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Boyleβs Law
At constant temperature (in Kelvin) and constant
moles of gas, the pressure of a gas is inversely
proportional to the gas volume.
1
Final condition:
P2 at V2
P1V1 = P2V2 = k
Initial condition:
P1 at V1
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Boyleβs Law
At constant temperature (in Kelvin) and constant
moles of gas, the pressure of a gas is inversely
proportional to the gas volume.
2
P1V1 = P2V2 = k
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Practice Problem
A sample of chlorine gas occupies a volume
of 946 mL at a pressure of 726 mmHg.
What is the pressure of the gas (in mmHg)
if the volume is reduced at constant
temperature to 154 mL?
3
P1 x V1 = P2 x V2
P1 = 726 mmHg
V1 = 946 mL
P2 = ?
V2 = 154 mL
P2 = P1 x V1
V2
726 mmHg x 946 mL
154 mL = = 4460 mmHg
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Charlesβs Law
At constant pressure and moles of gas, the volume
of a gas is directly proportional to the absolute
temperature in kelvin.
4
Hg
Hg
gas
gas
π½π
π»π=
π½π
π»π= π
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Practice Problem
A sample of carbon monoxide gas occupies
3.20 L at 125 0C. At what temperature (in
Kelvin) will the gas occupy a volume of
1.54 L if the pressure remains constant?
5
V1 = 3.20 L
T1 = 398.15 K
V2 = 1.54 L
T2 = ?
T2 = V2 x T1
V1
1.54 L x 398.15 K
3.20 L = = 192 K
V1/T1 = V2/T2
T1 = 125 (0C) + 273.15 (K) = 398.15 K
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Avogadroβs Law
At a specified pressure
and temperature, the
volume of a gas is
proportional to its
number of moles.
6
π½π
ππ=
π½π
ππ= π
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Breathe in, breathe out
7
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Ears Popping
8
http://abetterchemtext.com/gases/ear_pop.htm
Under normal conditions:
pressure inside the Eustachian
tube is equal to the pressure
on the ear canal.
At higher altitudes: pressure
inside the Eustachian tube is
greater than the pressure on
the ear canal.
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Up, up, and away
9
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What is STP?
Scientists defined a standard laboratory
temperature and pressure called STP.
What is the volume occupied by 1 mole of
any gas at STP?
10
Temperature = 273.15 K (0 Β°C)
Pressure = 1 atm = 760 torr
π =ππ π
π=
1 πππ 0.0821 πΏ ππ‘π πππβ1 πΎβ1 273.15 πΎ
1 ππ‘π
π = 22.4 πΏ standard molar volume
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Standard Molar Volume
11
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12
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Ideal Gas Law
13
PV = nRT
R = PV
nT =
1 atm x 22.414 L
1 mol x 273.15 K =
0.0821 atmΒ·L
molΒ·K
R is the universal gas constant;
the numerical value of R depends on the units used.
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Ideal Gas Law and Gas Density
14
PV = nRT and d = m
V
PV = m
MW
RT
MW x P
RT V
m = d =
, n = m
MW
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Learning Check
Rate the gases according to density from
lowest to highest assuming all of the gases
are maintained at the same pressure and
temperature.
15
MW x P
RT d =
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16
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Use gas laws to determine a balanced
equation
The piston-cylinder is depicted before and after
a gaseous reaction that is carried out at
constant pressure. The temperature is 150 K
before the reaction and 300 K after the
reaction. (Assume the cylinder is insulated.)
17
Which of the following balanced equations describes the reaction?
(1)A2(g) + B2(g) β 2AB(g) (2) 2AB(g) + B2(g) β 2AB2(g)
(3) A(g) + B2(g) β AB2(g) (4) 2AB2(g) + A2(g) + 2B2(g)
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Daltonβs Law of Partial Pressure
The total pressure of a mixture of gases is the
sum of the pressure of the individual gases.
V and T
are
constant
P1 P2 Ptotal = P1 + P2 18
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Type equation here.
20
We can express the partial pressure Pi in a mixture
of gases in terms of the total gas pressure, PT, and
the mole fraction of each gas in the mixture.
ππ = ππ΄ + ππ΅ =ππ΄π π
ππ+
ππ΅π π
ππ
ππ = ππ΄ + ππ΅
π π
ππ
ππ΄
ππ=
ππ΄π πππ
πππ πππ
=ππ΄
ππ=
ππ΄
ππ΄ + ππ΅
ππ΄ =ππ΄
ππππ
ππ΅ =ππ΅
ππππ
π·π = πππ·π»
Daltonβs Law
Factor out RT/V
Get ratio of PA/PT
Ptotal = P1 + P2