The Gas Laws Chapter 10. Our Atmosphere 99% N 2 and O 2 78% N 2 21% O 2 1% CO 2 and the Noble Gases.

The Gas Laws

Chapter 10

Our Atmosphere

99% N2 and O2

78% N2

21% O2

1% CO2 and the Noble Gases

0

10

20

30

40

50

60

70

80

Gas

Nitrogen

Oxygen

CarbondioxideandNobleGases

Pressure

Pressure = Force

Area (Needles, High Heels, Snow shoes) Caused by the collisions of gases against a

container We live at about 1 atmosphere of pressure

Barometer

Torricelli (1643) Height of column stayed

about 760 mm (760 torr) The higher the

elevation, the lower the mercury

Weather Rising pressure – calm

weather Dropping pressure –

storm (fast moving air)

Units of Pressure

All of the following are equal:760 mm Hg (760 torr)29.9 inches Hg (weather reporting)1 atmosphere (chemistry)101.3 kPa (kiloPascals, physics)

760 mm = 29.9 in = 1 atmosphere = 101.3 kPa

(1 psi = 14.7 atm)

Converting Pressures

Examples:

1. Express 485 torr in atmospheres. (0.638 atm)

2. Convert 2.4 atmospheres to mm Hg. (1824 mm Hg)

3. Convert 95.0 kPa to atmospheres and mm Hg. (0.938 atm, 712 mm Hg)

The Ideal Gas Law

PV = nRT

P = pressure in atmosphereV = volume in Litersn = number of molesT = Temperature in KelvinR = gas constant

• R = 0.0821 L-atm / mol-K

The Ideal Gas Law

Examples:

1. What is the pressure of a 1.45 mol sample of a gas in a 20.0 L container at 25oC? (1.77 atm)

2. What volume will 5.00 grams of H2 occupy at 10.0oC and 1 atm of pressure? (58.1 L)

3. How many grams of O2 are needed to occupy a 500.0 mL aerosol can at 20.0oC and 0.900 atmospheres? (0.600 g)

STP

Standard Temperature & PressureStandard Temperature = 0oC (273 K)Standard Pressure = 1 atm1 mole of a gas occupies 22.4 L at STP

1 mole or 22.4 L

22.4 L 1 mole

STP

Examples:

1. What volume will 0.180 moles of nitrogen gas occupy at STP?

2. How many grams of chlorine (Cl2) gas are present in 50.0 L at STP?

12.0 grams of Cl2 is introduced into a 2.00 L flask at 25o C.

a) Calculate the pressure of the gas

b) Convert the pressure to mm Hg.

c) Calculate the volume the gas would occupy at STP.

Combined Gas Law

P1V1 = n1RT1 P2V2 = n2RT2

Solve both equations for R

R = P1V1 R = P2V2

n1T1 n2T2

P1V1 = P2V2

n1T1 n2T2

Boyle’s Law

Boyle’s Law Apparatus Demo Boyle’s Law – The pressure and volume of a

gas are inversely related Bicycle pump example

Piston down – low volume, high pressurePiston up – high volume, low pressure

Boyle’s Law

Example:

1. The volume of a car’s cylinder is 475 mL at 1.05 atm. What is the volume when the cylinder is compressed and the pressure is 5.65 atm?

P1V1 = P2V2

n1T1 n2T2

(Answer: 88.3 mL)

Boyle’s Law

Example:

2. A weather balloon has a volume of 40.0 liters on the surface of the earth at 1.00 atm. What will be the volume at 0.400 atm as it rises?

P1V1 = P2V2

n1T1 n2T2

Charles Law

Charles Law – The temperature and volume of a gas are directly related“HOTTER = BIGGER”A gas increases in volume 1/273rd per degree

celsiusCan be used to find absolute zeroTemperature must be in Kelvin

Charles Law

1. A basketball has a volume of 12.0 L when blown up at 25.00 oC. What will be the volume if it is taken outside on a day when it is only 5.00 oC?

P1V1 = P2V2

n1T1 n2T2

Charles Law

Collapses to:

V1 = V2

T1 T2

Charles Law

2. If a tire contains 30.0 L of air at 10.0 oC, what volume will it occupy when it is driven and warms up to 50.0 oC? (34.2 L)

Gay-Lussac’s Law

Gay-Lussac’s Law = temperature and pressure of a gas are directly related

1. Gas in a spray can has a pressure of 5.00 atm at 25.0 oC. What will be the pressure at 400.0 oC? (11.3 atm)

P1V1 = P2V2

n1T1 n2T2

Avagadro’s Law

Avagadro’s Law = The volume of a gas is directly proportional to the moles present

“MORE = BIGGER”

1. A balloon has a volume of 1.00 L when 50.0 grams of N2 are in the balloon. What is the volume if an additional 25.0 grams of N2 are added? (1.50 L)

