# Thermodynamics: First Law, Calorimetry, Enthalpy. Calorimetry. Calorimetry: constant volume. Monday, January 23 CHEM 102H T.

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1 Thermodynamics: First Law, Calorimetry, Enthalpy Monday, January 23 CHEM 102H T. Hughbanks Calorimetry Reactions are usually done at either constant V (in a closed container) or constant P (open to the atmosphere). In either case, we can measure q by measuring a change in T (assuming we know heat capacities). Calorimetry: constant volume U = q + w and w = -P ex ΔV If V is constant, then ΔV = 0, and w = 0. This leaves U = q v, again, subscript v indicates const. volume. Measure ΔU by measuring heat released or taken up at constant volume.

2 Calorimetry Problem When g of quinone (C 6 H 4 O 2 ) is burned with excess oxygen in a bomb (constant volume) calorimeter, the temperature of the calorimeter increases by 3.26 C. The heat capacity of the calorimeter is known to be 1.56 kj/ C. Find ΔU for the combustion of 1 mole of quinone. Calorimetry: Constant Pressure Reactions run in an open container will occur at constant P. Calorimetry done at constant pressure will measure heat: q p. How does this relate to U, etc.? q P & ΔU U = q + w = q - PΔV At constant V, PΔV term was zero, giving U = q v. If P is constant and ΔT 0, then ΔV 0. In particular, if gases are involved, PV = nrt w p 0, so U q p

3 Enthalpy: A New State Function It would be nice to have a state function which is directly related to q p : (?) = q p We could then measure this function by calorimetry at constant pressure. Call this function enthalpy, H, defined by: H = U + PV Enthalpy Enthalpy: H = U + PV U, P, V all state functions, so H must also be a state function. ΔH = q p? Do some algebra, assuming that P is constant: H = U + (PV) = U + P V ΔH = q P But w = -PΔV, so: ΔH = ΔU + PΔV = (q + w) + PΔV ΔH = (q - PΔV) + PΔV = q And since we used constant P, this is ΔH = q p

4 Compare U & H H = U + P V (const. P) PΔV term due to expansion or compression. For solids & liquids, PΔV is small. Therefore, ΔH ΔU for condensed phase systems. For systems involving gases, ΔH and ΔU may differ considerably H for Physical Processes H = U + P V (const. P) If heat must be put in to the system to bring about a physical change, then ΔH > 0 for that process. For changes involving only condensed phases (solids & liquids), PΔV contribution is small. ΔH for physical processes can be qualitatively understood by thinking about intermolecular forces. Compare ΔU & ΔH; Examples A heat input of kj is required to melt one mole of ice at 1 atm. pressure. What is H? What is U? A heat input of kj is required to boil one mole of water at 1 atm. pressure. What is H? What is U?

5 Conclusion from example If volume changes are large, the difference between H and U can be significant. Volume changes are large when the number of moles of gas changes from the initial and final states. Since gases usually are approximately ideal, (PV) (nrt) = ( n)rt, so H = U + (PV) U + ( n)rt Heating curves (H 2 O shown) Melting and Boiling constitute jumps in the heating of a substance their sizes reflect strength of intermolecular forces overcome in the processes. All phase transitions occur at constant temperatures H solid!h fus = 6.01 kj mol 1 liquid!h vap = 40.7 kj mol kj mol 1 vapor T(K) Again, Heat Capacities For one mole of an ideal gas: U = 3 / 2 RT We ve seen that U = q v, therefore since C V = q V!T, C =!U! V!T = du \$ in the limit " # dt % & C V = 3 R for an ideal gas 2 We ve seen that H = q P, and H = (U + PV) since C P = q P!T, C =! H! P!T = dh \$ in the limit " # dt % & C P = 3 2 R + d(pv ) dt = 3 2 R + d(rt ) dt = 5 R for an ideal gas 2

6 Enthalpy & Chemistry Many reactions occur at constant P, so ΔH is a useful quantity. ΔH < 0 heat is released, so reaction is exothermic ΔH > 0 heat is absorbed, so reaction is endothermic ΔH is related to the amount of energy we might get out of a reaction. H vs. H We always talk about H, never H itself. (Same is true for U & U) Why? H is an energy, so we need some reference point. Absolute energy is not readily defined. Reaction Enthalpies Enthalpies don t just apply to changes in physical state, but to reactions too. Example: Fe(s) + 2S(s) > FeS 2 (s) H = kj If these chemicals constitute the system, then when the reaction occurs, kj of heat will be released into the surroundings if 1.0 mol of FeS 2 is formed. Note: this says nothing about the rate of the reaction or the conditions under which it would be practical to carry it out.

