Chapter 14

ΔH°

enthalpy

ΔH

enthalpy kJ/mol

ΔS°

entropy

ΔS

entropy kJ/K mol

-ΔH

exothermic

standard free energy of reaction (ΔG°rxn)

free-energy change for a reaction when it occurs under standard-state conditions. For a chemical reaction aA + bB → cC + dD ΔG°rxn = [cΔG°f (C) + dΔG°f (D)] - [aΔG°f (A) + bΔG°f (B)] Alternatively, ΔG°rxn = ΣnΔG°f (products) - ΣmΔG°f (reactants) * ΔG°f for any element in its most stable form at 1 atm is zero (O2)

°

means 'standard' (1 atm, 25°C)

ΔS°universe < 0

nonspontaneous process

ΔG

refers to the change in Gibbs Free Energy of a reaction. Gibbs Free Energy refers to the energy in a chemical reaction that can be used to do work kJ/mol

ΔS°universe > 0

spontaneous process

+ΔH

endothermic

Entropy (S)

(of a system is) a measure of how spread out or how dispersed the system's energy is - ΔS° rxn = not favorable entropy (for a spontaneous reaction) + ΔS° rxn = favorable entropy

Predicting the Sign of ΔS°sys (Several processes that lead to an increase in entropy are:)

- Melting - Vaporization or sublimation - Temperature increase - Reaction resulting in a greater number of gas molecules

sig fig rules:

1. Significant Digits All digits ( non-zero and zero) are considered significant except zeroes placed to the right of a decimal solely for spacing. 3 sig figs 4 sig figs 5 sig figs 250 m/s 3150 m/s 74850 m/s 25.0 m/s 315.0 m/s 7485.0 m/s 2.50 m/s 31.50 m/s 748.50 m/s 0.250 ml 3.150 ml 74.850 ml 0.0250 ml 0.3150 ml 7.4850 ml 0.00250 ml 0.03150 ml 0.74850 ml 0.000250 ml 0.003150 ml 0.074850 ml 700 m/s 7 000 m/s 70 000 m/s 8.07 x 106 m/s 8.007 x 106 m/s 8.0007 x 106 m/s 2. Multiplying / Dividing / Trigonometric Functions a) First perform all the operations, even if changing from one formula to another. b) Round off the result so that it has the same number of sig figs as the least of all those used in your calculation. Example: (2.5 m) x (2.01 m) x (2.755 m) = 13.843875 m Answer = 14 m (2 sig figs) (When measurements are multiplied or divided, the answer can contain no more significant figures than the least accurate measurement.) 3. Addition / Subtraction This principle can be translated into a simple rule for addition and subtraction: When measurements are added or subtracted, the answer can contain no more decimal places than the least accurate measurement. 150.0 g H2O (using significant figures) + 0.507 g salt 150.5 g solution 4. Multiplication / Division combined with Addition / Subtraction First, follow the order of operations that you learned in math. Use the appropriate sig fig rules, as stated above, depending on which operation you are performing at that time. (Example: 1. multiply/divide/trigonometric functions; or 2. add/subtract functions) At the end of each step, you must ask yourself, "What is the next operation that I will perform on the number that I just calculated?" If the next operation is in the same group of operations that you just used, (Example: 1. multiply/divide/trigonometric; or 2. add/subtract) then do NOT round off yet. If the next operation is from the other group, then you must round off that number before moving on to the next operation. 5. Exact Values All exact values or conversion factors have an infinite (never ending) number of significant figures. They are called exact values because they are measured in complete units and are not divided into smaller parts. You might count 8 people or 9 people but it is not possible to count 8.5 people. Examples of exact values: 12 complete waves ; 17 people ; 28 nails Examples of exact conversion factors: 60 s / minute ; 1000 m / km ; 12 eggs / dozen; 7 days / week

nonspontaneous process.

A process that does not occur under a specific set of conditions

spontaneous process.

A process that does occur under a specific set of conditions A process that results in a decrease in the energy of a system often is spontaneous: CH4(g) + 2O2(g) CO2(g) + 2H2O(l) ΔH° = -890.4 kJ/mol The sign of ΔH alone is insufficient to predict spontaneity in every circumstance: H2O(l) H2O(s) T > 0°C; ΔH° = -6.01 kJ/mol ice does not spontaneously form above 0 °C To predict spontaneity, both the enthalpy and entropy must be known

ΔS°surr = -ΔHsys/T

The change in entropy of the surroundings is directly proportional to the enthalpy of the system.

ΔS°sys = ΔS°rxn = ΣnS°(products) - ΣmS°(reactants)

The change in entropy of the system is the same as the change in entropy of a reaction.

ΔG > 0

The reaction is nonspontaneous in the forward direction.

ΔG < 0

The reaction is spontaneous in the forward direction.

Temperature

Tk = Tc + 273.15

Gibbs Free Energy Change, ΔG

Using the Gibbs free energy (G), we can make predictions about the spontaneity of reactions: ΔG = ΔH - TΔS ΔG < 0 The reaction is spontaneous in the forward direction. (reaction --> products) ΔG > 0 The reaction is nonspontaneous in the forward direction. ΔG = 0 The system is at equilibrium ** "above which" are key words that means the reaction is spontaneous - means that ΔG = 0 (at equilibrium- or will eventually reach that point) - so can set the other half of the equation = 0 as well

first law of thermodynamics

states that energy can be converted from one form to another, but cannot be created or destroyed ΔE=Ef -Ei ΔEsys = -ΔEsurr

second law of thermodynamics

states that for a process to be spontaneous, ΔS°universe must be positive. ΔS°universe = ΔS°sys + ΔS°surr ΔS°universe > 0 for a spontaneous process ΔS°universe < 0 for a nonspontaneous process ΔS°universe = 0 for an equilibrium process

standard entropy (S°)

the absolute entropy of a substance at 1 atm. Temperature is not part of the standard state definition and must be specified. For a chemical reaction: aA + bB → cC + dD ΔS° rxn = [cS°(C) + dS°(D)] - [aS°(A) + bS°(B)] Alternatively, ΔS° rxn = ΣnS°(products) - ΣmS°(reactants)

Enthalpy change (ΔH°)

the name given to the amount of heat evolved or absorbed in a reaction carried out at constant pressure

Thermodynamics

the study of the transformation between different forms of energy on a macroscopic scale

if ΔS > 0 & ΔH < 0

then ΔG is spontaneous According to the equation ΔG = ΔH - TΔS

important trends in entropy:

Ø S°gas > S° liquid > S° solid Ø S° increases with molar mass Ø S° increases with molecular complexity (see slides for example) Ø S° increases with the mobility of a phase (for an element with two or more allotropes) (Carbon has two common allotropes, diamond and graphite; graphite has greater mobility and thus greater entropy than diamond)

ΔSvap calculation using Gibb's free energy relationship

ΔGvap = ΔHvap + TΔSvap vaporization= liquid --> gas ΔGvap = 0 if at vaporization/boiling temp (100°C for water)