An Introduction of Chemical Thermodynamics as it applies to Water Geochemistry

1. An Introduction of Chemical Thermodynamicsas it applies to Water Geochemistry

2. Law of Conservation of Energy The total energy of the universe is constant and can neither be created nor destroyed; it can only be transformed from one state to another. The internal energy, U, of a sample is the sum of all the kinetic and potential energies of all the atoms and molecules in a sample. i.e. it is the total energy of all the atoms and molecules in a sample

3. SYSTEM OPEN ISOLATED CLOSED Systems & Surroundings In thermodynamics, the world is divided into a system and its surroundings A system is the part of the Universe under study, separated from the rest of the Universe by a well-defined boundary. The surroundings consist of everything else outside the system – rest of the universe. System Types of system Surroundings

4. OPEN SYSTEM: can exchange both matter and energy with the surroundings (e.g. open reaction flask, rocket engine), across its boundaries CLOSED SYSTEM: can exchange only energy with the surroundings (matter remains fixed) e.g. a sealed reaction flask. Closed systems have impermeable diathermal and moveable boundariesthat permit the transfer of heatand work between system and surroundings but prevent transfer of matter. ISOLATED SYSTEM: can exchange neither energy nor matter with its surroundings (e.g. a thermos flask) …entirely removed from environmental influences

5. Thermodynamic properties of a System/Matter • Extensive : Additive, and depends on the total mass of the system. Example: Volume • Intensive : Independent of the amount of matter present in the system. Example: pressure, temperature, density Change of state: when the properties of the system change it is called “change of state”. Example: when a quantity of gas in a cylinder is compressed by moving a frictionless piston, the system undergoes a “change of state”….State Variables

6. U = Ufinal - Uinitial U change in the internal energy INTERNAL ENERGY (U)-very imp concept Internal energy changes when energy enters or leaves a system Heat and work are 2 equivalent ways of changing the internal energy of a system

7. Change in internal energy Energy supplied to system as heat Energy supplied to system as work = + U like reserves of a bank: bank accepts deposits or withdrawals in two currencies (q & w) but stores them as common fund, U. q q w w U U = q (heat) + w (work)

8. Increase in volume, dV +dV Positive Work (Work is done by the gas) -dV Negative Work (Work is done on the gas) Work Done by An Expanding Gas Gas expands slowly enough to maintain thermodynamic equilibrium. Energy leaves the system and goes to the environment. Energy enters the system from the environment.

9. Work depends on the path taken in “PV space.” Pressure as a Function of Volume Work is the area under the curve of a PV-diagram.

10. Total Work Done To evaluate the integral, we must know how the pressure depends (functionally) on the volume. Work is the transfer of energy that takes place when an object is moved against an opposing force Definition: Work is defined as a quantity that flows across the boundary of a system during a change in its state and is completely convertible into the lifting of a weight in the surroundings.

11. The term Heat (Q) is properly used to describe energy in transit, thermal energy transferred into or out of a system from a thermal reservoir. Q U Heat • Q is not a “state” function --- the heat depends on the process, not just on the initial and final states of the system • Sign of Q : Q > 0 system gains thermal energy • Q < 0 system loses thermal energy BUT, the quantity Q - W does not depend on the path taken; it depends only on the initial and final states. Q - W internal energy.

12. The First Law of Thermodynamics statement of energy conservation for a thermodynamic system Heat and work are forms of energy transfer and energy is conserved. U = Q + Won change in total internal energy work done on the system heat added to system State Function Path Functions or U = Q - Wby Positive Q ->heat added to the system Positive W -> work done by the system

13. The First Law of Thermodynamics What this means: The internal energy of a system tends to increase if energy is added via heat (Q) and decrease via work (W) done by the system. . . . and increase via work (W) done on the system.

14. Enthalpy (H) On integrating between the limits initial and final stages, we can write from 1st Law, Or, For constant pressure, Therefore, and Replacing by Hi, This H is called enthalpy

15. First Law of Thermodynamics: Energy is Conserved ΔU = Ufinal - Uinital = q - w q = heat absorbed by the system from the surroundings w = work done by the system on the surroundings heat is random molecular motion while work is force times distanced moved under its influence Exothermic Processes release heat and have q<0 Endothermic Processes absorb heat and have q>0 Energy: The SI unit is joule (J) although we will frequently use calorie ; 1 cal = 4.2 J

16. The heat supplied is equal to the change in another thermodynamic property called enthalpy (H) i.e. H = Qp [only valid at constant pressure] As most reactions in chemistry take place at constant pressure we can say that: A change in enthalpy = heat supplied

17. EXOTHERMIC & ENDOTHERMIC REACTIONS Exothermic process: a change (e.g. a chemical reaction) that releases heat. A release of heat corresponds to a decrease in enthalpy. Exothermic process: H < 0 (at constant pressure). Condensation, crystallization of liquids Endothermic process: a change (e.g. a chemical reaction) that requires (or absorbs) heat. Absorption of heat corresponds to an increase in enthalpy. Endothermic process: H > 0 (at constant pressure). Evaporation, fusion, melting of solids

18. Vaporisation • Energy has to be supplied to a liquid to enable it to overcome forces that hold molecules together • endothermic process (H positive) • Melting • Energy is supplied to a solid to enable it to vibrate more vigorously until molecules can move past each other and flow as a liquid • endothermic process (H positive) • Freezing • Liquid releases energy and allows molecules to settle into a lower energy state and form a solid • exothermic process (H negative) • (we remove heat from water when making ice in freezer)

19. Heat of Reaction Let us consider A and B (compounds or elements) react to form a product A2B3. The change in enthalpy of the reaction in the standard state is: Heat of the reaction in the standard state standard enthalpy of formation of A2B3 A and B At equilibrium,

20. In general, is calculated by summing the standard enthalpies of the products and by subtracting the enthalpies of the reactants: n= molar coefficient of each reactant and product taken from a balanced equation, i= particular species involved in the reaction Units: kcal/mole Calorie: amount of heat required to raise the temperature of 1 g of water from 14.5 to 15.5C. Standard enthalpy of formation of ELEMENT is ZERO.

