CHEM 1120 Exam 4

Ch. 18, 19, 20

First law of thermodynamics

Energy is conserved in chemical processes

Second law of thermodynamics

Every spontaneous energy transaction requires the dispersal (or spreading out) of energy

Energy dispersal = entropy

Thermodynamics and Spontaneity

Thermodynamics preditcs whether a process will occur under the given conditions

• Processes that will occur are called spontaneous

• Nonspontaneous processes require energy input from outside

Spontaneity

Determined by comparing the chemical potential energy of the system before the reaction with the free energy of the system after the reaction

• If the system after the reaction has less potential energy than the system before the reaction, the reaction is thermodynamically favorable

• Spontaneity ≠ fast or slow

Reversibility of Processes

Any spontaneous process is irreversible because there is a net release of energy when it proceeds in that direction

• It will only proceed in one direction

A reversible process will proceed back and forth between the two end conditions

• Any reversible process is at equilibrium

• This results in no change in free energy

If a process is spontaneous in one direction, it must be nonspontaneous in the opposite direction

Spontaneous processes and energy

Spontaneous processes occur because they release energy from the system

Most spontaneous processes go from higher to lower potential energy

• Exothermic

But some spontaneous processes go from lower to higher potential energy

• Endothermic

Factors affecting whether a reaction is spontaneous

1. Enthalpy change, △H, is the difference between the sum of the internal energy and PV work energy of the reactants, and that of the products

2. Entropy change, △S, is the difference between the randomness of the reactants relative to the products

Enthalpy change, △H

Generally measured in kJ/mol

A reaction is generally exothermic if the bonds in the products are stronger than the bonds in reactants

• Exothermic = energy released, -△H

A reaction is generally endothermic if the bonds in the products if weaker than the bonds in the reactants

• Endothermic = energy absorbed, +△H

The enthalpy change is favorable for exothermic reactions and unfavorable for endothermic reactions

Entropy, S

Entropy is a thermodynamic function that increases as the number of energetically equivalent ways of arranging the components increases

Units of J/mol

S = k ln(W)

• k = Boltzmann constant = 1.38 × 10^-23 J/K

• W is the number of energetically equivalent ways a system can exist, or microstates

Random systems require less energy than ordered systems

Entropy and the first & second laws of thermodynamics

1. △E_univ = 0 = △E_syst + △E_surr

• the total energy of the universe cant change, but can be transferred

2. △S_univ = △S_syst + △S_surr

• for reversible processes, △S_univ = 0

• for irreversible processes, △S_univ > 0

• If the entropy of the system decreases, the entropy of the surroundings must increase

For a spontaneous process, when △S_syst is negative, △S_surr must be large and postive

Macrostates and Probabiliy

The macrostate with the highest entropy also has the greatest dispersal of energy

Changes in Entropy, △S

Entropy change is favorable when the result is a more random system

• △S is positive

Changes that increase entropy:

• Reactions whose products are in a more random state

• Solid < Liquid < Gas

• Reactions that have more product molecules than reactant molecules

• Increase in temperature

• Solids dissociating into ions upon dissolving

Heat exchange and △S_surr

• When a system process is exothermic, it adds heat to the surroundings, increasing the entropy of the surroundings

• When a system process is endothermic, it takes heat from the surroundings, decreasing the entropy of the surroundings

Quantifying entropy changes in the surroundings

q_surr = -q_sys

• The entropy change of the surroundings is proportional to the amount of heat (q) gained or lost

• The entropy change in the surroundings is also inversley proportional to the temperature

• At constant temperature and pressue , the relationship is as follows:

△S_surr = △H_sys / T

Gibbs free energy and spontaneity

Gibbs free energy, G, is the maximum amount of work energy that can be released to the surroundings by a system for a constant temperature and pressure system

• Often called chemical potential because it is analogous to the storing of energy in a mechanical system

△G_sys = △H_sys - T△S_sys

△S_univ is positve when spontaneous, so △G is negative

△G will be negative and spontaneous when:

• △H is negative and △S is positive (exothermic and more random)

• △H is negative and large and △S is negative but small

• △H is positive but small and △S is postive and large

When △G = 0 the reaction is at equilibrium

△G will be positive and unspontaneous when:

• △H is negative and small and △S is negative and large

  • or high temp

• △H is positive and △S if positive and small

  • or low temp

• △H is positive and △S is negative

When △G = 0 the reaction is at equilibrium

Standard States

The standard state is the state of a mterial at a defined set of conditions:

• Gas: pure gas at 1 atm pressure

• Solid or liquid: pure in most stable form at 1 atm pressure and temp of interest

• Solution: concentration 1 M

The third law of thermodynamics

The absolute entropy of a substance is the amount of energy is has due to dispersion of energy through its particles

For a perfect crystal at absolute zero, the absolute entropy is 0 J/mol K

Therefore every substance that isnt a perfect crytsal has some energy from entropy, so its always positive

△S: Change in entropy and chemical reactions

• When final condition is more random than intial condition, △S_sys is positive and entropy change is favorable for the process to be spontaneous

