1. Chemical thermodynamics I. Medical Chemistry László Csanády Department of Medical Biochemistry

2. What is thermodynamics? Thermodynamics is the study of the effects of work, heat, and energy on a system. body food (energy in chemical bonds) longterm storage (energy in chemical bonds) constant body temperature (heat) physical exercise (mechanical work)

3. What is thermodynamics? body ATP food (energy in chemical bonds) longterm storage (energy in chemical bonds) physical exercise (mechanical work) constant body temperature (heat) F 1 -F o -ATP synthase ADPATP

4. System and surroundings The "system" is the well defined part of the universe we are interested in. The "surroundings" is the rest of the universe, which is in contact with the system. system surroundings

5. Internal energy The internal energy (U) is the sum of all microscopic forms of energy of a system. U energy of motion of e - -s and molecules potential energy from chemical bonding potential energy from intermolecular attractions

6. Internal energy U is a state function State function: a property of the system that depends only on its present state, not on the pathway taken to reach that state. E.g.: p, V, T 2421 m 1500 m  h=921 m  U = U f - U i Therefore:

7. U is an extensive property Extensive property: a property of the system which is directly proportional to the amount of material in the system. Such properties are addivitive. Examples: mass (m), electric charge (Q). Internal energy Intensive property: a property of the system which does not depend on the system size. Such properties are not additive. Examples: temperature (T), pressure (p), density (  ).

8. The change in internal energy of a system equals the heat absorbed by the system (q) plus the work performed on the system (w): The first law of thermodynamics system surroundings heat (q) work (w) Heat: energy that flows because of a temperature difference Work: energy transfer due to mechanical movement  U = q + w

9. Mechanical work is done when a force F moves an object over a distance d: w = F · d Heat and mechanical work w p = - F·  h heating qpqp Mechanical work done at constant pressure: wpwp system atmospheric pressure = - (p·A)·  h = - p· (A·  h)= - p·  V

10. Restatement of the first law at constant pressure: Enthalpy  U = q P - p  V q P =  U + p  V Let us define a quantity: enthalpy (H): H =  U + pV At constant pressure the change in enthalpy of the system reflects the absorbed heat:  H =  U + p  V = q p

11. Enthalpy (i) H is a state function (because U, p, and V are all state functions) (ii) H is an extensive property: the total enthalpy of the system is the sum of the enthalpies of all the components in the system: H =  k H k Enthalpy change for a reaction: (i)   H = H final – H initial (ii)   H =  H(products) -  H(reactants) Hess's law: The enthalpy change for a chemical reaction depends only on the initial and final states, but is independent from the pathway taken.

12. Standard enthalpy change (  H˚): The reaction heat for a reaction in which reactants in their standard states yield products in their standard states. "Standard state": p=1 atm, and usually T=25 o C. Standard enthalpy change

13.  H of physical processes 1.1. Standard enthalpy of fusion (  H˚ fus ): the amount of heat required to change the state of 1 mol of substance from solid to liquid at its melting temperature. E.g.:  H˚ fus (H 2 O) = +6.0 kJ/mol 1.2. Standard enthalpy of vaporization (  H˚ vap ): the amount of heat required to change the state of 1 mol of substance from liquid to gas at its boiling temperature. E.g.:  H˚ vap (H 2 O) = +40.9 kJ/mol 1.  H associated with phase transitions 1.3. Standard enthalpy of sublimation (  H˚ subl ): the amount of heat required to change the state of 1 mol of substance from solid to gas at a fixed temperature. E.g.:  H˚ subl (ice) = +50.8 kJ/mol

14.  H of physical processes 2.1. Molar heat capacity at constant pressure (C m,p ): the amount of heat required to raise the temperature of one mole of substance by 1 o K. E.g.: C m,p (ice) = +38 J/(mol· o K) C m,p (water) = +75 J/(mol· o K) C m,p (steam) = +36 J/(mol· o K) 2.  H associated with temperature change

