of the balloons

Jacques Charles and Joseph-Louis Gay-Lussac (French scientists) were interested in the temperature-volume-pressure relationship for a gas in a hot air balloon

Charles and Gay-Lussac

Charles's Law: Volume-

TemperatureIf temperature increases volume increases

If temperature decreases volume decreases

Direct relationship between temperature and

volume (V/T = k) *Temperature must be in KELVIN

V1/T1 = V2/T2

(at constant pressure)

Practice Problems with

Charles’s Law1. Assume constant pressure: A balloon filled

with oxygen gas occupies a volume of 5.5 L

at 25°C. What volume will the gas occupy

at 100.0°C?

2. A sample of nitrogen gas is contained in a

piston with a freely moving cylinder. At

0.0°C, the volume of the gas is 375 mL. To

what temperature must the gas be heated

to occupy a volume of 500.0 mL?

Gay-Lussac's Law: Pressure-

TemperatureIf temperature increases pressure increases

If temperature decreases pressure decreases

Direct relationship between temperature and

volume (P/T = k) *Temperature must be in KELVIN

P1/T1 = P2/T2(at constant volume)

Practice Problems with

Gay-Lussac’s Law1. Assume a gas was at a constant volume: A

gas cylinder at room temperature (20°C) is

thrown into an incinerator where the

temperature reaches 500.0°C. If the gas

inside the container was initially at a

pressure of 1.0 atm, what pressure did it

reach inside the incinerator without

exploding?

The Combined Gas LawPressure-Volume-Temperature

Relationship of a gas at a

FIXED amount (PV/T = k)Temperature must be in Kelvin

P1V1/T1 = P2V2/T2

Practice Problems with

Combined Gas Law1. The volume of a gas at 27.0°C and

0.200 atm is 80.0 mL. What volume will

the same gas sample occupy at

standard conditions?

2. A gas occupying 75 mL at standard

conditions is heated to 17°C while the

pressure is reduced to 0.97 atm. What

is the new volume occupied by the gas?

Avogadro’s Law Equal volumes of gases at the same

temperatures and pressure contain

equal number of molecules

V = kn

n is moles of gas

Coefficients in reactions involving

gases = the relative # of molecules,

moles, and volumes

Practice Problems with

Avogadro’s LawOzone, O3, can be formed from diatomic

oxygen in the following reaction:

3O2(g) 2O3(g)

1. How many molecules of ozone are

formed from the reaction of 24 oxygen

molecules?

2. How many liters of ozone are formed

from 12 L of oxygen?

Volume at STPStandard Molar Volume: The volume

occupied by 1 mole of a gas at

standard temperature and pressure

1 mol = 22.4 L (at STP)

You are planning an experiment that requires 0.0580 mol

of NO. What volume would you need at STP?

Answer: 1.2992 L

Ideal Gas LawRelationship between: pressure-

volume-temperature-# of moles

PV = nRTn = # of moles

R = Universal Gas Law Constant

8.3145 J/mol K

Other values of R on Table 2 pg 384

Practice Problems with

Ideal Gas LawA 2.07 L cylinder contains 2.88 mol

of helium gas at 22°C. What is the

pressure in atmospheres of the

gas in the cylinder?

Graham’s Law of EffusionThe rates of effusion of gases at the

same temperature and pressure are

inversely proportional to the square

roots of their molar masses

½ MAvA2 = ½ MBvB

2

rate of effusion of A = √MB

rate of effusion of B √MA

MA = molar mass of gas A

vA = velocity of gas A

Practice Problems with

Graham’s Law

At 25°C, the average velocity of

oxygen molecules is 420 m/s.

What is the average velocity

of helium atoms at the same

temperature?