Physical Chemistry
Physical Chemistry at Batangas State University
Definition of Physical Chemistry
Branch of chemistry establishing and developing principles
Used to explain and interpret observations on matter's properties
Essential for modern techniques in determining structure and properties
Application of Physical Chemistry
Application of physics methods to chemical problems
Qualitative and quantitative study of general principles of matter behavior
Study of Physical Properties
Includes macroscopic, microscopic, atomic, and subatomic scales
Describes chemical properties at different levels of physical detail
Purpose of Physical Chemistry
Collect data to define properties of gases, liquids, solids, etc.
Systemize data into laws and provide a theoretical foundation
Approaches of Physical Chemistry
Phenomenological approach starts with macroscopic materials
Investigates macroscopic properties like pressure and volume
Disciplines in Physical Chemistry
Thermodynamics, kinetics, quantum mechanics, etc.
Study energy interconversion, molecular properties, chemical processes, etc.
Properties of Matter
Extensive properties depend on the amount of matter
Intensive properties are independent of the amount of matter
Systems and Equilibrium
Open, closed, and isolated systems with different heat and material transfer abilities
Energy and Work
Energy is conserved and can be transferred as mechanical work or heat
States of Gases
Perfect gas model with continuous random motion of molecules
State defined by amount of substance, volume, and temperature
Thermal Equilibrium and Energy Conservation
Objects in thermal equilibrium do not change state
Energy is conserved and transferred as work or heat
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Pressure is the amount of equal force applied to a specific area
Formula: p = F/A
Gases can be stored in separate containers with a movable wall
Higher pressure gas compresses the lower pressure gas until equilibrium is reached
Page 28
Manometer is a simple pressure measuring device
Uses a U-tube with a non-volatile viscous fluid
Pressure is directly proportional to the height difference of the two columns
Formula: p = ρgh
Page 30
Example of pressure calculation involving methane as an alternative automotive fuel
Given: 1 gallon of gasoline can be replaced by 655 g of CH4
Calculate the volume of methane at 25°C and 745 torr
Page 32
Pressure measured by mm of Mercury indicates the pressure that raises the column of Mercury in a barometer to that height
Page 34
Temperature describes the flow of energy between objects
Energy flows from higher temperature objects to lower temperature objects until equilibrium is reached
Types of separatory boundaries: Diathermic and Adiabatic
Page 39
Ideal gas obeys certain laws, real gas obeys these laws only at low pressures
Page 40
Laws of gas behavior: Boyle’s law, Charles’s or Gay-Lussac’s Law, Dalton’s Law of Partial Pressures, Graham’s Law of Diffusion
Page 43
Boyle’s Law states pressure and volume are inversely proportional
Example calculation based on Boyle’s Law
Page 44
Charles’ Law describes how gases expand when heated
Volume of a gas changes by the same factor as its temperature at constant pressure
Example calculation based on Charles’ Law
Page 49
Dalton’s Law of Partial Pressures example involving nitrogen and oxygen gases in a container
Calculate partial pressures of nitrogen and oxygen, then find the total pressure
Page 50
Using Ideal Gas Law to find total pressure in Dalton’s Law example
Calculate partial pressures of nitrogen and oxygen
Find the total pressure in the container
Amagat’s Law of Partial Volumes
Definition: Volume of an ideal gas mixture equals sum of component volumes at same temperature and pressure.
Formula: V = V1 + V2 + ... + Vn
Example Calculation using Amagat's Law (Page 52)
Given: 50 mol of oxygen gas and 190 mol of nitrogen gas at T = 298.15K, P = 1x10^5 Pa
Using Ideal Gas Law: Vtotal = (50+190) mol * (0.082056 m^3-Pa/mol-K) * 298.15K / 1x10^5 Pa
Calculations for VO2 and VN2: VO2 = 1.24 m^3, VN2 = 4.71 m^3
Total volume: Vtotal = VO2 + VN2 = 5.95 m^3
Graham’s Law of Diffusion (Page 53)
States that rates of diffusion vary inversely as square roots of densities or molecular weights.
Formula: µ1/µ2 = √(ρ2/ρ1)
Example Calculation using Graham’s Law (Page 54)
Given rates: RateHe/RateNe = 20.18 amu / 4.003 amu = 2.25
Helium gas diffuses 2.25 times faster than Neon gas.
Compressibility Factor (Page 55)
Definition: Z modifies ideal gas law for real gas behavior.
Formula: Z = pVm / RT
Ideal gas: Z = 1, but real gases deviate.
Obtained from equations of state or compressibility charts.
Kinetic Molecular Theory (Page 59)
Assumptions: Gases consist of molecules in continuous motion, negligible volume, no significant intermolecular forces.
Average kinetic energy remains constant at constant temperature.
Average kinetic energy proportional to absolute temperature.
