Gas Laws

Table of Contents:

I. Kinetic Molecular Theory

II. Ideal vs. Real Gases

III. Vapor Pressure

IV. Avogadro's Law

V. Boyle's Law

VI. Charles' Law

VII. Gay-Lussac's Law

VIII. Combined Gas Law

IX. Dalton's Law of Partial Pressures

X. Ideal Gas Law

XI. Density of Gases

XII. Graham's Law of Diffusion

POWER POINT SLIDES

Gas Laws

I. Kinetic Molecular Theory

The four tenets (for our purposes) of the KMT of gases

A. The particles of a gas move in random straight-line motion.

check THIS SITE out

B. The volume of the gas particles themselves are insignificant

compared to the volume of the overall container.

C. The intermolecular forces of attraction (IMF's) between

particles are considered negligible (KE>IMF)

Why? gases are typically nonpolar and exhibit extremely weak VanDerWaals

forces, higher temp = faster motion

D. Collisions between particles is considered elastic meaning

no energy is lost.

What would happen to gases if this were not true?

II. Ideal vs. Real Gases

An ideal gas is a gas which obeys all of the tenets of the KMT and

adheres to gas law calculations all of the time.

There are NO ideal gases because, in truth, gas particles exhibit

some IMF's (however small) and can be liquefied

under conditions of high pressure and low temperature.

Therefore all gases are real gases which act like ideal gases under

all but the aforementioned conditions. The gases

with the smallest forces of attraction will be the most ideal, and

also the hardest to liquefy. The gases with relatively

large forces of attraction will be the least ideal and easiest to

liquefy.

MOST IDEAL GAS: #1 He (bp=4K) #2 H2(bp=20K)

LEAST IDEAL GASES: Rn (bp=211K), NH3(bp=240K),

H2O(bp=373K)

III. Vapor Pressure - CLICK HERE (for applet)

Definition: The upward force exerted by a liquid as it's particles

jump into the gaseous phase.

A. High vapor pressure (v.p.) - liquids with high vapor

pressure tend to have relatively weak IMF's therefore jump

easily into the gaseous phase.

1. Examples: Acetone, Ethanol, gasoline, perfumes

(notice that all of theses liquids give off a strong odor)

2. Table H - use this table to determine the v.p. of different

liquids at given temperatures.

B. Low vapor pressure - liquids with strong IMF's will not

readily turn into a gas

C. Boiling Point - The b.p. of any liquid is the temperature at

which it's Vapor Pressure = Atmospheric Pressure

D. Increasing the temperature of a liquid will increase it's

Vapor Pressure.

1. You will notice that the lower the vapor pressure of a

liquid the hotter you will need to heat it to get it to boil.

CHALLENGE QUESTION: What are the TWO ways to

get a liquid to boil?????

IV. Avogadro's Law - 1 mole of any gas at STP (273K,

101.3kPa) occupies 22.4 Liters

*see derivation under Ideal Gas Law notes.

V. Boyle's Law

A. History -

B. There is an INVERSE relationship between the pressure

and volume of a has at constant temperature.

1. As pressure on a gas increases it's volume will decrease

and vice versa.

a. Example: As the pressure on a gas is doubled it's

volume will be reduce to one half.

2. Any pressure x volume in this sample = constant. P x V

= k

3. Therefore P1 x V1 = P2 X V2

a. PRACTICE PROBLEMS:

(1) The pressure on 5 L of gas increases from

101.3 kPa to 202.6kPa at constant

temperature. What is the new volume it will

occupy? 2.5L

(a) The sample of gas initially at 2 atm and

occupying 6.4L is allowed to expand to

9.6L at constant temperature. What will the

new pressure be? 1.33 atm

(2) If the pressure on 30L a gas triples it’s

volume will be? 10L

b. ONLINE PRACTICE: CLICK HERE

ONLINE ANIMATION: CLICK HERE

VI. Charles' Law

A. History -

B. There is a DIRECT relationship between the

temperature(absolute) and volume of a gas at constant

pressure.

1. As the temperature of a gas increases it's volume also

increases proportionately. Therefore if you double

temperature (K) of a gas the volume will also double.

Halving the temperature will halve the volume.

2. You will notice from the graph above that dividing any

volume by it's corresponding temperature equals a

constant.

Therefore:

3. Practice Problems:

a. A 20 L sample of oxygen is heated from 20oC

to 40oC at constant pressure. What is the new

volume?

21.37L

b. What temperature must a 15 ml sample of

gas initially at 600K be changed to to occupy

5 ml?

200K

4. Online Practice: CLICK HERE

Online Animations: CLICK HERE

5. Demo: green-fountain--chemistry-experiment.mov

VII. Gay-Lussac's LawA.

B. This is the same relationship as Charles' Law therefore the

equation and the graph will be synonymous.

C. Practice Problem

1. The temperature on a gas at 50 kPa, at

constant volume, is raised from 200oC to

400oC. What is the new pressure in kPa, torr?

