Physical Chemistry (TKK-2446) 16/17 Semester 2 Physical Chemistry (TKK-2446) Instructor: Rama Oktavian Email: Oktavian.rama2@gmail.com Office Hr.: M. 10 – 12, T. 10 – 12, W. 09 – 10, F.10 – 15

Outlines 1. Kinetic theory of gas 2. Condensed phase 3. Properties of liquids 4. Solid structure

Learning check Molar mass of gas In an experiment to measure the molar mass of a gas, 250 cm3 of the gas was confined in a glass vessel. The pressure was 152 Torr at 298 K and, after correcting for buoyancy effects, the mass of the gas was 33.5 mg. What is the molar mass of the gas?

Learning check Dalton’s partial pressure A gas mixture consists of 320 mg of methane, 175 mg of argon, and 225 mg of neon. The partial pressure of neon at 300 K is 8.87 kPa. Calculate (a) the volume and (b) the total pressure of the mixture.

Learning check Dalton’s partial pressure A vessel of volume 22.4 dm3 contains 2.0 mol H2and 1.0 mol N2 at 273.15 K initially. All the H2 reacted with sufficient N2 to form NH3. Calculate the partial pressures and the total pressure of the final mixture.

Kinetic theory of gases Kinetic theory of gas observes molecular motion in gases In the kinetic model of gases we assume that the only contribution to the energy of the gas is from the kinetic energies of the molecules The pressure that a gas exerts is caused by the collisions of its molecules with the walls of the container.

Kinetic theory of gases Pressure and molecular speed relation (1) Where M = mNA, the molar mass of the molecules, and c is the root mean square speed of the molecules, the square root of the mean of the squares of the speeds, v, of the molecules: (2)

Kinetic theory of gases Pressure and molecular speed relation Justification Consider the movement of gas the momentum before collision is the momentum after collision is the change in momentum is the difference between final and initial momentum

Kinetic theory of gases Pressure and molecular speed relation Justification The distance that molecule can travel along the x-axis in an interval ∆t is written as if the wall has area A, then all the particles in a volume will reach the wall

Kinetic theory of gases Pressure and molecular speed relation Justification The number density of particles is where n is the total amount of molecules in the container of volume V and NA is Avogadro’s constant The number of molecules in the volume x

Kinetic theory of gases Pressure and molecular speed relation Justification At any instant, half the particles are moving to the right and half are moving to the left Therefore the number of molecules will become The total momentum change within interval Δt is x

Kinetic theory of gases Pressure and molecular speed relation Justification The total momentum change within interval Δt is x Where M = mNA

Kinetic theory of gases Pressure and molecular speed relation Justification Rate of change of momentum can be written as total momentum divided by time interval rate of change of momentum is equal to the force (by Newton’s second law of motion)

Kinetic theory of gases Pressure and molecular speed relation Justification the pressure, the force divided by the area, is rate of change of momentum is equal to the force (by Newton’s second law of motion) Not all the molecules travel with the same velocity, so the detected pressure, p, is the average (denoted ) of the quantity just calculated

Kinetic theory of gases Pressure and molecular speed relation Justification To write an expression of the pressure in terms of the root mean square speed, c, we begin by writing the speed of a single molecule, v, as because the molecules are moving randomly, all three averages are the same, it follows

Kinetic theory of gases Pressure and molecular speed relation Justification

Kinetic theory of gases Pressure and molecular speed relation Using Boyle’s Law and ideal gas Law the root mean square speed of the molecules in a gas at a temperature T must be the higher the temperature, the higher the root mean square speed of the molecules, and, at a given temperature, heavy molecules travel more slowly than light molecules

Kinetic theory of gases Pressure and kinetic energy relation Kinetic energy of molecule is defined as M = mNA N = nNA

Kinetic theory of gases Pressure and kinetic energy relation Using Boyle’s Law and ideal gas Law k is Boltzmann constant k = 1.3806488 × 10-23 m2 kg s-2 K-1

Condensed Phase The definition of “condensed” 1. reduced in volume, area, length, or scope; shortened: a condensed version of the book. 2. made denser, especially reduced from a gaseous to a liquid state. 3. thickened by distillation or evaporation; concentrated: condensed lemon juice. http://dictionary.reference.com/browse/condensed

Condensed Phase The definition of “condensed phase” Solid and Liquid are condensed phase because the particles are very close together. There are strong intermolecular forces

Condensed Phase The definition of “condensed phase” made denser, especially reduced from a gaseous to a liquid state.

Liquid state Structure of liquids

Liquid state Structure of liquids Substances that can flow are referred as fluids. Both gases and liquids are fluid

Liquid state Structure of liquids The particles that form a liquid are relatively close together, but not as close together as the particles in the corresponding solid. The particles in a liquid have more kinetic energy than the particles in the corresponding solid. As a result, the particles in a liquid move faster in terms of vibration, rotation, and translation. Because they are moving faster, the particles in the liquid occupy more space, and the liquid is less dense than the corresponding solid.

