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Prentice Hall ©2004 Ppt17b
Ppt 17b, Continuation of Gases & Gas LawsPpt 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).
3. Density of Gases Ideas & Calculations
• Can use Ideal Gas Law here (or memorize variant)
1
Prentice Hall ©2004 Ppt17b
Important CommentImportant 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]
2
Prentice Hall ©2004 Ppt17b
The Ideal Gas Law01The Ideal Gas Law01
• Ideal gases obey an equation incorporating the laws
of Charles, Boyle, and Avogadro:
• 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)
(a fundamental constant) PV
PV nRT RnT [same for all gases, conditions]
3
1 molat STP
(1 mol)(0.08206)(273.15 K)22.414..L
1 atm nRT
VP
Prentice Hall ©2004 Ppt17b
The Ideal Gas Law02The Ideal Gas Law02
• 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?
4
Prentice Hall ©2004 Ppt17b
What if more than one variable changes?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?
1 1 2 2 1 1 2 2
1 1 2 2 1 2
(n constant) PV PV PV PV
RnT n T T T
1 22 1
2 1
x x P T
V VP T
5
Prentice Hall ©2004 Ppt17b
Example #2Example #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?
6
Prentice Hall ©2004
Gases Worksheet-I PracticeGases Worksheet-I Practice
• Proportional relationships / calculations
Ppt17b 7
Prentice Hall ©2004
The Ideal Gas Law--Applications 04The 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)
R R
n PPV n T
V T a fixed value
(at a given P & T, for any gas!)
• Implication? The concentration of gas particles is “fixed” at a
given T and P!
8Ppt17b
Prentice Hall ©2004
At the same T & P, [gas] is “fixed” (sample size does not matter)
(identity of the gas does not matter)
At the same T & P, [gas] is “fixed” (sample size does not matter)
(identity of the gas does not matter)
…same number of particles per L
Same T & P …
He
Ar
H2
He
Ppt17b 9
Prentice Hall ©2004
Density of a gas at fixed T and P does depend on gas identity (molar mass)!
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!
x m n
d MMV V
x g mol g
L L mol
• 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)
This slide is intended to make a conceptual connection, not give you another equation to memorize!
10
Prentice Hall ©2004
Summary (of prior few slides): At the same T & P, concentration is constant, but density varies with MM
Summary (of prior few slides): At the same T & P, concentration is constant, but density varies with MM
…different densities for different gaseous substances, because mass
Same # particles / L, but…
per particle (and thus per mole) varies!
He
Ar
H2
He
Greatest density b/c greatest MM 11
Prentice Hall ©2004
Practical Application: Will gases (or balloons filled with
them) float or sink (in air)? MM is the key!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?Ppt17b 12
Prentice Hall ©2004
The bottom line? Density of a gas depends on molar mass, T, & P, but not on “amount”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
Ppt17b 13
Prentice Hall ©2004
The Ideal Gas Law—Applications (Examples)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?
Ppt17b 14