Ppt 17b, Continuation of Gases & Gas Laws
1.
Individual Gas Laws Combine to Form the Ideal
Gas Law.
2.
Ideal Gas Law Problems-I
•
Find one variable if the other three are known
(“one state” problem)
•
Problems in which the state of a gas changes
(“two state” problem).
Density of Gases Ideas & Calculations
3.
•
Can use Ideal Gas Law here (or memorize variant)
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Ppt17b
1
Important Comment
•
In all previous laws, the proportionality constant,
k1 , is not a fundamental constant of nature; it
would depend on the conditions [the values of
the other variables being held constant]
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Ppt17b
2
The Ideal Gas Law
01
•
Ideal gases obey an equation incorporating the laws
of Charles, Boyle, and Avogadro:
PV
PV  nRT 
 R (a fundamental constant)
nT
[same for all gases, conditions]
•
The gas constant R = 0.08206 L·atm·K–1·mol–1
•
STP conditions are 273.15 K and 1 atm pressure
•
1 mole of an ideal gas occupies 22.41 L at STP
(molar volume = V of 1 mol)
nRT
(1 mol)(0.08206)(273.15 K)
1 mol
V
 

 22.414..L
at STP
P
1 atm
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Ppt17b
3
The Ideal Gas Law
•
02
Sulfur hexafluoride (SF6) is a colorless, odorless,
very unreactive gas. Calculate the pressure (in
atm) exerted by 1.82 moles of the gas in a steel
vessel of volume 5.43 L at 69.5°C.
•
What is the volume (in liters) occupied by 7.40 g of
CO2 at STP?
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Ppt17b
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What if more than one variable changes?
•
Oxygen gas is normally sold in 49.0 L steel containers at a
pressure of 150.0 atm. What volume would the gas
occupy if the pressure was reduced to 1.02 atm and the
temperature raised from 20oC to 35oC?
PV
PV
1 1
R 2 2
n1T1
n2T2

PV
PV
1 1
 2 2
T1
T2
(n constant)
P1 T2
 V2  V1 x x
P2 T1
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Ppt17b
5
Example #2
•
An inflated balloon with a volume of 0.55 L at sea
level, where the pressure is 1.0 atm, is allowed to
rise to a height of 6.5 km, where the pressure is
about 0.40 atm. 1) Assuming that the temperature remains
constant, what is the final volume of the balloon? 2) Assuming
that the temperature at sea level is 22°C and the
temperature at 6.5 km is -28°C, what is the final
volume of the balloon?
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Ppt17b
6
Gases Worksheet-I Practice
•
Proportional relationships / calculations
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Ppt17b
7
The Ideal Gas Law--Applications
•
04
Recall: At the same T and P, equal volumes of
gases contain equal numbers of molecules.

•
V  n (P, T constant)
Implication?

The concentration of gas particles is “fixed” at a
given T and P!
n
P
PV  nRT 

 a fixed value
V RT
(at a given P & T, for any gas!)
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Ppt17b
8
At the same T & P, [gas] is “fixed”
(sample size does not matter)
(identity of the gas does not matter)
Same T & P  …
He
H2
Ar
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He
…same number of particles per L
Ppt17b
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Density of a gas at fixed T and P
does depend on gas identity (molar mass)!
Density is “number density” x mass per particle
• Which equals concentration x molar mass!
•
g mol
g

x
L
L
mol
m
n
d

x MM
V
V
•
This slide is intended
to make a conceptual
connection, not give
you another equation
to memorize!
One could substitute in for n/V here to get an
equation that relates d, P, T, and MM,
–
but I don’t think it’s really “worth it” (see answer key comments)
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10
Summary (of prior few slides):
At the same T & P, concentration
is constant, but density varies with MM
Same # particles / L, but…
He
H2
Ar
Greatest density b/c
greatest
MM
Prentice
Hall ©2004
He
…different densities for different
gaseous substances, because mass
per particle (and thus per mole) varies!
11
Practical Application: Will gases (or balloons filled with
them) float or sink (in air)? MM is the key!
•
Air is about 80% N2 and 20% O2  MM(air)  29 g/mol
Substance or
Mixture
Molar Mass
(g/mol)
Floats or sinks in
air? (at same T, P)
H2
2.0
floats
He
4.0
floats
Air
~29
Neither
(but balloon would sink
b/c the rubber makes
dballoon slightly > dair)
CO2
44
sinks
Quiz: Would a neon balloon float or sink? Argon?
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Ppt17b
12
The bottom line? Density of a gas depends
on molar mass, T, & P, but not on “amount”
•
Since amount does not matter, I prefer to PICK A
CONVENIENT AMOUNT* to solve problems that
relate to gas density and molar mass!

No need to memorize or derive separate
equations (although if you want to do so, more power to you!)
* 1 L of gas, if density is given; 1 mol of gas, if
molar mass (or formula) is given
Prentice Hall ©2004
Ppt17b
13
The Ideal Gas Law—Applications (Examples)
•
What is the molar mass of a gas with a density of
4.07 g/L at a pressure of 3.42 atm and 35°C?
•
What is the density of uranium hexafluoride, UF6,
(MM = 352 g/mol) under conditions of STP?
•
To what temperature must a sample of CO2 be
raised at 1.97 atm in order for the density to
become 3.38 g/L?
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Ppt17b
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