lecture Real Gases.pdf

Chapter 10: GasesPart 3: Real Gases

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Prepare for Recitation October 20thALEKS Objective 8 due October 18thANGEL Quiz 8, October 20th

Lecture 22: October 12thLecture 23: October 14thLecture 24: October 17th

Read: Ch. 10.1-10.9

Additional Preparation: BLB 10: 5,23,30,45,71,75,82-84; Packet 10: 1-15BLB 25: 11,12,25

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By the end of Todays Lecture you should know:

Kinetic-molecular theoryReal gases (van der Waals)

KEY QUESTIONS: THE BIG PICTURE

Chapter 10: GasesPart 3: Real Gases

What does partial pressure mean?What type of mixtures do gasses form?What state equation can we use to describe mixtures of gasses?

Remember: macroscopic properties come from microscopic origins

How does the energy of a molecule in a gas compare with intermolecular forces?

How can we describe mixtures of gasses?

How do real gasses differ from ideal gasses?

Effusion and Diffusion

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Note: Diffusion is more complicated due to collisions between gas molecules, but it also obeys Grahams Law.

Grahams Law of Effusion:

M2

M1

r1

r2=

Effusion:

Diffusion:

Heavy molecules diffuse (or effuse) more ______ than lighter ones.

1M

r proportional to

Practice Problem

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An unknown gas effuses at a rate 1.49 times faster than Cl2. What is the molecular weight of the gas?

A. 16.0 g/molB. 31.9 g/molC. 47.6 g/molD. 106 g/molE. 157 g/mol

Collisions and Diffusion

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The rate of diffusion follows Grahams Law

At STP molecules collide ~ 1010 times per second

N2 speed = 500 m/s

but

in 1 s it collides 1010 times

What happens to the MFP as density and pressure decrease?

Mean Free Path (MFP):

Review of Density and Molar Mass

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The Ideal Gas Law

The Connection between moles and mass

The Ideal Gas Law becomes:

The definition of density:

Density and the Ideal Gas Law:

n moles = m (mass)M (molar mass)

d = mV

Practice Problem

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Silicon tetrachloride is a starting material for the production of electronics-grade silicon. Calculate the density of pure silicon tetrachloride vapor at 85oC and 758 torr.

A. 0.238 g/LB. 5.77 g/LC. 1.00 g/LD. 24.3 g/LE. 0.056 g/L

Real Gases Deviate from Ideal Behavior

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For an ideal gas:

For a non-ideal gas (a real gas) this is not true for ____ pressure or ___ temperature.

Reasons:

1. Molecules have finite size.

2. Molecules exert attractive forces (IMF)

PV = nRTPV

nRT = 1

PVnRT > 1

PVnRT < 1

KMT and Non-Ideal Gas Behavior

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Kinetic Molecular Theory has 5 key postulates:

1) straight-line motion in random directions

2) Molecules are small & have no volume

3) No intermolecular interactions

4) Elastic collisions

5) Mean kinetic energy temperature

E = mv2

Deviations from ideal gas behavior are caused because gas molecules/atoms have ___________ and have _______________when they are close together.

Why does PV = nRT ?

Real Gases: At High Pressure, Postulate 2 in KMT is Not True

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At low pressures, deviation from ideal behavior is small.

At high pressures, use of the ideal gas law leads to an appearance of larger n.

For 1 mole of ideal gas: PV/RT = 1

Real Gases: At Low Temperature, Postulate 3 in KMT is Not True

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At low T or high P, attractive forces lead to the appearance of a smaller n.(IMF cause molecules to stick together)

As temperature increases the behavior of real gases becomes more ideal.

For 1 mole of ideal gas: PV/RT = 1

How Do We Account for This Behavior?

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High Pressure

Very High Pressure

Low Pressure

As Temperature increases the behavior of real gases becomes more ideal

Attractive forces lead to the appearance of a smaller volume or smaller n (depending on which was given)

Finite molecular volume leads to repulsion and the appearance of a larger volume or larger n

Attractive forces and finite molecular volume have minimal impact

@ high temps the kinetic energy overcomes the attractive forces

Non-Ideal Behavior and Measured Pressure

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For any gas we can measure P, V, T

But at higher P, the measured P is too small because of attractive forces

The amount of missing P is proportional to:1) the size of the attractive forces (a)2) the frequency of collisions (n/V)2

To compensate, use:

Non-Ideal Behavior and Measured Volume

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For any gas we can measure P, V, T But at higher P, the measured V is too

large because of the finite molecular volume per mole (b)

Actual volume:

Vactual = Vmeasured Vexcluded

To compensate, use:

(BLB Figure 10.25)

van der Waals Equation

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The Equation of state for REAL gases:

The Equation of state for IDEAL gases:

PV = nRT

nRTnbVaVnP =+ ))(( 2

2

Table 10.3 lists van der Waals constants (a,b) for various gas molecules.

Practice Problem

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What is the pressure P of 1.0 mol Cl2 in a 2.0 L vessel at 273 K?

Ideal Gas:

van der Waals:a = 6.49 L

2 atmmol2

b = 0.0562 L/mol

KMT and Non-Ideal Gas Behavior:Does This Make Sense?

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Kinetic Molecular Theory has 5 key postulates and two have causedproblems:2) Molecules are small & have no volume

3) No intermolecular interactions


2


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Molecules are small & have no volume.

At LOW Pressure:The volume of the container is ________compared with the volume of the particles

At HIGH pressures:The volume of the particles becomes ________ and the volume available to the gas is _________ the container volume


2

Gas b (L/mol) SizeNe 0.0171Ar 0.0322Kr 0.0398Xe 0.0510


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Molecules in a gas have no interactions.

At LOW Temperature:Intermolecular forces tend to be _________and the KE is insufficient to overcome themAt HIGH Temperature:The KE of the particles becomes ________the intermolecular forces and the behavior of the gas becomes __________


2

Gas a (atm L2/mol2) IMF StrengthCH4 2.25NH3 4.17H2O 5.46

What You Should Know

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Kinetic Molecular Theory How does KMT explain the pressure and

temperature of a gas, the gas laws, and the rates of effusion and diffusion?

Real Gases What effect does the V of a gas particle

have when we assume an ideal gas? What effects do intermolecular forces

have on the observed properties of gases when we assume an ideal gas?

How does the van der Waals Equation explain the properties of real gases?

In what way do you expect a real gas to deviate from ideal behavior as pressure is increased from low to high?

In what way do you expect a real gas to deviate from ideal behavior as temperature increases?

Chapter 10: GasesPart 3: Real GasesChapter 10: GasesPart 3: Real GasesEffusion and DiffusionPractice ProblemCollisions and DiffusionReview of Density and Molar MassPractice ProblemReal Gases Deviate from Ideal BehaviorKMT and Non-Ideal Gas BehaviorReal Gases: At High Pressure, Postulate 2 in KMT is Not TrueReal Gases: At Low Temperature, Postulate 3 in KMT is Not TrueHow Do We Account for This Behavior?Non-Ideal Behavior and Measured PressureNon-Ideal Behavior and Measured Volumevan der Waals EquationPractice ProblemKMT and Non-Ideal Gas Behavior:Does This Make Sense?KMT and Non-Ideal Gas Behavior:Does This Make Sense?KMT and Non-Ideal Gas Behavior:Does This Make Sense?What You Should Know

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lecture Real Gases.pdf