7 Reaction Enthalpy If H reaction is negative, energy is given off. Exothermic If H reaction is positive, energy is absorbed. Endothermic We can NOT predict whether a reaction will occur based only on H! Energy Diagram activated complex Enthalpy reactants ΔH rxn E a products Thermodynamic Quantity Reaction Coordinate Using Bond Enthalpies Imagine running the reaction as follows: break every bond in reactants, giving a collection of atoms make new bonds among these atoms to form products reactants free atoms products Will each step cost energy, or release energy?

8 Standard States Define a standard state: The enthalpy of an element in its most stable physical form at 1 atm and 25 C is equal to zero. Gives a reference for each element, since they are not interconverted in chemical processes This definition fixes all ΔH values, since H is a state function. Tabulating & Using ΔH Exhaustive tabulation of ΔH s (for all possible reactions) is not feasible. Exploit the fact that ΔH is a state function to get maximum useful information from a more reasonable amount of data. Standard Enthalpy of Formation, ΔH f Formation Reactions For any compound we can write a formation reaction in which: Elements in 1 mole of standard states compound ΔH for such a reaction is called the standard enthalpy of formation, ΔH f, for the compound. Also called heat of formation

9 Formation Reactions Elements in 1 mole of standard states compound C (s, graphite) + 2 H 2 (g) CH 4 (g) 1/2 N 2 (g) + 3/2 H 2 (g) NH 3 (g) Always one mole of product, so often need to use fractional coefficients. Many such reactions can not actually be carried out. (But values can be found indirectly & tabulated.) Using ΔH f s ΔH =? C 6 H 12 O O 2 6 CO H 2 O Since H is a state function, we can create any # of intermediate states. Use ΔH for these steps to find the ΔH we want. Path Independence ΔH = H products - H reactants This does not specify what might exist between reactants and products. ΔU is path independent. We can imagine any set of steps that get us from the reactants to the products. Because it is path independent, we say ΔH is a state function.

10 H is a state function! C 6 H 12 O O 2 6 CO H 2 O ΔH 1 ΔH ΔH 2 ΔH 4 3 A B C Because H is a state function: ΔH rxn = ΔH 1 + ΔH 2 + ΔH 3 + ΔH 4 ΔH 1, ΔH 2, etc. refer to the individual steps Using ΔH f s to find ΔH rxn Choose a useful path for the reaction. Reactants ΔH f, reactants Elements in standard states ΔH f, products Products ΔH rxn = ΔH f, products - ΔH f, reactants Problem Given the ΔH f s below, find ΔH for the combustion of one mole of glucose at 298 K. glucose(c 6 H 12 O 6, s) ΔH f = kj/mol CO 2 (g) ΔH f = kj/mol H 2 O(l) ΔH f = kj/mol (Data are from Appendix 2 in your book.)

11 Hess s Law For any reaction, we can write: ΔH rxn = Σ nδh f (products) - Σ nδh f (reactants) n s are the stoichiometric coefficients from the balanced chemical equation. This lets us find ΔH for any reaction from a table of ΔH f s. Another Problem - Hess s Law Acetylene torches are used in welding. Chemical reaction involved is: C 2 H 2 (g) + 5/2 O 2 (g) 2 CO 2 (g) + H 2 O (g) Find ΔH for this reaction. Estimate the maximum temperature which could be obtained in an acetylene flame. Some useful data are on the next slide. Data For Problem Heat of formation (ΔH f ) C 2 H 2 (g) kj/mol CO 2 (g) H 2 O(g) Heat capacities (C p ) C 2 H 2 (g) 44 J/mol K CO 2 (g) 37 H 2 O(g) 36

