Physical Chemistry 1CHEM 3310

Chem 3310Credit hrs: 4 (3+1)Prerequisite: chem 2020 Level: 5th

Class Time: Thursday Lecture 10:00 AM-12:30 PM Monday Lab. 12:00 – 2:00 PMOffice Hours: Sunday 10:00- 12:00 PM, Monday 10:00 -12:00 PMText book: Atkin’s, Except First Lecture from General Chemistry book, Chang 3rd Edition.

الدرجات توزيع

100 points

Class Workاالعمال الفصلية

60 points 2 Exams 2 x 10= 20 points

Final Examالنهائي االختبار

40 points Oral Exams+ Quizzes

2 x 10 = 20 points

CHEM 3310 Course Plan

Week # Topic

1,2 Gases & Kinetic Molecular Theory (KMT)

3,4 First Law of Thermodynamics & Thermochemistry

5,6 Second & Third Laws of Thermodynamic

7 Chemical Equilibrium

8 Phases & Solutions

9,10 Phase Equlibria

11 Solutions of Electrolytes

12 Electrochemical Cells

A pure gas consists of a large number of identical molecules separated by distances that are great compared with their size

( sizes of molecules are negligible comparing to distances).

The gas molecules are in constant motion and they collide to one another. And collide to walls of container. Collisions among molecules are elastic.

Pressure = Force

Area

The Four Postulates of the Kinetic Theory

• The molecules exert neither attractive nor repulsive on one another. No energy lost.

• The average kinetic energy of molecules is proportional to temperature of the gas in kelvin. Any two gases at the same temperature will have the same average kinetic energy. Where m is the mass, u is molecular speed.

The Four Postulates of the Kinetic Theory

KE = ½ mu2

Compressibility of Gases:• Gases are compressed hence molecules are

separated by large distances compressed easily.

Application of Kinetic Molecular Theory (KMT) to the Gas Laws

Experimentally P a 1/V

• Collisions of gas molecules with walls of container causes Pressure.

• Collision rate is (the number of molecular collisions with walls per second).

• Volume of container decreases the number density (number of molecules per unit volume of the gas) increases- collision rate increases. pressure of a gas is inversely proportional to volume that gas occupies.

• KMT explained Boyle’s Law as:P a collision rate with wall of container.Collision rate a number densityNumber density a 1/VP a 1/V

Boyle’s Law

Experimentally P a T

Average kinetic energy is proportional to absolute

temperature K. Consequently number of collisions of gas

molecules increases , and thus the pressure increases.

KMT explained Charles’ Law as:P a collision rate with wallCollision rate a average kinetic energy of gas moleculesAverage kinetic energy a TP a T

Charles’ Law

P a n ( number of moles)

KMT explained Avogadro’s Law as: P a collision rate with wall Collision rate a number density Number density a n P a n

Avogadro’s Law

Experimentally

Ptotal = SPi

Consider a case in which two gases, A and B, are in a container of volume

Ptotal = P1 + P2

Ptotal = Spi

KMT explained Dalton’s Law of Partial Pressure as:Molecules do not attract or repel one anotherP exerted by one type of molecule is unaffected by the

presence of another gasPtotal = SPi

Dalton’s Law of Partial Pressures

Charles’ law: V a T (at constant n and P)

Avogadro’s law: V a n (at constant P and T)

Boyle’s law: V a (at constant n and T)1P

V a nT

P

V = constant x = RnT

P

nT

PR is the gas constant

PV = nRT

Ideal Gas Law

Maxwell analyzed the behavior of gas molecules at different temperature.

Distribution curves tells us: • Peak of each curve represent the

most probable speed( speed of largest number of molecules)

• Most probable speed increases as temp. increases (i.e. shifts toward right)

• Curve flatten out with increasing temp. indicates larger number of molecules are moving at greater speed.

Maxwell speed distribution curves for N2 @ three different temps.

Distribution of Molecular Speeds

Lighter gas molecules move faster

than heavier gases.