Application of Kinetic Molecular Theory to Gas Laws (Pages 60-61)
Volume increase at constant temperature leads to pressure decrease (Boyle's Law).
Temperature increase at constant volume leads to pressure increase (Charles's Law).
Kinetic Molecular Theory of Ideal Gas (Pages 62-63)
Explanation of a single molecule's motion in a container.
Force exerted on the wall equals change in momentum per unit time.
Momentum change during elastic collisions.
Page 64
Change of momentum is -2𝑚𝑢𝑥
Each collision with the wall occurs after the molecule travels a distance of 2x
Number of collisions a molecule makes in unit time is 2𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑜𝑙𝑙𝑖𝑠𝑖𝑜𝑛 𝑖𝑛 𝑢𝑛𝑖𝑡 𝑡𝑖𝑚𝑒 = 𝑢𝑥 2𝑥
Change of momentum per unit time is 𝐹 = 𝑚 𝑑𝑢 𝑑𝑡 = −2𝑢𝑥𝑚 𝑢𝑥 2𝑥 = − 𝑚𝑢𝑥 2 𝑥
Page 65
Force Fw exerted on the wall by the particle is 𝐹𝑤 = −𝐹 = 𝑚𝑢𝑥 2 𝑥
Pressure in the X-direction, Px, is 𝑷𝒙 = 𝑵𝒎𝒖𝒙 𝟐 𝑽 = 𝒎𝒖𝒙 𝟐 𝑽
Page 66
Distribution of molecular velocities in an assembly of N molecules
Pressure should be written as 𝑷𝒙 = 𝑵𝒎𝒖𝒙 𝟐 𝑽
Page 67
Expressions for velocity components in Y and Z directions
Average over all molecules gives 𝑢2 = 𝑢𝑥 2 + 𝑢𝑦 2 + 𝑢𝑧 2
Page 68
Mean of 𝑢𝑥 2, 𝑢𝑦 2, 𝑢𝑧 2 values are equal
Final expression for pressure on any wall: 𝑷 = 𝑵𝒎𝒖𝟐 𝟑𝑽
Page 69
Relation with Boyle’s law and Charles’ law
Substituting nRT for PV: 𝒏𝑹𝑻 = 𝟏 𝟑 𝑵𝒎𝒖𝟐
Page 71
Boltzmann constant = 1.380622 𝑥 10−23𝐽/𝐾
Total Kinetic Energy: 2/3 𝑛𝐸𝑘 = 𝑛𝑅𝑇 or 𝑬𝒌 = 𝟑/𝟐𝑹𝑻
Page 72
Sample problem: Given values for T, kB, mN2
Calculations for average kinetic energy per molecule
Page 73
Sample problem: Calculations for mass and velocity
Mass conversion to kg and calculation of velocity
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Molecules behave as rigid spheres in elastic collisions
Two kinds of molecules: A and B with diameters dA and dB
Collision occurs when distance between centers of A and B is dAB = (dA + dB)/2
Collision diameter is important in molecular collisions
Page 76
Number of collisions experienced by one molecule of A in unit time is ZA = πdAB^2uANB/V
Collision frequency is calculated for molecular collisions
Page 77
Expression for ZA when only A molecules are present: ZA = 2πdA^2uANAV/V
Collision frequency is determined for molecular collisions
Page 78
In a mixture with molecules A and B of different masses, average relative speed is (uA^2 + uB^2)^1/2
Modification of collision calculations for mixtures with different masses
Page 79
Total number of A-B collisions per unit volume per unit time is ZAB = πdAB^2uANANB/V^2
Collision density is defined as the number of collisions divided by volume and time
Page 80
Average relative speed in mixtures with different masses is (uA^2 + uB^2)^1/2
Collision density calculation is modified for mixtures with different masses
Page 81
Average relative speed of two A molecules is uAA = 2uA
Corrected expression for collision density when only A molecules are present
Page 82
Example scenario with Nitrogen and Oxygen in a container at 300K
Given collision diameters and partial pressures for N2 and O2
Calculate ZA and ZAB for nitrogen and oxygen molecules at 300K and 3000K
Overall, the text discusses the concept of molecular collisions, collision frequency, collision density, and calculations involving different types of molecules in mixtures.
