Physical Chemistry

Physical Chemistry CE 541

What is Physical Chemistry Is the science that deals with laws that is related (or that govern) chemical phenomena such as: • Gas laws • Oxidation-reduction reactions • Equilibrium relationship

Thermodynamics Is the study of energy changes accompanying physical or chemical processes

Thermodynamics (a). Heat and Work Heat Is a form of energy passing from one body to another as a result of temperature difference Heat Units • Calorie [heat required to raise the temperature of one gram of water one degree Celsius,  C] • British thermal unit (Btu) [heat required to raise the temperature of one pound of water by one degree Fahrenheit,  F] Btu = 252 Calories = 1,054 Joules (J)

Specific heat of a substance [heat required to raise the temperature of 1 gram of the substance by one degree Celsius,  C] Where • C = specific heat • q = heat added in Calories or Joules • M = weight of the substance, grams • T = raise in temperature,  C

For water at 15  C C = 1.000 Cal or 4.184 J / gram-degree C Heat of fusion : heat required to melt a substance at its normal melting temperature. Heat of vaporization : heat required to evaporate a substance at its normal temperature of boiling

Work Measured in: Force  Distance Work (dw) is equivalent to: Pressure  Volume Change Then, (dw) = P  dV Work Units • foot – pounds (ft-lb) • Joules ( 1 Cal = 4.184 J) • Btu (1 Btu = 778 ft-lb)

Work and Heat are forms of Energy. Therefore, Work = Heat

Thermodynamics (b). Energy Conservation-of-energy Law "Any heat or work which flow into or out of the system must result in a change in the total energy stored in the system" E = q -  • E = change in energy • q = heat flowing into the system •  = work done by the system

q is positive (+ve) if the system absorbs the heat • q is negative (-ve) if the system gives off the heat •  is +ve if the system does the work •  is –ve if the surroundings do the work on the system

If the chemical system does not expand or contract (volume is constant), then: E = qv • qv = heat absorbed in a constant-volume system In Environmental Engineering Applications, most of the systems are open, so they operate under constant pressure rather than constant volume

Thermodynamics (c). Enthalpy (H) H = E + PV Where • H = enthalpy • E = internal energy of the system • P = pressure on the system • V = volume of the system

Enthalpy A thermodynamic function of a system, equivalent to the sum of the internal energy of the system plus the product of its volume multiplied by the pressure exerted on it by its surroundings.

At constant pressure system, Heat absorbed by the system = qp Work done by the system can be obtained by integrating dw = P dv  = P (V2 – V1) then, change in internal energy is: E = E2- E1 = qp -  = qp – [P (V2 – V1)] Or (E2 + PV2) – (E1 + PV1) = qp

(E2 + PV2) is the final enthalpy (E1 + PV1) is the initial enthalpy So, H2 – H1 = qpH = qp (T and P are constant) • +ve heat means endothermic reaction (absorbs heat) • -ve heat means exothermic reaction (evolves heat) Change of enthalpy or heat of a given reaction can be found in Tables such as (Table 3-1)

To calculate heat of a reaction: • Write a balanced equation • Find standard enthalpy of reactants • Find standard enthalpy of products Then, Heat = (products) – (reactants)

Example (Problem 3.1) Determine the heat of combustion of ethane gas. The enthalpy of a chemical element (at its standard state) at 25 C and 1 atm is zero. For example, at standard states, O2 is gas, Mercury is liquid, Sulfur is crystal. Study Examples A and B on page 54

Thermodynamics (d) Entropy Is based on the second law of thermodynamics, which states "All systems tend to approach a state of equilibrium" In chemistry, we are interested in entropy to check the position of the equilibrium of a chemical process. Where • S = entropy of the system • T = absolute temperature • qrev = amount of heat that the system absorbs if a chemical change is brought about in an infinitely slow reversible manner

+ve S indicates that change can occur spontaneously • -ve S indicates that change tends to occur in reverse direction • Zero S indicates that system is at equilibrium

Entropy For a closed thermodynamic system, entropy is a quantitative measure of the amount of thermal energy not available to do work.

