Properties of Gases

Gases expand into any available volume

• gas molecules escape from open containers.

Gases are completely miscible

• once mixed they will not spontaneously separate.

Gases are described in terms of T, P, V and n

Volume, Amount and Temperature

• A gas expands uniformly to fill the container in which it is placed

– The volume of the container is the volume of the gas – Volume may be in liters, mL, or cm3

• The temperature of a gas must be indicated on the Kelvin scale

– Recall that K = °C + 273.15

• Amount of a gas is the number of moles

Pressure

• Pressure is force per unit area

– In the English system, pounds per square inch or psi – Atmospheric pressure is about 14.7 psi

Pressure Units

SI:

1 pascal (Pa) = 1 kg m-1s-2 = 1N m-2 others: 1 bar = 105 Pa = 100 kPa

1 atm = 101.325 kPa = 1.01325 bar

1 atm = 760 torr = 760 mm Hg

1 atm = 14.7 lb/in2

KINETIC MOLECULAR THEORY

A gas consists of tiny molecules in rapid, random motion. Gas molecules:

• are small compared to the distances between them

easily compressed.

mix completely with other gases.

• move randomly at very high speeds.

• have small attractions/repulsions for each other.

all gases behave the same way.

• make elastic collisions with each other.

don’t slow over time & fall to bottom of container

KINETIC MOLECULAR THEORY

Kinetic energy Ek = 1/2 mv2

• When gas molecules collide, their speed and direction changes.

• All gas molecules are constantly moving:

– average speed is directly proportional to T (K).

– the distribution of speeds can be calculated.

The Ideal Gas Law

The ideal gas law is a combination of:

Boyle’s Law

V 1

P

fixed n and T

Charles’s Law

VT

fixed n and P

IDEAL GAS LAW

PV = nRT or V = nRT

P

Avogadro’s Law

Vn

fixed P and T

Methods in Solving Gas Law’s Problem

Given: P, V

Constant: n and T

Given: T, V

Constant: n and P

Analyze the problem

(What are the given and the required)

Boyle’s Law

P1 V1 = P2 V2

Charles Law

V1 / T 1 = V 2 / T 2

Given: T, P

Constant: n & V

Gay-Lussac’s Law

P1 / T 1 = P 2 / T2

Given: n, V

Constant: T and P

Avogadro’s Law

V1 / n 1 = V 2 / n 2

Given: T, P, V

Constant: n

Combined Gas

P1V1 /T1 = P2V2 / T2

T, P, V, n

Ideal Gas Eq’n

PV = nRT

Rewriting the Ideal Gas Law in Density

Terms

m

PV

RT

MM m P MM d

V

R T

Sample Problems:

1. A gas sample contained in a cylinder equipped with a moveable piston occupied 300. mL at a pressure of 2.00 atm.

What would be the final pressure if the volume were increased to 567 mL at constant temperature?

2. Several balloons are inflated with helium to a volume of 0.82

L at 26°C. One of the balloons was found several hours later; the temperature had dropped to 21°C. What would be the volume of the balloon when found, if no helium has escaped? 3. A sample of gas occupies 363. mL at STP. Under what pressure would this sample occupy 236. mL if the temperature were increased to 819°C?

4. Calculate the pressure needed to contain 2.54 mol of an ideal gas at 45°C in a volume of 12.75 L.

5. Nitrogen is slightly less dense than is a sample of air at the same temperature and pressure.

(a) Calculate the density of N2, in g/L, at 1.25 atm and 35°C.

(b) If the average molecular weight of the air is 29.2, what is the density of air at the same conditions?

Gas Mixtures & Partial Pressures

Dalton’s law of partial pressures

“The total pressure of mixture of gases is the sum of the partial pressure of the individual gases in the mixture.”

Ptotal = P1 + P2 + P3 + …

Gas Mixtures & Partial Pressures

Mole Fractions

Ptotal = n1RT / V + n2RT / V + ...

= (n1+ n2 + ...) RT / V

Ptotal = ntotalRT / V

So

P1 / Ptotal = n1/ntotal = X1

P2 / Ptotal = n2 /ntotal = X2

etc.

with X1 = mole fraction of gas 1 = (n1 / ntotal ) etc.

