Our Atmosphere
The Gas Laws
99% N2 and O2



Chapter 10
78% N2
21% O2
1% CO2 and the Noble
Gases
80
Nitrogen
70
60
50
Oxygen
40
30
20
10
0
Gas
Carbon
dioxide
and
Noble
Gases
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

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)
1
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 atmosphere
V = volume in Liters
 n = number of moles
 T = Temperature in Kelvin
 R = 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 & Pressure
Standard Temperature = 0oC (273 K)
Standard Pressure = 1 atm
 1 mole of a gas occupies 22.4 L at STP


1 mole
22.4 L
or
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.
2
Boyle’s Law
Combined Gas Law
P1V1 = n1RT1
P2V2 = n2RT2
Boyle’s Law Apparatus Demo
Boyle’s Law – The pressure and volume of a
gas are inversely related
 Bicycle pump example


Solve both equations for R
R = P1V1
n1T1
R = P2V2
n2T2


Piston down – low volume, high pressure
Piston up – high volume, low pressure
P1V1 = P2V2
n 1T 1
n2T2
Boyle’s Law
Pressure
Pressure vs. Volume
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
Volume
(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
n 1T 1
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
celsius
 Can be used to find absolute zero
 Temperature must be in Kelvin


3
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?
Charles Law
Collapses to:
V1
T1
= V2
T2
P1V1 = P2V2
n 1T 1
n2T2
Gay-Lussac’s Law
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 = 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
4
Avagadro’s Law

Avagadro’s Law = The volume of a gas is
directly proportional to the moles present

1.
“MORE = BIGGER”
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)
Gas Density and Molar Mass

Remember
D = mass
volume
Molar Mass = mass
moles
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)
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?
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?
(ANS: 5.9 g/L)
5
Ex 4
n = (0.967 atm)(0.936 L)
(0.0821 L-atm/mol-K)(304 K)
Calculate the average molar mass of dry air if it
has a density of 1.17 g/L at 21oC and 740.0
torr.
n = 0.0363 mol
mass = 137.456 g – 134.567 g = 2.89 g
MM = 2.89 g
0.0363 mol
=
79.6 g/mol
ANS: 29.0 g/mol
Gases and Reaction
Stoichiometry: Ex 1
Calculate the molar mass of a gas whose
density is 2.59 g/L at STP.
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)
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: 16.4 L)
(Ans: 73.1 g)
6
Dalton’s Law of Partial
Pressures
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 – 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)
b)
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)
If the total pressure is 766 torr, what are the
pressures of all of the other gases?
If the atmosphere is 78.0% N2 and 21.0% O2,
what are their pressures on this humid day?
Mole Fraction
Mole fraction = moles gas A
total moles
= XA
PA = XAPtot
7
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 =
XN2 =
0.200 mol =
0.700 mol
0.500 mol =
0.700 mol
0.286
PN2 = XN2Ptot
PN2 = (0.714)(745 torr) = 532 torr
0.714
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
PAr
PCH4
PO2 = XO2Ptot
PO2 = (0.286)(745 torr) = 213 torr
= (0.82)(1220 torr) = 1000 torr
= (0.12)(1220 torr) = 150 torr
= (0.06)(1220 torr) = 73 torr
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.
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%)
Gas Collection Over Water
Ptot = Pgas + PH2O
ANS: 1.03 atm H2 and 1.02 atm O2
8
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.
Ptot = PO2 + PH2O
PO2 = Ptot - PH2O
PO2 = 765 torr – 25 torr = 740 torr (0.974 atm)
How many moles of gas were collected?
2KClO3(s)  2KCl(s) + 3O2(g)
n = PV/RT
n = (0.974 atm)(0.250 L)
(0.0821 L-atm/mol-K)(299K)
= 0.00992 mole
Ex 2
How many grams of KClO3 were decomposed?
2KClO3(s)  2KCl(s) + 3O2(g)
0.00992 mol
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: 0.811 g KClO3
Root Mean Square Speed of atoms/molecules
m = (3RT/M)1/2
M = molar mass (kg/mol)
R = 8.314 J/mol-K
ANS: 1.26 g
Graham’s Law of Effusion – the higher the molar
mass of a gas, the slower it moves
v1 =
v2
m2
m1
Calculate the rms speed of NH3 and HCl (25oC).
9
Graham’s Law Example
At the same temperature, how much faster does
an He atom move than an N2 molecule?
Graham’s Law Example
Which is faster (and by how much): Cl2 or O2?
(Ans: O2 is about 1.5 times faster)
(Ans: 2.65 times faster)
Ideal Gas
(Kinetic Molecular
Theory)
Real Gases
(Van der Waals
Equation)
Compressible (1000X less
dense than liquids)
Rapid Constant Motion
Temp a KE (1/2mv2)
Elastic Collisions
Real Gases
1.
2.
No Volume
Volume of molecules –
Important at high pressures
No Attraction
Molecular attraction –
Important at low temperatures
(colder, “stickier”)
Would the ideal gas law work better on Mars
(0.6 kPa pressure) or Venus (9300 kPa)?
Explain.
Would the ideal gas law work better for H2O
or Ar? Explain.
10
1.
2.
3.
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?
What is the volume at STP of 22 grams of
CO2?
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 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.
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
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)
20. a) 646 torr b) 105 kPa
c)
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)
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)
42. a) 13.9 kg
b) 9760 L
c)
d) 1.96 X 104 kPa
.
76.
78.
0.862 atm
3.81 atm
5.61 atm
273 K
a) Same # molecules b) N2 more dense
c) Ave KE are equal d) CH4 effuses
faster
a) SF6 < HBr < Cl2 < H2S < CO
b) 517 m/s (CO)
325 m/s (Cl2)
11
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