Gases

Chapter 13

GasesThe Nature of Gases

The Molecular Basis of Gas BehaviorPressureCompressibility Diffusion

The Nature of GasesGases expand to fill their container.

Gases exert pressure on their container.

Gases are compressible.

The Molecular Basis of Gas Behavior

Gas molecules are in constant motion.

Gas molecules are small compared to the distances between them.

Collisions between molecules are elastic.

The collisions of gas molecules with other objects creates pressure.

Units of Pressure760 mmHg (aka 760 Torr)

= 1.000 atm

= 101.3 kPa

= 14.69 psi

Gas Laws• Avogadro’s Hypothesis

• Boyle’s Law

• Charles’ Law

• Gay-Lussac’s Law

• The Combined Gas Law

• Ideal Gas Law

• Dalton’s Law

• Graham’s Law

AVOGADRO’S HYPOTHESIS- Equal volumes of gases at the same temperature

and pressure have an equal number of molecules.

BOYLE’S LAWPressure is inversely proportional to the

volume if the temperature and quantity are constant. Temperature, T, is measured in Kelvin and quantity, n, in moles.

PV = k1 if T and n are constant

P1V1 = P2V2

PROBLEM SET1. What is the pressure of a gas if 4.50 liters at

2.5atm of pressure is changed to a volume of 5.00 liters?

2.The volume of a gas is 22. 9 ml at 345mm of Hg. What is the volume at 500. mm of Hg?

CHARLES’ LAWObservation made by Charles:

For 1 liter of any gas at 00C and 1 atm, a change in temperature of 10C changes the volume by 1/273 of the original volume.

The volume of a gas is directly proportional to the Kelvin temperature if quantity and pressure are constant.

V / T = k2 if n and P V1 /V2 = T1 /T2

are constant

PROBLEM SET1.The volume of a gas is 44.3ml at 250C. What is

the volume at 100.0C?

2.The volume of a gas is 19.4 liters at -450C. What is the volume at standard state temperature?

3.If the volume of a gas is 56.4m3 at 750C, what temperature in 0C changes the volume to 40.0m3?

GAY-LUSSAC’S LAWThe pressure exerted by a gas is directly

proportional to the Kelvin temperature if volume and quantity are held constant.

P/T = k3

P1 / T1 = P2 / T2

What are the implications of 0 K on molecular motion and Kelvin temperature on KE?

1. The volume of a gas is 34.6 cm3 at 170C and 245 mm of Hg. What is the volume at STP?

2. The volume of a gas is 65 liters at SS. What is the pressure in cm of Hg at 100.0C in a volume of 60. liters?

3. The volume of a gas is 19.0 ml at -350C and 2.51 atm. What temp. changes the volume to 20.0 ml at 3.00 atm?

PROBLEM SET ON GAS LAWS

1. A gas has a pressure of 3.14 atm at -230C. What is the pressure at 270C?

2. A gas has a volume of 56.0ml at 670.torrs. What is the volume at 800. torrs?

3. A gas has a volume of 33.0 liters at 100.0C. What temperature in Celsius changes it to 15.0 liters?

MORE OF THE SAME4. A gas has a volume of 24.6 dl at -130C and

45.3cmHg. What is the volume at STP?

5. The molar volume of a gas at STP is 22.4 liters. What is it at SS?

6. A gas has a volume of 24.5 kl at 270C and 2.61 atm. What temperature in Celsius changes the volume to 30.0 kl at 1.00 atm?

Cole’s LawTo one head of finely shredded cabbage, add:

1 cup mayonaise

1 TBSP sugar

1 TSP vinegar

Salt and Pepper to taste

IDEAL GAS LAWQuantity, n, temperature, T, Volume, V, and

pressure, P, are all variables.

a. V/T = k2 V = k2T

b. P/n = k3 P = k3n

Therefore,PV = (k3n)(k2T) or PV = k2k3nT

k2k3 is called R, the ideal gas law constant

PV = nRT

CALCULATING R1. The molar volume of any gas is 22.4 L/mole at

STP. Find R.

Values of R0.0821 (liter·atm) / (mole·K)

62.4 (liter·mm Hg) / (mole·K)

8.32 (liter·kPa) / (mole·K)

PROBLEM SET1. What is the volume of 18.0g of CO2 at 150C

and 8.18 atm.

2. Find the temperature of 4.04 g of Ne in a volume of 10.0 liters at 45.6cm Hg.

3. What is the mass of C3H8 in 20.0 liters at 50.0C at 715mm Hg?

4. 16.0g of gas X has a volume of 13.6 liters at 250C and 1.15 atm. What is its molecular mass?

DensityDensity is Mass divided by Volume

D = M/V

This can also be written as

D•V = M

O2 has a density of 1.43g/l at STP. What is its density at 1000C and .500 atm?

DensityD•V = M

If the volume of a constant amount of gas is changed, the mass does not change.

Thus D1•V1 = M = D2•V2

So density and volume are inversely related.

DensitySimilarly we find that

Density and pressure are directly related.

Density and temperature are inversely related.

Density

Problem:

O2 has a density of 1.43g/l at STP. What is its density at 100 0C and .500 atm?

If the density of a gas is 1.25 g/l at SS, what is the density at 1000 mm Hg and 55 0C

DALTON’S LAW OF PARTIAL PRESSURE

The total pressure exerted by a mixture of gases is equal to the sum of each gas’s partial pressure.

PT = P.P.s

1. 10.1 g Ne, 8.00g O2, and 2.80g N2 are at a total pressure of 120.mmHg. Find each gas’s partial pressure.

2. 16.0gO2, 2.0gH2, 8.00gCH4, and 8.0gHe are at total pressure of 4.00atm. Find each gas’s PP.

GRAHAM’S LAW OF DIFFUSIONThe rate at which gaseous molecules diffuse is

inversely proportional to the square roots of their molecular masses if the temperature is the same.

1. What is the relative velocity of He to CH4 at the same temperature.

2. What is the relative velocity of H2 to O2 at 250C?

3. What is the relative velocity of SO2 to HI at 1000 K?4. Gas X moves at a relative velocity that is 2.50 times that of

O2. What is the molecular mass of X? D = M D = Molar Mass V Molar Volume*

*22.4 l/mole at STP and 24.5 l/mole at SS5. Find the density of SO3 at STP and SS6. A gas has a density of 3.45g/l at SS. What is its molecular

mass?

7. What is the mass of 18.0 liters of CH4 at STP?

8. What is the mass of 18.0 liters of CH4 at 30.0C and 45.0cm of Hg?

9. What is the volume of 20.0 grams of C2H6 at SS?

10.What is the volume of 20.0 grams of C2H6 at 150C and 1.25 atm?

DensityIf P1V1 = P2V2

T1 T2

and V1 = M / D1 V2 = M / D2

Then

P1 = P2 _

D1 T1 D2 T2