Page 83
Example Solution for calculating the values of N2 and O2 using the ideal gas law
N2 calculation: 1.93 x 10^25 at 300K
O2 calculation: 5.07 x 10^24 at 300K
Page 84
Example Solution for total number of collisions with unlike molecules
N2: 1.33 x 10^9 s^-1
O2: 5.08 x 10^9 s^-1
Page 85
Example Solution for total number of collisions per cubic meter per second
N2, O2: 2.57 x 10^34 m^-3 s^-1 at 3000K
Page 87
Maxwell's work on the kinetic theory of gases
Formulated Maxwell-Boltzmann kinetic theory of gases in 1866
Showed that temperatures and heat are related to molecular movement
Page 88
Maxwell Distribution of Speeds
Showed distribution of speeds in a gas with an analytical equation
Higher temperatures have broader distributions of speeds
Lighter molecules have broader speed distributions than heavier ones
Page 89
Quantities related to Maxwell Distribution of Molecular Speeds
Mean-square speed, square root of mean-square speed, average speed, most probable speed, average translational energy
Page 90
Maxwell-Boltzmann distribution Law
Conversion of Maxwell distribution of speeds to an equation for energy distribution
Page 91
Maxwell-Boltzmann distribution Law
Replacement of variables in Maxwell distribution equation to obtain the distribution law
Main Ideas
Page 92
Mean free path (𝜆) is the average distance a molecule travels between two successive collisions.
Calculated using the formula 𝜆 = 𝑉 / (2𝜋𝑑^2𝑁𝐴).
The magnitude of dA's is crucial for kinetic theory of gases to calculate collision numbers and mean free path.
Page 93
Mean free time is the average time before a randomly picked electron has its next collision.
It is independent of the elapsed time since the prior collision.
Mean free time is determined by the formula involving the radius (r) of the atom being analyzed.
Page 94
Example problem: Finding the mean free time for argon atoms at specific conditions.
Given parameters include MAr, T, p, rAr, and kB.
Page 98
Real gases exhibit properties not explained by the ideal gas law.
Factors to consider include compressibility effects, variable specific heat capacity, van der Waals forces, non-equilibrium thermodynamic effects, and molecular dissociation.
Real gases deviate from ideal gases, especially at high pressures or near condensation.
Page 100
Real gases deviate from ideality due to two factors: volume not approaching zero at high pressure and intermolecular forces.
Interactions become significant at low temperatures when molecular motion slows down.
Page 101
Compression factor (Z) accounts for the deviation of real gases from ideal behavior.
Repulsive forces assist gas expansion, while attractive forces aid compression.
Page 102
The compression factor, Z, is the ratio of the measured molar volume to the molar volume of a perfect gas at the same pressure and temperature.
Page 105
For real gases, the compression factor (Z) can be less or more than one.
Z<1 indicates positive deviation, with deviations being low at low pressures.
Page 109
Critical constants like critical temperature (Tc), molar volume (Vc), and pressure (pc) are unique to each substance.
Substances with dense phases above Tc are known as supercritical fluids.
Page 110
Supercritical fluids are defined by their critical temperature (TC) and critical pressure (pC).
The critical point is where a substance can exist as both vapor and liquid in equilibrium.
Page 111
Carbon dioxide's critical point is at 73.8 bar and 31.1°C.
Moving along the boiling curve increases pressure and temperature, affecting the density of the gas and liquid.
Page 112
Johannes Diderik van der Waals won the Nobel Prize for his work on the equation of state for gases and liquids.
The van der Waals equation includes coefficients a and b to represent molecular forces and volume.
Page 113
Summary equations derived from the van der Waals equation are provided.
These equations relate to critical volume, temperature, pressure, compressibility factor, and other properties.
Page 114
A sample problem involves calculating the pressure difference between methane and an ideal gas using van der Waals constants.
Page 115
Another sample problem involves determining the van der Waals constants for water and comparing them to the universal gas constant.
Page 116
A sample problem asks for the critical temperature and pressure of Ne gas using van der Waals constants.
Page 117
The principle of corresponding states states that all fluids at the same reduced temperature and pressure have similar compressibility factors.
Reduced variables are used for comparing different gases.
Page 118
The principle of corresponding states is an approximation that works best for gases with spherical molecules.
It may fail for non-spherical or polar molecules.
Page 119
Equations of state describe the state of matter under specific physical conditions.
They relate state variables like temperature, pressure, and volume.
Page 120
Virial equations relate to the forces of interaction between gas molecules.
Coefficients B and C in the virial equation are temperature-dependent.
Page 121
For real gases with large volumes and high temperatures, isotherms are similar to ideal gases with small differences.
The perfect gas law is considered the first term in a power series.
Page 122
Virial equations of state show how coefficients B and C affect the behavior of gases at different pressures.
Deviations from ideal gas behavior occur as pressure increases.
Page 123
Cubic equations of state include Redlich and Kwong, Soave Redlich Kwong, and Peng–Robinson equations.
Page 124
The Redlich and Kwong equation, introduced in 1949, is an improvement over previous equations but has limitations in calculating vapor-liquid equilibrium accurately.
Cubic Equations of State
Redlich and Kwong Equation (RK)
The Redlich-Kwong equation is suitable for gas phase property calculations when the pressure to critical pressure ratio is less than half of the temperature to critical temperature ratio.
