Physical Chemistry 1 CHEM 3310

Chem 3310 Credit 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 PM Office Hours: Sunday 10:00- 12:00 PM, Monday 10:00 -12:00 PM Text book: Atkin’s, Except First Lecture from General Chemistry book, Chang 3rd Edition.

توزيع الدرجات 100 points Class Work الاعمال الفصلية 60 points 2 Exams 2 x 10= 20 points Final Exam الاختبار النهائي 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

The Four Postulates of the Kinetic Theory 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. KE = ½ mu2

Application of Kinetic Molecular Theory (KMT) to the Gas Laws Compressibility of Gases: Gases are compressed hence molecules are separated by large distances  compressed easily.

Boyle’s Law Experimentally P a 1/V KMT explained Boyle’s Law as: 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 density Number density a 1/V P a 1/V

Charles’ Law Experimentally P a T KMT explained Charles’ Law as: 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 wall Collision rate a average kinetic energy of gas molecules Average kinetic energy a T P a T

Avogadro’s 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

Experimentally Ptotal = SPi Dalton’s Law of Partial Pressures 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 another P exerted by one type of molecule is unaffected by the presence of another gas Ptotal = SPi

Ideal Gas Law 1 Boyle’s law: V a (at constant n and T) P Charles’ law: V a T (at constant n and P) Avogadro’s law: V a n (at constant P and T) V a nT P V = constant x = R nT P R is the gas constant PV = nRT

Distribution of Molecular Speeds 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 = 3RT M  M: molar mass Heavier gas is more slowly than lighter gas. R = (8.314 J/mol K), T is the temperature in kelvin

Example Calculate the root mean- square speeds of helium atoms and nitrogen N2 molecules in m/s at 25oC. Solution R= 8.314 J/K. mol, OR 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/mol Molar mass He = 4 x 10-3 Kg/mol

For Nitrogen 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 For real gases. PV/RT ≠ 1 As pressure increases and temperature decreases, real gases deviate from ideal gas behavior, The value ≠ (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

Volume of gas molecules can be ignored Behavior of Ideal Gas Low pressure High Pressure Volume of gas molecules can’t be ignored. Volume of gas molecules can be ignored V ideal = volume of distances separate molecules V measured = volume of distances separate molecules + volume of particles

Van Der Waals’ Correction of Volume V ideal = V measured - nb Where: n: number of moles b: constant related to molecular volume

Behavior of Real Gas Kinetic Theory of Gases postulates: 2- Pressure on the walls of a container is caused by molecular collisions with walls of container. No attractive forces between molecules It is applicable at high temperature It in inapplicable low temperature Why????

Behavior of Real Gas At High Temperature: , molecules have high kinetic energy an move very fast, so potential energy due to attractive forces between molecules can be ignored. At low temperature, molecules move very slow because they have small kinetic energy, therefore collisions with container wall decrease

Van Der Waals’ Correction of Pressure Van Der Waals’ Equation for Real Gases

High Temperature and Low Pressure. Behavior of Real Gas To make real gases have similar behavior to the ideal gases. They should be under High Temperature and Low Pressure.

Real Gases: Deviations from Ideality 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

P = (3.5 mol)(0.08206 L atm mol-1 K-1)(320K) (5.2 L) P = 17.7 atm Solution 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

2) Van der Waals Equation 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.