Notice that:

X1 + X2 + X3 + ….. = 1

Sample Problem:

6. A gaseous mixture contains 3.23 g of chloroform, CHCl3 , and 1.22 g of methane,

CH4 . Assuming that both compounds remain as gases, what pressure is exerted by the mixture inside a 50.00-ml metal container at

275o C? What pressure is contributed by the

CHCl3.

Collecting Gases Over Water

Gases are often collected over water.

gas

Ptotal = Pgas + Pwater

Pgas? Subtract the water vapor pressure from Ptotal

gas + H2O vapor Sample Problem:

7. A nitrogen sample occupies 249 mL at STP. If the same sample were collected over water at

25°C and 750. torr, what would be the volume of the gas sample? *VP of water at 25oC is 23.8 mmHg. * Taken from Vapor Pressure –Temperature data/list

GAS STOICHIOMETRY

MASS (g) of

Compound B

Assume that the gas behaves Ideally

Use Ideal Gas Equation to solve for MOLE of Gas A

MOLE of Gas A

Use mole ratio of

B and A

Use mole ratio of

A and B

Use Molar mass (g/mol) of compound

B

MOLE of

Compound B

Sample Problem:

8. During a collision, automobile air bags are inflated by the N2 gas formed by the explosive decomposition of sodium azide, NaN3.

2NaN3 2Na + 3N2

What mass of sodium azide would be needed to inflate a 25.0-L bag to a pressure of 1.40 atm at 25°C?

9. What mass of KNO3 would have to be decomposed to produce

21.1 L of oxygen measured at STP?

2KNO3(s) + heat 2KNO2(s) + O2(g)

Effusion of Gases

• Diffusion

– Gases move through space from a region of high concentration to a region of low concentration

• You can smell an apple pie baking as the particles responsible for the odor diffuse through the room

• Effusion

– Gas particles will escape through a small hole

(orifice) in a container

• Air will slowly leak out of a tire or balloon through pores in the rubber

Graham’s Law of Effusion rate of effusion of B MMA

MM

rate of effusion of A

B

1

2

• The rate at which gas B escapes divided by the rate at which gas A escapes is equal to the square root of the ratio of the molar mass of gas A to gas B

Effusion of Gases

Ammonia and Hydrogen Chloride

Sample Problem

10. A student of CHM12-3L performed an experiment on Graham’s Law using concentrated HCl and

NH4OH, placed in two separate test tubes. A diffusion tube, 13.1 cm in length, was inserted simultaneously to the two test tubes and allowed the reaction to proceed. A few minutes later, a white appeared on the diffusion tube. Using these data, calculate the distance travelled by the two gases.

REAL GASES

A gas behaves ideally at low P (≤ a few atm.) and at high T (well above the boiling point).

N2

2.0

CH4

1.0

1.5

H2

ideal gas

0 0.5

PV/nRT

At high P and/or low

T, gases deviate significantly from ideal behavior.

2.5

Ideal gas:

PV/nRT = 1 at all P

0

200

400

600

Pressure (atmosphere)

800

REAL GASES

Deviations from ideality occur because:

• (Weak) molecular attraction is accentuated at:

high P = close together.

low T = low energy = slow moving.

• Gas molecules have a finite volume.

The van der Waals equation: n2a P + 2 V – nb = nRT

V

Attraction correction finite V correction VAN DER WAALS CONSTANTS

Atoms:

London only

Molecules:

London only

London + dipole

Gas

He

Ne

Ar

H2

N2

O2

Cl2

CO2

CH4

NH3

H2O

a

L2 atm mol-2

0.034

0.211

1.35

0.244

1.39

1.36

6.49

3.59

2.25

4.17

5.46

b

L mol-1

0.0237

0.0171

0.0322

0.0266

0.0391

0.0318

0.0562

0.0427

0.0428

0.0371

0.0305

a and b both grow larger as molecule size and complexity increase.

Sample Problem

11. You want to store 165 g of CO2 gas in a 12.5-L tank at room temperature (25°C). Calculate the pressure the gas would have using (a) the ideal gas law and (b) the van der Waals equation. For CO2, a = 3.59 atm L2/mol2 and b = 0.0427 L/mol.

Homework No. 1

Page 159 Chemistry for Eng’g Students by Brown

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