1. The volume of 0.0400 mol of a gas is 500.0 mL at 1.00 atm and 20.0 oC. What is the volume at 2.00 atm and 30.0oC? (259 mL)

Gas Density and Molar Mass

RememberD = mass Molar Mass = mass

volume moles

Ex 1

What is the density of carbon tetrachloride vapor at 714 torr and 125oC? (HINT: Pretend 1 L, solve for n)

(4.43 g/L)

Ex 2

The average molar mass of atmosphere of Titan (Saturn’s largest moon) is 28.6 g/mol. If the surface temperature is 95 K and the pressure 1.6 atm, calculate the gas density of Titan’s atmosphere?

(ANS: 5.9 g/L)

Ex 3

A 936 mL flask masses 134.567 g empty. When it is filled with gas to a pressure of 735 torr at 31.0oC, it is found to mass 137.456 g. What is the molar mass of the gas?

n = (0.967 atm)(0.936 L)

(0.0821 L-atm/mol-K)(304 K)

n = 0.0363 mol

mass = 137.456 g – 134.567 g = 2.89 g

MM = 2.89 g = 79.6 g/mol

0.0363 mol

Ex 4

Calculate the average molar mass of dry air if it has a density of 1.17 g/L at 21oC and 740.0 torr.

ANS: 29.0 g/mol

Calculate the molar mass of a gas whose density is 2.59 g/L at STP.

Gases and Reaction Stoichiometry: Ex 1

1. What mass of Al is needed to produce 50.0 L of H2 at STP?

2Al(s) + 6HCl(aq) 2AlCl3(aq) + 3H2(g)

(ANS: 40.2 g Al)

Gases and Reaction Stoichiometry: Ex 2

2. What volume of NO gas measured at 0.724 atm and 25oC will be produced from the reaction of 19.5 g of O2?

4NH3(g) + 5O2(g) 4NO(g) + 6H2O(l)

(Ans: 16.4 L)

Gases and Reaction Stoichiometry: Ex 3

3. Car safety bags are inflated through the decomposition of NaN3. How many grams of NaN3 are needed to produce 36.0 L of N2 at 1.15 atm and 26.0oC?

2NaN3(s) 2Na(s) + 3N2(g)

(Ans: 73.1 g)

Gases and Reaction Stoichiometry: Ex 4

4. How many liters of H2 and N2 at 1.00 atm and 15.0oC are needed to produce 150.0 grams of NH3?

N2(g) + 3H2(g) 2NH3(g)

Dalton’s Law of Partial Pressures

Dalton’s Law – the total pressure of a gas is equal to the sum of the partial pressures

Ptot = PA + PB + PC + PD +…..

Patm = PN2 + PO2 + Prest

1 atm = 0.78atm + 0.21atm + 0.01atm

Dalton’s Law of Partial Pressures

1. Three gases are mixed in a 5.00 L container. In the container, there are 255 torr of Ar, 228 torr of N2, and 752 torr of H2. What is the total pressure? (1.63 atm)

Dalton’s Law of Partial Pressures

2. On a humid day, the partial pressure of water in the atmosphere is 18.0 torr.

a) If the total pressure is 766 torr, what are the pressures of all of the other gases?

b) If the atmosphere is 78.0% N2 and 21.0% O2, what are their pressures on this humid day?

Dalton’s Law of Partial Pressures

3. What is the total pressure (in atm) exerted by a mixture of 12.0 g of N2 and 12.0 g of O2 in a 2.50 L container at 25.0o C? (HINT: Calculate the moles of each gas, then use PV=nRT twice). (ANS: 7.87 atm)

Mole Fraction

Mole fraction = moles gas A = XA

total moles

PA = XAPtot

Mole Fraction: Ex 1

A gas mixture contains 0.200 mol of oxygen and 0.500 mole of nitrogen. If the total pressure is 745 torr, what is the partial pressure of the two gases?

XO2 = 0.200 mol = 0.286

0.700 mol

XN2 = 0.500 mol = 0.714

0.700 mol

PO2 = XO2Ptot

PO2 = (0.286)(745 torr) = 213 torr

PN2 = XN2Ptot

PN2 = (0.714)(745 torr) = 532 torr

Ex 2

The atmosphere of Titan is 82 mol % nitrogen, 12 mol % argon, and 6 mol % methane. Calculate the partial pressure of each gas if the total pressure on Titan is 1220 torr.

PN2 = (0.82)(1220 torr) = 1000 torr

PAr = (0.12)(1220 torr) = 150 torr

PCH4 = (0.06)(1220 torr) = 73 torr

Ex 3

What is the mole fraction and mole percent of oxygen in exhaled air if PO2 is 116 torr and the Ptotal is 760 torr?