Liquid properties Thermal expansion Compressibility Vapor pressure intermolecular forces will play a major role in explaining their physical properties. Thermal expansion Compressibility Vapor pressure

Liquid properties How to describe P-V-T relationship in liquid state? The dependence of the volume of a solid or liquid on temperature at constant pressure can be expressed by where : α is coefficient of thermal expansion V0 is volume of liquid at 0 C t is temperatur in Celcius

Liquid properties How to describe P-V-T relationship in liquid state? V0 is function of pressure and expressed as where : is volume of liquid at 0 C and 1 atm V0 is volume of liquid at 0 C is coefficient of compressibility

Liquid properties General definition of and Equation of state for liquid V = V(p,T) Take the partial derivative

Liquid properties General definition of and Volume expansivity Isothermal compressibility EoS for liquid can be written as:

Liquid properties General definition of and Volume expansivity The value is usually small Isothermal compressibility

Liquid properties General definition of and

Liquid properties The effect of pressure change to volume change of liquids If we take atm-1 , then for a pressure of two atmospheres, the volume of the condensed phase is The decrease in volume in going from 1 atm to 2 atm pressure is 0.001 % Liquid is incompressible fluid

Liquid properties EoS for liquids Find the volume change when acetone is changed from 293.15 K and 1 bar to 273.15 K and 10 bar

Liquid properties Viscosity Surface tension Vapor pressure Other properties of liquid Viscosity Surface tension Vapor pressure

Liquid properties the resistance of a liquid to flow Viscosity the resistance of a liquid to flow Intensive property of liquids Viscosity depends on: - The attractive forces between molecules - Temperature - The viscosity of liquids decreases with increase the temperature

Liquid properties Effect of temperature M.A. Mehrabian, M. Khoramabadi, (2007) "Application of numerical methods to study the effect of variable fluid viscosity on the performance of plate heat exchangers", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 17 Iss: 1, pp.94 - 107

Liquid properties Surface tension the amount of energy required to increase the surface area of a liquid by a unit amount Stronger intermolecular forces cause higher surface tension Water has a high surface tension (H-bonding)

Liquid properties Surface tension

Liquid properties Phase change

Liquid properties Phase change Energy Changes Accompanying Phase Changes • melting or fusion:ΔHfus> 0 (endothermic) • vaporization:ΔHvap> 0 (endothermic) • sublimation:ΔHsub> 0 (endothermic). •deposition: ΔHdep < 0 (exo). •condensation: ΔHcon < 0 (exo). • freezing: ΔHfre < 0 (exo). •The following sequence is endothermic: heat solid → melt → heat liquid → boil → heat gas •The following sequence is exothermic: cool gas → condense → cool liquid → freeze → cool solid

Liquid properties Heating curve

Liquid properties Vapor pressure Vapor pressure the pressure exerted by its vapor when the liquid and vapor are in dynamic equilibrium Dynamic equilibrium is a condition in which two opposing processes occur simultaneously at equal rates Some of the molecules on the surface of a liquid have enough energy to escape the attraction of the bulk liquid. •These molecules move into the gas phase. As the number of molecules in the gas phase increases, some of the gas phase molecules strike the surface and return to the liquid.

Liquid properties Vapor pressure as function of temperature

Liquid properties Evaporation vs boiling evaporation is a surface phenomenon - some molecules have enough kinetic energy to escape Boling point is the temperature at which the vapor pressure is equal to the external pressure, bubbles form

Liquid properties Normal boiling point The temperature at which the vapor pressure is equal to 1 atm

Solids Crystalline solid the units that make up the solid are arranged in a very regular, repeating pattern. Amorphous solid An amorphous solid lacks the long range order of a crystalline solid. Most plastics are amorphous solids. (they are polymers)

Solids Covalent Network Solids In a covalent network solid, all of the atoms in a crystal are held together by covalent bonds. Some examples of covalent network solids are diamond (C), boron nitride (BN), and silicon dioxide (SiO2).

Solids Ionic Solids An ionic solid consists of oppositely charged ions, held together by strong electrostatic interactions. Binary compounds made up of a metal and a nonmetal are in this category. Example: NaCl

Problems EoS of liquids Express the volume expansivity and theisothermal compressibility as functions of density p and its partial derivatives For water at 323.15 K (50°C) and 1 bar, K = 44.18 x10-6 bar-1. To what pressure must water be compressed at 323.15 K (50°C) to change its density by 1 %? Assume that K is independent of P.

Problems Castellan prob 5.7

Thank You !