PV = nRT - Georgia Institute of...

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Week 3 CHEM 1310 - Sections L and M 1

Wed | Sep 12, 2007

Chapter 5: Gases– Gas Stoichiometry– Partial Pressure– Kinetic Theory– Effusion and Diffusion

Exam #1 - Friday, Sep 14– Attendance is mandatory!– Practice exam today in recitation


PV = nRT

THE GASEOUS STATE

Pressure atmVolume litersn molesR L atm mol-1K-1

Temperature Kelvin

Ideal Gas Law

Earlier… used the Ideal Gas Law to determine mass.

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PRS Question #1

What mass of argon is contained in an 18.6L containerat 20°C if the pressure is 2.35 atm?

(1) 21.9 g

(2) 72.6 g

(3) 322 g

(4) 1.82 kg

PV =mass

(MW)x RT


What mass of argon is contained in an 18.6L containerat 20°C if the pressure is 2.35 atm?

(1) 21.9 g

(2) 72.6 g

(3) 322 g

(4) 1.82 kg

PRS Question #1- Solution

Mass = P x V x MW

R x T

Mass = (2.35 atm) x (18.6L) x (39.948 g/mol)

(0.08206 L atm mol-1 K-1) x (293.15K)

Mass = 72.6 g

What else can be determined using the Ideal Gas Law?

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PV = nRT

Gas Density

Ideal Gas Law

PV = RTmass

(MW)

massV

= P (MW)RT

= density


PRS Question #2

What is the density of carbon tetrafluorideat 1.00 atm and 50 ºC?

1) 0.0377 g/L2) 0.244 g/L3) 3.32 g/L4) 21.4 g/L

PV = nRT What do we need to do tosolve this problem?

(1) Know chemical formula

(2) Convert Ideal Gas Law intodensity equation

(3) Be mindful of units

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Gas Density Calculation


Chemical Formula forcarbon tetrafluoride CF4

Density = [P x (MW)]/RT

P = 1.00 atm; MW = 88 g/mol; R = 0.08206 L atm mol-1K-1; T = 50 + 273.15 = 323.15K


Gas Density Calculation


Density = 3.32 g/L

(1.00 atm) (88 g/mol)

(0.08206 L atm mol-1K-1) (323.15K)

Density = [P x (MW)]/RT

1) 0.0377 g/L2) 0.244 g/L3) 3.32 g/L4) 21.4 g/L

PV = nRT

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PV = nRT

Molar Mass

Ideal Gas Law

PV = RTmass

(MW)

mass x= RTPV

MW


Mixtures of Gases

Dalton’s Law of Partial PressuresThe total pressure of a mixture of gasesequals the sum of the partial pressures

of the individual gases.

Ptotal = PA + PB

PAV = nART

PBV = nBRT

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Partial Pressures in Gas Mixtures

Ptotal = PA + PB

PA = nARTV

PB = nBRTV

Ptotal = PA + PB = ntotal RT

V


Mole Fractions

nA

ntotal

nB

ntotal

ntotal = nA + nB

The mole fraction of a component in a mixture isdefined as the # of moles of the components that are in

the mixture divided by the total # of moles present.

XA = XB =

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Mole Percents

nA

ntotal

Mole fractions must range from 0 – 1.Multiply mole fractions by 100 for mole percents.

XA = 0.5

Mole % = 50%

x 100XA =


For Ideal Gases…

PA = nARTV

Ptotal = ntotalRTV

PA nARTVPtotal ntotal RTV

= =nA

ntotal

Therefore…

PA = XA Ptotal

= XA

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Example Problem

Some sulfur is burned in excess oxygen.The gaseous mixture produced contains

23.2 g O2 + 53.1 g SO2 only.Its total pressure is 2.13 atm.

What is the partial pressure of SO2(g)?

PSO2 = XSO2

Ptotal

Calculate


Example Problem

The gaseous mixture produced contains23.2 g O2 + 53.1 g SO2 only.

# mol O2 = 23.2 g x1 mol O2

31.98 g O2

= 0.725 molO2

# mol SO2 = 53.1 g x1 mol SO2

64.06 g SO2

= 0.829 molSO2

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Example Problem

What is the partial pressure of SO2(g)?

X 0.829 mol0.725 mol + 0.829 mol

= 0.533SO2=

PSO2= XSO2

Ptotal = 0.533 x 2.13 atm

= 1.14 atm


Kinetic Theory of Gases

Separation by large distances compared to size

Constant movement in random directions with adistribution of speeds.

No force exerted except during collisions

Direction = straight line except between collisions

Collisions are elastic; no energy lost duringcollisions

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Molecular Collisions in Gases

Greater impulseon container

walls when themass of the gas

is greater

P ∝ mass




walls when thedensity increases

P ∝ N

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walls when theaverage speed

increases

P ∝ (speed)2


Molecular Speeds

PV = nRT PV = (1/3) Nmū2

Recall: N = nN0 and m = M/N0

nRT = (1/3) (nN0) (M/N0) ū2

RT = (1/3) Mū2 ū2 = (3RT)/M

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Molecular Speeds

M

3RTuu2

rms==

NOTE: Use SI units here…R = 8.31447 J mol-1K-1, where J = kg m2 s-2

T = KM = g/mol, where you would convert to kg/mol


Molecular Speeds

�

uavg =8RT

pM

NOTE: Use SI units here…R = 8.31447 J mol-1K-1, where J = kg m2 s-2

T = KM = g/mol, where you would convert to kg/mol

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Molecular Speed Distribution

Temp is a measure of the average kinetic energy of molecules when

their speeds exhibit the Maxwell-Boltzmann

distribution.


Molecular Motion

A gas molecule at ordinaryconditions follows a

straight path only for ashort time before colliding

with another molecule.The overall path is a

zig-zag.

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Diffusion and Effusion

DIFFUSIONthe spontaneous molecular mixing of materials

(usually liquids or gases) without chemicalcombination

EFFUSIONthe spontaneous movement of the molecules of

a gas through a hole whose size is smallcompared to their mean free path


Effusion

Which gas will effuse faster? How to determine this?

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Comparing Effusion Rates

Molecular weight of He = 4.0025 g/molūHelium is proportional to √(1/4) = 0.5

Molecular weight of O2 = 32 g/molūOxygen is proportional to √(1/32) = 0.176

Helium gas has a faster avg speed than O2 gas,therefore He will effuse faster than O2.


He Effuses Faster Than O2

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Final Reminders

Exam Study Notes online Practice Exams– Recitation today– Online via WebAssign

Homework– 5-7% students forget to submit their WebAssign

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PV = nRT - Georgia Institute of...

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