CHEM 1811 Lecture # 19
1
IDEAL GAS LAW
•
pV = n R T
relates conditions that define the state of a gas sample
an equation of state
-
a.k.a.
-
four variable quantities with certain relationships
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calculate any one quantity from the other three
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perform algebraic rearrangements
e.g.
•
p = nRT/V
n = pV/RT
display relations using graphs
p
p
for n & T constant
n & V constant
V
•
molar volume
e.g.
EXAMPLE
T
VM = V/n = RT/p
units:
L/mol
at STP
22.4 L/mol
for any gas
try graphing
P/T vs. n
VM vs. n
density and volume
What is the volume of a 0.144 g sample of methane (CH4) at STP?
molar mass
M = 16.04 g/mol = m/n
mass = m
V ? = n R T / p = m R T / M p = (0.144 g) (0.0821 L atm K-1 mol-1) (273 K)
(16.04 g/mol) (1 atm)
= 0.201 L
CHEM 1811 Lecture # 19
EXAMPLE
2
comparing gas densities
Which gas has the largest density at STP?
helium, xenon, or air
He:
(4.00 g/mol) / (22.4 L/mol) = 0.179 g/L
Xe:
(131.3 g/mol) / (22.4 L/mol) = 5.86 g/L
air:
(28.8 g/mol) / (22.4 L/mol) = 1.29 g/L
helium balloons float in air
EXAMPLE
xenon balloons sink
molecular formula from gas measurements
An unknown hydrocarbon is 85.7 % carbon by mass. A 1.77 g sample in a
1.50 L flask at 17 °C exerts a pressure of 508 Torr. What is the molecular
formula?
n ?= pV/RT =
molar mass
(508/760 atm) (1.50 L)
(0.0821 L atm K-1 mol-1) (290 K)
=
0.0421 mol
M = (1.77 g) / (0.0421 mol) = 42.04 g/mol
(1 mol) (42.04 g/mol) (85.7 g C/100 g gas) (1 mol C/12.01 g C) = 3.00 mol C
(1 mol) (42.04 g/mol) (14.3 g H/100 g gas) (1 mol H/1.008 g H) = 6.00 mol H
∴
C3H6
CHEM 1811 Lecture # 19
3
GAS STOICHIOMETRY
•
•
usually measure amount of gas by volume used
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need to know T and p to compute n from V
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usually assume ideal behavior
balanced chem. equ. relates mole amounts (n)
EXAMPLE
volume of a gas product
Potassium azide (KN3) is a solid explosive used in vehicle airbags for safety.
What volume of nitrogen gas at STP is formed when 50.0 g KN3 explodes?
2 KN3 (s) → 2 K (s) + 3 N2 (g)
V ? = nRT/p
= (50.0 g) (1 mol KN3/81.1 g) (3 mol N2/2 mol KN3) (22.4 L/mol)
=
20.7 L
EXAMPLE
(very suddenly)
pressure in a bomb
1.00 kg of trinitrotoluene (TNT) is sealed inside a 1.00 L bomb. Given the
following simplified reaction that achieves a temperature of 2000 K, what
pressure can be formed before it blows up?
C7H5N3O6
{draw structure}
2 C7H5N3O6 (s) → 7 CO (g) + 4 H2O (g) + 3 C2N2 (g) + H2CO (g)
p ? = (1000 g) (1 mol TNT/ 227.2 g) (15 mol gas/ 2 mol TNT)
x (0.0821 L atm K-1 mol-1) (2000 K) / (1.00 L) = 5418 atm
= 79,640 psi