Soave Redlich Kwong Equation (SRK)
Soave replaced the temperature term in the Redlich-Kwong equation with a function involving temperature and the acentric factor.
The acentric factor measures how a substance's properties differ from those predicted by the Principle of Corresponding States.
Peng – Robinson Equation of State
Developed in 1976 to meet specific goals like expressibility in terms of critical properties and acentric factor.
Should provide accuracy near the critical point and be applicable to natural gas processes.
Selected Equations of State
The Peng-Robinson Equation of State is a key equation for fluid property calculations.
Introduction to Thermodynamics
Thermodynamics studies energy changes in systems.
It involves energy conversion, directions of change, and molecular stability.
Systems and Surroundings
Systems are objects of interest, while surroundings are everything outside the system.
Different types of systems include open, closed, and isolated systems.
State and Path Functions
State functions depend only on initial and final states, while path functions depend on the sequence of steps.
Examples of state functions are internal energy and enthalpy.
Laws of Thermodynamics
The Zeroth Law states conditions for thermal equilibrium.
The First Law emphasizes energy conservation and the equivalence of heat and work.
Joule's experiments established the relationship between work and heat, leading to the concept of mechanical equivalent of heat.
Joule's Experiment
Joule demonstrated the quantitative relationship between work and heat, establishing heat as a form of energy.
He introduced the concept of mechanical equivalent of heat denoted by 'J'.
Page 148
Joule's first law relates heat generated by electric current in a conductor
Formula: Q = I^2 * R * t
Joule's second law states internal energy of ideal gas remains constant with volume and pressure changes, but changes with temperature
Page 149
Joule's law: Heat generated in a conductor is proportional to current, resistance, and time
Proportional to: square root of current, resistance, and time
Page 150
Energy is the capacity to do work, measured in Joules or kJ per mol
Work is a form of energy transferred in and out of a system, stored in organized motion of molecules
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Heat is a form of energy transferred in and out of a system, stored in random motion of molecules
Energy transfer due to temperature difference is heat
Page 154
First law of thermodynamics: Internal energy is a state function, dependent on the system's state
Page 155
Work is energy transferred during a state change, convertible to lifting a weight
Heat is energy transferred due to temperature difference
Page 157
Exothermic process releases heat, endothermic absorbs heat
Adiabatic system doesn't allow heat transfer
Page 158
Temperature changes in endothermic and exothermic processes in adiabatic and diathermic systems
Page 159
Kinetic energy formula: KE = 1/2 * mv^2
Potential energy formula: P = mgh
Page 160
Internal energy is the total energy of a system from kinetic and potential energy of molecules
Change in energy (ΔU) is the difference between initial and final internal energy
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Internal energy changes by work (w) and heat transfer (q)
Conservation of energy formula: ΔU = Q + W
Page 169
Heat and work change system's energy equivalently
Isolated system has no change in internal energy: ΔU = 0
Page 170
Infinitesimal changes in state and energy connect small changes in heat and work to total energy
Expansion work involves changes in volume due to gas expansion
Page 171
Expansion work leads to volume change, like gas expansion against atmospheric pressure
Examples: thermal decomposition of CaCO3, combustion of octane
Page 172
Work done against external pressure: dW = -PexAdz
Change in volume: dV = Adz
Page 173
Expansion work involves moving an object against opposing force and changes in volume.
Page 174
Force acting on the piston is equivalent to raising a weight during expansion
Compressing the system is similar, but with initial volume greater than final volume
Free expansion has no opposing force, resulting in work done being zero
Page 177
Work done by a gas expanding against constant pressure is represented by shaded area in an indicator diagram
Page 178
Reversible processes occur when system is infinitesimally close to equilibrium
Maximum work is obtained in reversible processes between specific initial and final states
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Isothermal reversible expansion occurs when system is in contact with constant thermal surroundings
Page 183
Work in reversible expansion at constant temperature is represented by area under the isotherm
More work and maximum pushing power are obtained from reversible expansion
Page 186
Irreversible processes involve finite departures from equilibrium and cannot be reversed by infinitesimal changes
Page 187
Conditions of irreversibility include heat transfer through a finite temperature difference, friction, plastic deformation, etc.
Page 189
Isochoric process has fixed pressure and both work and heat exist
Isobaric process has constant pressure
Page 191
Isothermal process work is calculated using W = -nRT ln(Vf/Vi)
Page 192
Adiabatic process involves no heat transfer
Page 195
Work done in isothermal expansion is calculated using W = -nRT ln(Vf/Vi)
Page 197
Adiabatic compression of hydrogen is analyzed to find final pressure and temperature
Page 198
Final pressure and temperature of hydrogen after adiabatic compression are calculated
Page 196
Work done in isothermal expansion of hydrogen is calculated
Page 184
Sample problem on calculating work done in different scenarios
Page 185
Solution to the sample