PO2 = XO2Ptot

XO2 = PO2/Ptot

XO2 = 116 torr/760 torr = 0.153 (15.3%)

Ex 4

A mixture contains 2.15 g H2 and 34.0 g of O2. Calculate the partial pressure of each gas if the total pressure is 2.05 atm.

ANS: 1.03 atm H2 and 1.02 atm O2

Gas Collection Over Water

Ptot = Pgas + PH2O

Ex 1

A sample of KClO3 is decomposed as shown. If 250 mL of gas are collected at 26oC and 765 torr total pressure, calculate the partial pressure of O2.

2KClO3(s) 2KCl(s) + 3O2(g)

Ptot = PO2 + PH2O

PO2 = Ptot - PH2O

PO2 = 765 torr – 25 torr = 740 torr (0.974 atm)

How many moles of gas were collected?

n = PV/RT

n = (0.974 atm)(0.250 L) = 0.00992 mole

(0.0821 L-atm/mol-K)(299K)

How many grams of KClO3 were decomposed?

2KClO3(s) 2KCl(s) + 3O2(g)

0.00992 mol

ANS: 0.811 g KClO3

Ex 2

When a sample of NH4NO2 is decomposed, 511 mL of N2 are collected over water at 26oC and 745 torr total pressure. How many grams of NH4NO2 were decomposed?

NH4NO2(s) N2(g) + 2H2O(g)

ANS: 1.26 g

Root Mean Square Speed of atoms/molecules

= (3RT/M)1/2

M = molar mass (kg/mol)

R = 8.314 J/mol-K

Calculate the rms speed of NH3 and HCl (25oC).

Graham’s Law of Effusion – the higher the molar mass of a gas, the slower it moves

v1 = m2

v2 m1

Graham’s Law Example

At the same temperature, how much faster does an He atom move than an N2 molecule?

(Ans: 2.65 times faster)

Graham’s Law Example

Which is faster (and by how much): Cl2 or O2?

(Ans: O2 is about 1.5 times faster)

Ideal Gas (Kinetic Molecular

Theory)

Real Gases(Van der Waals

Equation)

Compressible (1000X less dense than liquids)

Rapid Constant Motion Temp KE (1/2mv2)

Elastic Collisions

No Volume Volume of molecules – Important at high pressures

No Attraction Molecular attraction – Important at low temperatures (colder, “stickier”)

Real Gases

1. Would the ideal gas law work better on Mars (0.6 kPa pressure) or Venus (9300 kPa)? Explain.

2. Would the ideal gas law work better for H2O or Ar? Explain.

1. A gas has a volume of 800.0 mL at -23.00 °C and 300.0 torr. What would the volume of the gas be at 227.0 °C and 600.0 torr of pressure?

2. What is the volume at STP of 22 grams of CO2?

3. 2.50 g of XeF4 gas is placed into an evacuated 3.00 liter container at 80°C. What is the pressure in the container?

The atmosphere of Jupiter is composed almost entirely of hydrogen (H2) and helium (He). If the average molar mass of Jupiter’s atmosphere is 2.254 g/mole, calculate the percent composition.

(ANS: 87.3% H2, 12.7% He)

The atmosphere of Mars is composed of CO2, N2 and 1.6% Ar. If the average molar mass of the gases in Mars’ atmosphere is 43.28 g/mole, calculate the percentages of CO2 and N2.

20. a) 646 torr b) 105 kPa c) 0.862 atm

d) 1.306 atm e) 2.53 bar

22.a) 1.60972 X 10-5 Earth atm

b) 9,100 kPa

26. a) 2.31 L b) 6.67 L

34.a) 33.4 L b) 1170 K c) 3.81 atm

d) 0.230 mol

36. 0.0050 g Ne

38.8.8 X 1019 O3 molecules

40. a) a) 5.07 atm b) 1.17 L c) 5.61 atm

42.a) 13.9 kg b) 9760 L c) 273 K

d) 1.96 X 104 kPa

.

46. CO2 < SO2 < HBr

50. a) 5.63 g/L b) 171 g/mol

54. 50.0 g CaH2

56. 71.9 kg Fe

62. Ptot = 23.3 atm

66. PN2=0.389 atm, PH2=0.968, PNH3 =0.496 atm

68. a) XO2=0.149, XN2= 0.239, XH2=0.612

b) PO2=0.303atm PN2=0.488 atm PH2=1.25atm

70. a) 0.115 atm

b) 0.206 atm

c) Pt = 0.321 atm

76. a) Same # molecules b) N2 more dense

c) Ave KE are equal d) CH4 effuses faster

78. a) SF6 < HBr < Cl2 < H2S < CO

b) 517 m/s (CO) 325 m/s (Cl2)