Thermodynamics (e). Free Energy In environmental engineering processes, both entropy and energy are needed in order to determine which processes will occur spontaneously. G = H – TS Where • G = free energy • H = enthalpy (J) • T = absolute temperature ( K) [ K =  C + 273] • S = entropy (J /  K)

At constant temperature and pressure: G = H - TS Since H = E + PV Then H = H2 – H1 = (E2 + P2V2) – (E1 + P2V1)

At constant P H = E + PV Since E = q -  Then H = q -  + PV

From At constant T TS = qrev If the system change is very slow, then energy loss is MINIMUM q = qrev  = max

In this case, PV represents the work that is wasted during the expansion of the system. Therefore:-G is the difference between the maximum work and the wasted work, which can be described as the useful work available from the system change. So:

If a system changes from a to b, then: • -ve G means that the system or process can proceed • +ve G means that the system or process can proceed in the reverse direction (b to a) • Zero G means that the system or process is at equilibrium and can not proceed in either direction. At standard state of elements and at 25 C and 1 atm, the free energy ( ) is zero. For values of , see Table 3-1.

Consider the following reaction: aA + bB  cC + dD Taking into consideration the concentration of reactants and products:

Where • G = reaction free-energy change (J) • = standard free-energy change (J) • R = universal gas constant = 8.314 J / K-mol = 1.99 cal / K-mol • T = absolute temperature in Kelvin ( K) • [ ] = activities of A, B, C, and D • and

At equilibrium; G = zero So, At equilibrium • K = equilibrium constant Therefore,

Comparison between Q and K • Q < K means the reaction proceeds from left to right • Q > K means the reaction proceeds from right to left • Q = K means the reaction is at equilibrium Study Examples A, B, C, and D page 58-59.

Thermodynamics (f). Temperature Dependence of K From relationship between • G and K • G and H In environmental engineering practices, the temperature range is limited and, therefore, H is constant. So, Study Example page 60

Osmosis Flow direction from dilute solution to concentrated solution is more rapidly than the other direction (concentrated  diluted)

In order to oppose that flow, pressure to the salt solution can be applied to produce equilibrium. That pressure is called osmotic pressure () •  = osmotic pressure, atm • R = 0.0882 l-atm / mol-K • T = absolute temperature, K • VA = volume per mole of solvent = 0.018 liter ( for water) • PA and PA = vapor pressure of solvent in the dilute and concentrated solutions, respectively

For dilute solutions, the reduction in vapor pressure of a solvent is directly proportional to the concentration of particles in solution. So, • c = molar concentration of particles In environmental engineering Reverse Osmosis is used to demineralized brackish waters

Dialysis and Electro-Dialysis Dialysis is a phenomena that is related to the principle of OSMOSIS

Main Membrane Processes • Are used to separate substances (solutes) from a solution (solvent) • The main membrane processes are • Dialysis • Electro-dialysis • Reverse osmosis • Driving forces that cause mass transfer of solutes are: • Difference in concentration (dialysis) • Difference in electric potential (electro-dialysis) • Difference in pressure (reverse osmosis)

Dialysis • Consists of : • Separating solutes of different ionic or molecular size • Solution • Selectively permeable membrane • The driving force is the difference in the solute concentration across the membrane

Batch Dialysis Cell • Solution to be dialyzed is separated from solvent by a semi-permeable membrane • Small ions and molecules pass from solution to solvent • Large ions and molecules do not pass due to relative size of membrane pore • The mass transfer of solute through the membrane is given by • M = mass transferred per unit time (gram/hour) • K = mass transfer coefficient [gram/(hr-cm2)(gram/cm3)] • A = membrane area (cm2) • C = difference in concentration of solute passing through the membrane (gram/cm3)

Applications of Dialysis • Sodium hydroxide was recovered from textile wastewater at: • Flowrate = 420 – 475 gal/day • Recovery of 87.3 to 94.6% • Dialysis is limited to small flows due to small mass transfer coefficient (K)

Electro-Dialysis • The driving force is an electromotive force • If electromotive force is applied across the permeable membrane: • An increased rate of ion transfer will occur • This results in decrease in the salt concentration of the treated solution • The process demineralizes • Brackish water and seawater to produce fresh water • Tertiary effuents

How it Works? • When direct current is applied to electrodes: • All cations (+vely charged) migrate towards cathode • All anions (-vely charged) migrate towards anode • Cations can pass through the cation-permeable membrane (C) but can not pass through (A) • Anions can pass through the anions-permeable membrane (A) but can not pass through (C) • Alternate compartments are formed • Ionic concentration in compartments is less than or greater than that in the feed solution

Physical Chemistry