15.  H of physical processes  H for converting 1 mol -10 o C ice into 100 o C steam: ice -10 o C ice 0 o C C m,p (s)·  T 0.4 kJ water 100 o C 7.5 kJ C m,p (l)·  T 4 kJ C m,p (g)·  T steam -10 o C 50.8 kJ subl H˚H˚ steam 100 o C 40.9 kJ vap H˚H˚ water 0 o C 6 kJ fus H˚H˚  H 1 =(50.8+4) kJ = 54.8 kJ  H 2 =(0.4+6+7.5+40.9) kJ = 54.8 kJ  H 1 =  H 2 heat required for phase transition heat required for temperature rise

16.  H of physical processes 3. Standard enthalpy of solution (  H˚ soln ): the amount of heat required to dissolve 1 mol of substance in a large excess of solvent under standard conditions (T=25 o C, p=1atm). E.g.:  H˚ soln (HCl)= -75 kJ/mol in H 2 O ii. Breaking solvent-solvent attractions (endothermic) E.g.: H-bonds in water  H˚ of solvation (in water:  H˚ hyd ): C + (g) +A - (g)  C + (aq) +A - (aq) (exothermic) Factors that contribute to  H˚ soln : i. Breaking solute-solute attractions (endothermic) E.g., for ionic solids: lattice enthalpy (  H˚ lat ) is the amount of heat required to break 1 mol of solid crystal into gaseous ions CA (s)  C + (g) +A - (g) (Note: sometimes defined vice versa!) iii. Forming solvent-solute attractions (exothermic)

17.  H of physical processes Calculate  H˚ soln for NaCl: NaCl(s) + aq Na + (aq) + Cl - (aq) +4 kJ/mol  H˚ soln Na + (g) + Cl - (g) + aq +787 kJ/mol  H˚ lat -783 kJ/mol  H˚ hyd  H˚ soln =  H˚ lat +  H˚ hyd =(+787 + (-783)) kJ/mol= +4 kJ/mol

18.  H of chemical processes 4. Standard enthalpy of formation (  H˚ f ): the amount of heat required to form 1 mol of a substance in its standard state (T=25 o C, p=1atm) from its elements in their reference forms. Reference forms of elements: The most stable form of the element under standard conditions (T=25 o C, p=1atm). Element Reference form hydrogenH 2 (g) carbonC(s, graphite) oxygenO 2 (g) nitrogenN 2 (g) Element Reference form sulfur S 8 (s, rhombic) bromineBr 2 (l) electrone - (g) protonH + (aq)

19.  H of chemical processes Example standard enthalpies of formation: Substance  H˚ f Reaction of formation (kJ/mol). water -286 H 2 (g)+1/2 O 2 (g)  H 2 O(l) steam -242 H 2 (g)+1/2 O 2 (g)  H 2 O(g) sulfuric a. -808 H 2 (g)+1/8 S 8 (s)+2 O 2 (g)  H 2 SO 4 (l) methane -74 C(s)+2 H 2 (g)  CH 4 (g) glucose -1275 6 C(s)+6 H 2 (g)+3 O 2 (g)  C 6 H 12 O 6 (s) elements involved reactantsproducts  H˚ f (reactants)  H˚ f (products)  H˚ reaction =  H˚ f (prod)-  H˚ f (react) H 2 (g)+1/2 O 2 (g) H 2 O(l) -286 kJ -242 kJ  +44 kJ H 2 O(g)

20.  H of chemical processes 5. Heat of combustion (  H˚ c ): the enthalpy change for the complete combustion of 1 mol of compound with oxygen under standard conditions. E.g.: CH 4 (g)+2O 2 (g)  CO 2 (g)+2H 2 O(l)  H˚ c =-890 kJ/mol

21.  H of chemical processes Combustion heat data can be used to calculate standard enthalpies of formation + 2 O 2 (g) CO 2 (g) + 2 H 2 O(l)  H˚ c (CH 4 )= -890 kJ/mol  H˚ c (H 2 )= -284 kJ/mol  H˚ c (C)= -396 kJ/mol  H˚ c (C+2H 2 )= -964 kJ/mol These can be determined experimentally  H˚ f for methane:  H˚ f (CH 4 )=-74 kJ/mol C(s) + 2 H 2 (g) CH 4 (g)