71.1 kPa , 533.7 torr

D. Cool online animation CLICK HERE

E. Green Fountain Demo CLICK HERE

VIII. The Combined Gas Law

The Combined Gas Law is nothing more than the combination of

the three laws we have just discussed. In most circumstances it is

preferable to simply use the CGL when answering questions

about temp, volume and pressure of any gaseous sample. It has

the advantage of being able to incorporate changing two variables

at once and still being able to calculate for the third. If anything

is held constant, simply cross that out of the equation.

A. Practice Problems:

1. A 100ml sample of gas initially at 200K and 2 atm is

heated to 400K and the pressure is reduced to 1 atm.

What will the new volume be?

2. The volume of a gas-filled balloon is 30.0 L at 313 K

and 153 kPa. What would the volume be at STP?

IX. Dalton's Law of Partial Pressure

A. Dalton's law of partial pressures states that the

total pressure exerted by a gaseous mixture is

equal to the sum of the partial pressures of each

individual component in a gas mixture. This

empirical law was observed by John Dalton in

1801 and is related to the ideal gas laws. (This is the

same John Dalton

who proposed the idea of the "atom")

B. Ptotal = P1 + P2 + . . . Pn

• Pt is the total pressure of a sample which contains a mixture

of gases

• P1, P2, P3, etc. are the partial pressures (in the same units) of

the gases in the mixture

It is important to understand that the partial

pressure, as well as partial volume is a

direct result of the molar ratio (fraction) of

each gas.

C. Example:

1. A sample of gas contains 1 mole O2 and 1 mole He and 2

moles of N2 at STP. What are the partial pressures of each

component?

D. Gas Collection over Water:

1.

2. In order to ensure that a sample of gas will contain only

the gas you are intending they are typically collected

through water displacement, or "over water." However,

there is an unavoidable problem. The gas will contain

some water vapor due to the vapor pressure of water at

that temperature. This means that the total pressure

inside the bottle is the sum of two pressures - the gas

itself and the added water vapor.

WE DO NOT WANT THE WATER VAPOR

PRESSURE.

So we get rid of it by subtraction.

Pdry gas = Ptotal - Pwater vapor Table H For

cool video click HERE

PRACTICE PROBLEMS:

3. A sample of hydrogen gas is collected over water at 14.0 oC.  The pressure of the resultant mixture is 113.0 kPa. 

What is the pressure that is exerted by the dry hydrogen

alone? Pdry gas =835.8mmHg

4. A mixture of oxygen, hydrogen and nitrogen gases exerts

a total pressure of 278 kPa.  If the partial pressures of

the oxygen and the hydrogen are 112 kPa and 101 kPa

respectively, what would be the partial pressure exerted

by the nitrogen? Pnitrogen = 65 kPa

5. 130 mls. of oxygen gas is collected over water at 22oC

and 753torr. What is the volume of the dry gas alone?

Step 1- from table H we determine the v.p. of H2O= 6kPa or

45 torr.

PT = PO2 + PH2O

PO2 = 753 torr - 45 torr

PO2 = 708 torr

Step 2- VO2 = (708 torr / 753 torr) x 130mls

VO2 = 122.2 mls.

Follow-up question: What volume would this gas occupy

at STP?

Using the CGL and the answer from above: VO2 =

119 mls

X. Ideal Gas Law

Only ONE set of conditions are given,

Moles or mass of a gas is given/asked.

A. PV=nRT

The ideal gas law is used when:

1. Only ONE set of conditions are given

2. Moles or mass of a gas is given/asked

B.

C. These units are derived according to which pressure value

is given: R = PV/nT

D. Avogadro's Law:

E. Practice Problems:

1. What is the volume of 3.00 moles of Cl2 at 300. torr

and 500. K? 312L

2. What would the pressure be on 10.0g H2 if it occupied

20.L at a temp. of -100.0oC? 3.5atm, 360kPa, 2700torr

F. Online Practice: CLICK HERE

XI. Density of Gases

A. At STP the density calculation is quite simple. We can use

the formula D = m/V

Since all gases will occupy 22.4L (avogadro's Law) calculating

density is simply a matter of

substituting in the gases molar mass.

Densities of common gases at STP:

1. DCO2 = 44 g / 22.4 L = 1.96 g/L

2. DO2 = 32 g / 22.4 L = 1.43 g/L

3. DN2 = 28 g / 22.4 L = 1.25 g/L

4. DXe = 131.3 g / 22.4 L = 5.86 g/L

5. DHe = 4 g / 22.4 L = .18 g/L

B. If a gas is not at STP you need to incorporate the Ideal Gas

Law as well.

1. D = m * P / n * R * T (in terms of mass and moles) or

2. D = m.w. * P / R * T (in terms of m.w.)

C. Practice problems:

1. What is the density of hydrogen sulfide gas if the pressure is

205kPa and the temperature is 220K? 3.8 g/L

2. Two moles of a gas at 150 K have a density of 2 g/L and a

mass of 45g. What is the pressure of the system? 5.84 L

3. What is the density of ammonia gas at 683 torr and 250.1K?

0.744 g/L

XII. Graham's Law of Diffusion

A. Diffusion is the ability of a gas to pass through a medium from

high to low concentration.

B. The diffusion rate of gases are directly related to their molar

masses, the SMALLER a gas the FASTER it diffuses through a

medium.

C.

D. Think running backs in football. Small and agile guys get

through the line faster than bigger, more bumbling ones.