He is faster than N2,

N2 is faster than Cl2

The distribution of speeds of three different gases at the same temperature

urms = 3RTM

M: molar mass Heavier gas is more slowly than lighter gas. R = (8.314 J/mol K), T is the temperature in kelvin

Distribution of Molecular Speeds

Example

Calculate the root mean- square speeds of helium atoms and nitrogen N2 molecules in m/s at 25oC.

Solution1. R= 8.314 J/K. mol, OR2. R= 0.082 L atm K−1 mol−1

3. Molar mass should be Kg/mol

Solution

R= 8.314 J/K. mol, R= 0.082 L atm K−1 mol−1, Molar mass = 4 g/molMolar mass He = 4 x 10-3 Kg/mol

smxu

smxu

skgkgmxu

SKgmJ

KgJxx

xxu

/1036.1

/1086.1

./1086.1

/11

/1086.1104

298314.83

3

226

226

22

63

M

RTurms

3

For Nitrogen

smu

smxu

molkgx

KmolKJu

/515

/1065.2

/10802.2

)298)(./314.8(3

225

2

Molar mass = 28.02g/ mol Molar mass N2= 2.802 x10-2 Kg/mol

Deviation of Real Gas Behavior

For 1 mole of ideal gas at any pressure and temperature.

PV/RT = 1

18

•As pressure increases and temperature decreases, real gases deviate from ideal gas behavior, • The value ≠ (1)

•For real gases. PV/RT ≠ 1

Why does real gas behavior deviate from ideal gas behavior?

Kinetic Theory of Gases postulates:

1- Volume of gas molecules ignored relative to the total volume of gas occupies the whole container.

It is applicable at low pressure i.e. volume is big.It in inapplicable at high pressure i.e. volume is small

20

Behavior of Ideal Gas

Volume of gas molecules can’t be ignored.

Volume of gas molecules can be

ignored

Low pressure

High Pressure

V ideal = volume of distances separate moleculesV measured = volume of distances separate molecules + volume of particles

V ideal = V measured - nb

Van Der Waals’ Correction of Volume

Where:n: number of molesb: constant related to molecular volume

21

Behavior of Real Gas

2- Pressure on the walls of a container is caused by molecular collisions with walls of container.

No attractive forces between molecules

Why????

22

Kinetic Theory of Gases postulates:

It is applicable at high temperatureIt in inapplicable low temperature

23

•At High Temperature: , molecules have high kinetic energy an move very fast, so potential energy due to attractive forces between molecules can be ignored.

Behavior of Real Gas

•At low temperature, molecules move very slow because they have small kinetic energy, therefore collisions with container wall decrease

Van Der Waals’ Equation for Real Gases

24

Van Der Waals’ Correction of Pressure

• To make real gases have similar behavior to the ideal gases. They should be under

High Temperature and Low Pressure.

Behavior of Real Gas

25

PROBLEM:

Given that 3.5 moles of NH3 occupy 5.2 L at 47oC, Calculate the pressure of the gas in (atm) using

1. The ideal gas equation

2. The van der Waals equation, where a= 4.17 atm

L2/mol2, b= 0.0371 L/mol

Real Gases: Deviations from Ideality

Solution

1) Ideal Gas Equation

PV = nRT

P = nRT/V V= 5.2 L n = 3.5 mol

T = 47 + 273= 320 K

P = (3.5 mol)(0.08206 L atm mol-1 K-1)(320K)

(5.2 L)

P = 17.7 atm

R= 0.0821 L. atm/K.mol

P + n a

VV nb nRT

2

2

atmP

KmolKatmLmolLLatmP

LmolLmolnb

atmL

molmolatmL

V

an

2.16

)320)(./.0821.0)(5.3()130.02.5)(89.1(

130.0)/0371.0)(5.3(

89.1)2.5(

)5.3)(/17.4(2

222

2

2

Lowering the actual gas indicates attraction forces between NH3 gas molecules results in a lower gas pressure than that of an ideal gas under the same condition.

2) Van der Waals Equation