361 Lec 7 Fri 9sep15 TODAY 0. Why H = q (if p ext =p=constant and no useful work) 1. Constant Pressure Heat Capacity (what we usually use) 2. Heats of Chemical Reactions: r H (mechanics of obtaining from the table of standard heats of formation ) 3. I can get r H from table, BUT, how to get r U??? 4. What exactly is f H 0? 5. Hesse s Law (adding/subtracting chemical reactions): an example of exploiting the fact that changes in state functions are independent of path. 1
Enthalpy: (defined because of the small work against atmosphere) H = U + pv by definition (always true) dh =? = du + d(pv) = H = U + (pv) = (not U + p V + V p) H = q (IF p ext = p = constant, and only p atmosphere V work done) because U = q + w = q - p atmosphere V + w useful and pv = p atmosphere V The annoying -p atmosphere V term cancels! du + pdv + Vdp U + p 2 V 2 p 1 V 1 H for an ideal gas? H = U + (pv) by definition pv = nrt (ideal gas) (pv) = (nrt) = nr T We know U = 0 if T = 0, so H also = 0 for ideal gas if isothermal process 2
Heat Capacity of Gases at Constant Pressure: C p 1 atm p = 1 atm What happens if we heat the gas while keeping p = p ext = constant = 1 bar? But, expansion does some work, which has a cooling effect. T is smaller C = q/ T, so C is larger. q Heating make the molecules move faster, making the pressure increase, which causes expansion. pv= nrt p V= nr T More heat will be needed to raise the temperature than if volume is kept constant. C p > C v, always 3
How much more heat is required? H = U + pv what is pv? pv = nrt if ideal gas but H = q (if p= p ext = constant and only p atmosphere V work possible) At constant Volume U = q (if no useful work done) q = C V T = U At constant Pressure H = q (if no useful work done) q = C P T = H= U + (pv) = U + (nrt) C P T = C V T + nr T C P = C V + nr 4
361 Lec 7 Fri, 6sep13 Very very high pressure applied to a solid will often turn it into another crystal form that is more dense, e.g., graphite into diamond. 5
Heats of CHEMICAL REACTIONS ( r H) (and Phase Changes treated the same way) State 1 State 2 Reactants Products Tabulated at 1 bar and some T (usually 298 K) (note that this is constant T and p) so, q = q p = H In general: if weak bonds STRONG BONDS then the reaction is very EXOTHERMIC == chemical energy r H = Σ H i (products) - Σ H i (reactants) (this is an abstract useless statement) In practice, we use a Table of standard heats of formation r H 0 = Σ f H 0 298 (products) - Σ f H 0 298 (reactants) 6
From a table of f H 0 298 for a few dozen reactions we can know the r H 0 for thousands of reactions that may have never been measured. 7
Consider a generic chemical reaction aa + bb cc + dd where the a,b,c,d = the stoichiometric numbers and A,B,C,D are chemicals r H 0 = c f H 0 (C) + d f H 0 (D) a f H 0 (A) b f H 0 (B) Example: C 6 H 12 O 6 (s) + 6O 2 ---> 6CO 2 (g) + 6H 2 O(g) -1274.4 0-393.5-241.8 f H 0 kj mol-1 r H 0 = 6 ( 393.5) + 6 ( 241.8) ( ( 1274.4 6 ( 0 ) ) = 2537.4 kj/mol as written you MUST always associate the r H 0 with a balanced reaction 8
What EXACTLY is f H 0 298??? f H 0 298 = Standard Heat of Formation (at 25 o C) The superscript 0 means that all reactants and products are in their standard state, which means: Gases: 1 bar and ideal Liquids and solids: 1 bar applied and pure Solutes: 1 molar (usually) and ideal (no solute-solute interaction) Note that temperature is NOT part of the definition. (There is a different table for every temperature.) ------------------------------------------------------------------------------------------- f means formation of 1 mole from the most stable form of the elements at the given temperature (298 in this case) ---------------------------------------------------- Quiz: What chemical reaction has: H 2 (g) + 1/2O 2 (g) H 2 O(g) H 2 (s) + 1/2O 2 (s) H 2 O(g) 1. H 298 = f H 0 298 for H 2 O (g) 2. H 5 = f H 0 5 for H 2 O (g) 3. Why is f H 0 298 = 0 for H 2 (g), O 2 (g), N 2 (g)...? H 2 (g) H 2 (g) 9
We will constantly be using: Powerful Exploitation of State Function Concept in Thermodynamics State 1 H unknown or unmeaureable State 3 known H 1 known H 2 State 2 can be ANYTHING Path does not matter: H is a STATE FUNCTION H unknown = H 1 + H 2 When applied to chemical reactions this trick is known as Hesses Law 10
Hesse s Law is a: Powerful Exploitation of State Function Concept in Thermodynamics Reactants known H f 0 (1) H unknown or unmeaureable Products known + H f 0 (3) Elements in most stable form (solid, liquid or gas) Path does not matter: H is a STATE FUNCTION H 0 unknown =+ H f 0 (prod) - H f 0 (react) 11
Bond Enthalpies Another Exploitation of State Function Concept in Thermodynamics Reactants sum of reactant bond enthalpies H unknown or unmeaureable Products sum of reactant bond enthalpies Gaseous ATOMS Path does not matter: H is a STATE FUNCTION H 0 unknown =+ H f 0 (reactants) - H f 0 (products) Why the sign change??? Bond Enthalpy DEFINED as Enthalpy of bond breaking (not making) 12
Bond Energies (Enthalpies) 13
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