21. Heat Capacity When heat is transferred to an object, the temperature of the object increases. When heat is removed from an object, the temperature of the object decreases. The relationship between the heat ( q ) that is transferred and the change in temperature ( ΔT ) is The proportionality constant in this equation is called the heat capacity ( C ). The heat capacity is the amount of heat required to raise the temperature of an object or substance one degree. The temperature change is the difference between the final temperature ( Tf ) and the initial temperature ( Ti ). Heat capacity can be measured experimentally. Unit of T is Kelvin.

22. At constant pressure, From the definition of Enthalpy, So after rearranging, On integration between the limits, T0 (standard temperature) to T (any other temperature), The equation enables us to calculate enthalpy of formation of compound at temperature T.

23. Second Law of Thermodynamics the disorder (or entropy) of a system tends to increase • Entropy is a measure of disorder • Low entropy (S) = low disorder • High entropy (S) = greater disorder In any reversible process the change in the entropy of the system (dS) is equal to the heat received by the system (dQ) divided by the absolute temperature T. dS=dQ/T for reversible process dS>dQ/T for any spontaneous irreversible process Entropy is a state function

24. Dissolving disorder of solution disorder of surroundings Total entropy change entropy change of system entropy change of surroundings = + • must be an overall increase in disorder for dissolving to occur

25. 1. If we freeze water, disorder of the water molecules decreases , entropy decreases ( -ve S , -ve H) 2. If we boil water, disorder of the water molecules increases , entropy increases (vapour is highly disordered state) ( +ve S , +ve H)

26. A spontaneous change is a change that has a tendency to occur without been driven by an external influence e.g. the cooling of a hot metal block to the temperature of its surroundings A non-spontaneous change is a change that occurs only when driven e.g. forcing electric current through a metal block to heat it

27. A chemical reaction is spontaneous if it is accompanied by an increase in the total entropy of the system and the surroundings • Spontaneous exothermic reactions are common (e.g. hot metal block spontaneously cooling) because they release heat that increases the entropy of the surroundings. • Endothermic reactions are spontaneous only when the entropy of the system increases enough to overcome the decrease in entropy of the surroundings

28. Gibbs Free Energy (State function) 2nd law implies that the increase in the H of a system during a reversible change in its state at constant T is diminished because a certain amount of the H is consumed by an increase in the entropy of the system. The relation between enthalpy & entropy can be defined as follows: G=H-TS Gibbs free energy Entropy Enthalpy In standard state, Unit: kcal/mol Standard Gibbs free energy of formation of a compound is the change in the free energy of the reaction by which it forms from the elements in the standard state. forward reaction 0 > >0 backward reaction Driving force of a chemical reaction For the reaction, Is negative, the reaction proceeds from left to right. if positive, the reaction proceeds from right to left.

29. Derivation of the Law of Mass action G=H-TS or, G=U+PV-TS or, dG=dU+PdV+VdP-TdS [at constant temp, dT=0] or, dG=dQ-PdV+PdV+VdP-TdS [dU=dQ+PdV, 1st law] Since, dS=dQ/T, dQ=TdS Therefore, dG=VdP According to Ideal Gas Law, V=RT/P So, we can write, On integration, , gives Since P0 =1 atm, ln P0 = 0, Molar free energy of ideal gas at pressure P Molar free energy in the standard state

30. Molar free energy is also called the chemical potential μ The previous equation can be written as For n mole of an ideal gas, we can write, means,

31. van’t Hoff Equation After rearranging, On differentiation, Since, , and Therefore, Multiplying by dT, On integration,

32. Chemical Equilibria: G depends upon concentration (S changes with concentration) GA = GA° + RT ln[A]; GA° is the standard free energy of A, R = 2.0 cal/deg-mole = 8.3 J / deg-mole. For the reaction aA + bB == cC + dD ==>ΔG = ΔG° + RT ln ([C]c [D]d) / [A]a [B]b) DG° is the standard free energy change for this reaction when reactants and products are in their standard states. This principal is very important, because it shows that a reaction can be caused to go in either direction by changing the concentrations of products and reactants; this often occurs in living organisms. At equilibrium, ΔG = 0 ==> ΔG° = - RT ln ([C]c [D]d) / [A]a [B]b) = -RT ln Keq Note: ln Keq = -ΔH°/R (1/T) + ΔS°/R ==> a van't Hoff plot of LnKeq vs. 1/T allows one to calculate ΔH° and ΔS°, and, of course ΔG° Note that a 10x change in Keq corresponds to a 5.7 kJ / mole (1.3 kcal/mole) change in ΔG° which is less than half the energy of a hydrogen bond.