22.  H of chemical processes Combustion heat data can be used to calculate standard reaction heat values + 5 O 2 (g) 3 CO 2 (g) + 4 H 2 O(l)  H˚ c (C 3 H 8 )= -2220 kJ/mol  H˚ c (H 2 )= -284 kJ/mol  H˚ c (C 3 H 6 )= -2060 kJ/mol  H˚ c (C 3 H 6 +H 2 )= -2344 kJ/mol  H˚for propene hydrogenation: C 3 H 6 (g)+H 2 (g)  C 3 H 8 (g)  H˚=-124 kJ/mol C 3 H 6 (g) + H 2 (g) C 3 H 8 (g) These can be determined experimentally

23.  H of chemical processes Because by definition reaction heat is the heat absorbed during the reaction,  H˚ appears on the left- hand side (as a "reactant"): reactants +  H˚  products Thermochemical equation: a chemical equation in which the reaction enthalpy is explicitly included. Thermochemical equations can be added up to obtain the equation for a multistep reaction. CH 4 (g)+2O 2 (g) - 890 kJ  CO 2 (g)+2H 2 O(l) (exothermic) C 3 H 8 (g) + 124 kJ  C 3 H 6 (g)+H 2 (g) (endothermic) Alternatively: reactants  products -  H˚ CH 4 (g)+2O 2 (g)  CO 2 (g)+2H 2 O(l) + 890 kJ (exothermic) C 3 H 8 (g)  C 3 H 6 (g)+H 2 (g) - 124 kJ (endothermic)

24.  H of chemical processes Calculation of standard enthalpies of formation from combustion heat data using the thermochemical equation formalism (i) C(s)+2H 2 (g)+2O 2 (g)  CO 2 (g)+2H 2 O(l)+964 kJ (ii) CH 4 (g)+2O 2 (g)  CO 2 (g)+2H 2 O(l)+890 kJ  H˚ f for methane: C(s)+2H 2 (g)  CH 4 (g)+74 kJ C(s)+2H 2 (g) – CH 4 (g)  (964 – 890) kJ (i) – (ii):

25.  H of chemical processes Calculation of standard reaction heat values from combustion heat data using the thermochemical equation formalism (i) C 3 H 6 (g)+H 2 (g)+5O 2 (g)  3CO 2 (g)+4H 2 O(l)+2344 kJ (ii) C 3 H 8 (g)+5O 2 (g)  3CO 2 (g) + 4H 2 O(l) + 2220 kJ  H˚ for propene hydrogenation: C 3 H 6 (g)+H 2 (g)  C 3 H 8 (g)+124 kJ/mol C 3 H 6 (g)+H 2 (g) – C 3 H 8 (g)  (2344 – 2220) kJ (i) – (ii):

26.  H of chemical processes 6. Average bond enthalpy (  H˚ A-B ): the average enthalpy change for breaking 1 mole of A-B bonds in a molecule in the gas phase under standard conditions. E.g.: CH 4 (g)  C(g)+4H (g)  H=+1648 kJ/mol=4·  H˚ C-H A-B  H˚ A-B (kJ/mol) C-H 412 C-C 348 O-H 463 A-B  H˚ A-B (kJ/mol) C=C 611 C  C 833 H-H 436

27.  H of chemical processes Estimation of standard reaction heat values from average bond enthalpies  H˚  1047 – 1172 = - 125 kJ/mol  H˚   H˚ A-B (bonds broken) -  H˚ A-B (bonds formed)  H˚ for propene hydrogenation: H H CC H C H H H H H + CC H C H H H H H H H Bonds broken:  H˚ A-B 1x(C=C) 611 1x(H-H) 436  H˚ A-B (broken)=1047 Bonds formed:  H˚ A-B 1x(C-C) 348 2x(C-H) 2·412  H˚ A-B (formed)=1172