12 Thermochemical (Born-Haber) Cycle M(g) + X(g) I(M) E X M + (g) + X (g) S M + ( 1 / 2 )D X2!H L M(s) + ( 1 / 2 )X 2 (g)!h f MX(s) S M : sublimation Enthalpy of Metal (298 K) 108 D X2 : dissociation Energy of X 2 bond (298 K) 242 I(M) : Ionization Enthalpy of Metal M 496 E X : electron attachment Enthalpy of X atom 349 H L : Enthalpy for separation of salt to ions theory Values for (kj/mol) Thermochemical (Born-Haber) Cycle M(g) + X(g) I(M) E X M + (g) + X (g) S M + ( 1 / 2 )D X2!H L M(s) + ( 1 / 2 )X 2 (g)!h f MX(s) H L = V min = N A (e 2 /r min )[Z+ Z ](1 - r*/r min )A for, r min = Å (5.162 a.u.) 776kJ/mol Experiment (Born-Haber cycle): H f = S M + ( 1 / 2 ) D X2 + I(M) E M H L for, measured value of H f is -411kJ/mol -411 = (242/2) H L H L = 787 (- 2 for C p correction) = 785 kj/mol Rocksalt () type: ccp stacked ; all octahedral holes filled

13 Ionic Bonding; Lattice Energies Energy Lattice Energies - Details V = VCoulomb + Vrepulsion r = cation-anion distance ion - ion Coulomb interactions repulsions between ion cores eg., -type: (cgs units - a factor of 1/4!!0 must be included to convert to SI) V Coulomb = + 6 (e 2 / r )Z + Z + 12 (e 2 /!2r )(Z + ) (e 2 /!3r )Z + Z + 6 (e 2 / 2r )(Z + ) type: V Coulomb = N A (e 2 /r)[z + Z ]! A A = [ /!2 8 /!3 + 6 / 2 24 /!5 +...]!2!3 The Madelung constant: a geometrical parameter that is the same for all compounds of a given structure type Ion core Ion core repulsions Vrepulsion = + N A C exp{-(r/r*)} estimated from compressibilities, r* is always much smaller than a typical internuclear distance (~ Å). V = N A (e 2 /r)[z+ Z ]A + N A C exp{-(r/r*)} Minimize (set (dv/dr) = 0) to obtain: C exp{-(r min /r*)} = - e 2 [Z+ Z ] A r*/(r min ) 2 Alternative: Vrep = + N A (B/r n ) ion core n He 5 Ne 7 Ar 9 Kr 10 Xe 12 V min = N A (e 2 /r min )[Z+ Z ](1 r*/r min )A V min = N A (e 2 /r min ) [Z+ Z ](1 1 / n )A Bond Enthalpies and Reactions We can measure the strength and length of chemical bonds. (some easily, some with great difficulty) Energy of a particular type of bond (carbon - hydrogen, etc.) approximately (but not exactly) the same in different molecules. This is because bonds are often mainly localized and because orbitals used to make bonds are similar in different molecules.

14 Using Bond Enthalpies: Reaction Energy Average bond enthalpies are tabulated. We can use these to estimate the enthalpy change for any chemical reaction for which bond enthalpies are known. Decide whether the reaction was likely to succeed, evaluate possible fuels, etc. Reaction Enthalpy Reactants Products Reaction Enthalpy: Enthalpy taken in or given off during reaction H = H products H reactants Using Bond Energies Can use bond energies to find the energy required or released in these imaginary steps. Get H by combining these. H reaction = Σ BE reactants - Σ BE products ( Σ means summation ) NOTE: Because bond energies are defined relative to ATOM energies, this has a reactants minus products - not usual!

15 Acrylonitrile Synthesis 2 C 3 H NH 3 +3 O 2 6 H 2 O + 2 H 2 C=CH C N Use bond enthalpies to estimate ΔH for this reaction. Some data are on next slide. Some Bond Enthalpies (kj/mol) Diatomic molecules (actual values) H H O=O C O 1071 Other bonds (avg. values) C C 348 C=C 612 C C 837 C H 412 C=N 615 C N 890 N H 388 N=O 630 O H 463 Thermodynamics & Chemistry Study of the energy changes associated with chemical or physical processes. Chemical applications of principles you will study in physics & engineering reaction energy, fuels, etc. Goal - to be able to predict whether or not a given reaction can occur, using simple tabulated data.

16 Thermodynamics vs. Kinetics Thermodynamics tells us things about the eventual outcome of a chemical reaction, but NOT about how fast the reaction might be. To know if something will happen fast, we need to consider kinetics. Need both thermodynamics and kinetics to assess practical usefulness of a reaction.

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