• When final condition is more orderly than the inital condition, △S_sys is negative and entropy chnage is unfavorable for the process to be spontaneous

Relative standard entropies

States:

• Gas > Liquid > Soild

Molar Mass:

• The larger the molar mass, the larger the entropy

Allotropes (dif arrangement of same atom):

• The less constrained the structure, the larger entropy

Molecular Complexity:

• Larger, more complex molecules generally have larger entropy

Dissolution:

• Dissolved solids generally have larger entropy

The standard entropy change △S°

• The standard entropy change is the difference in absoulte entropy between the reactants and products under standard conditions

• The standard enthalpy of formation △H_f° of a pure element is 0 kJ/mol, however, the absoulte entropy at 25 C is always positive

Calculating △G°

• At 25 C or 298 K use the following equation

• At temperatures other than 25 C, assuming the change in △H° and △S° is negligible, △G° = △H° - T△S°

• Or △G_total° = △G_rxn1° + △G_rxn2° + …

Standard free energies of formation

• The free energy of formation △G_f° is the change in free energy when 1 mole of a compound forms from its consitutent elements in their standard states

• The free energy of formation of pure elements in their standard states is zero

△G° Relationships

• If a reaction can be expressed as a series of reactions, the sum of the △G values of the individual reactions is the △G of the total reaction

  • △G is a state function

• If a reaction is reversed, the sign of its △G value reverses

• If the amount of materials is multiplied by a factor, the value of △G if mutipled by the same factor

  • The value of △G of a reaction is extensive (depends on amount)

What is free energy?

• Free energy is the maximum amount of energy released from a system that is available to do work on the surroundings

• For many exothermic reactions, some of the heat released as a result of the enthalpy change goes into increasing the entropy of the surroundings, so it isnt available to do work

• Even some of this free energy is generally lost to heating up surroundings

Free energy of an exothermic reaction

• △G° is less than △H° because some of the released heat energy is lost to increase the entropy of the surroundings

Free energy and reversible reactions and real reactions

• The change in free energy is a theoretical limit upon the amount of work that can be done

• If the reaction achieves its theoretical limit, it is a reversible reaction

• In a real reaction, some (if not most) of the free energy is lost as heat

• Therefore, real reactions are irreversible

△G under nonstandard conditions

• △G = △G° only when the reactants and products are in their standard states

  • Their normal state at that temp

  • 1 atm

  • 1 M

• Under nonstandard conditions: △G = △G° + RT ln(Q)

  • Q is reaction quotient

• At equilibrium △G = 0

  • △G° = -RT ln(K)

△G° and K

• Because △G_rxn = 0 at equilibrium

  • △G° = -RT ln(K)

• When K<1, △G° is positive and the reaction is spontaneous in the reverse direction under standard conditions (nothing will happen with no products)

• When K>1, △G° is negative and the reaction is spontaneous in the forward direction under standard conditions

• When K=1, △G° is 0 and the reaction is at equilibriu under standard conditions

Why is the equlibrium constant temperature dependent?

• The eqution is in y = mx+b

• The graph of ln K vs inverse T is a straight line with slope (-△H°/R) and y-intercept (△S°/R)

Oxidation-reduction (redox)

• Reactions where electrons are transferred from one atom to another are called oxidation-reduction reactions

• Atoms that lose electrons are oxidized, atoms that gain electrons are being reduced.

Oxidation occurs when:

• the oxidation number of an element increases;

• an element loses e-

• a compound adds oxygen

• a compound loses hydrogen

• a half-reaction has e- as products

Reduction occurs when

• the oxidation number of an element decreases;

• an element gains e-

• a compound loses oxygen

• a compound gains hydrogen

• a half-reaction has e- as reactants

Half-reactions

• The redox reaction is split into two separate half-reactions

  • An oxidation reaction (e- as products)

  • A reduction reaction (e- as reactants)

Balancing redox reactions

1. Assign oxidiation states

2. Write oxidation and reduction half-reactions, including e-

3. Balance half-reactions by mass

• First balance elements other than H and O

• Add H₂O where O is needed

• Add H+ where H is needed

• If the reactuon is carried out in a basic solution, neutralize H+ with OH-

4. Balance half reactions

• Balance charge by adjusting electrons

• Balance electrons between half reactions

5. Add half reactions together

6. Check by counting atoms and total charge on both sides

Electrochemistry

• The study of redox reactions that produce or require an electric current

• The conversion between chemical energy and electrical energy is carried out in an electrochemical cell

• Spontaneous redox reactions take place in a voltaic cell (also known as a galvanic cell)

• Nonspontaneous redox reactions can be made to occur in an electrolytic cell by the addition of electrical energy

Voltaic Cells: Spontaneous redox reacrions

• Electrical current: the amount of electric charge that passes a point in a given period of time

• A spontaneous redox reaction doesnt require external energy to proceed

  • △G is negative

• Voltaic cells produce an electrical current, but to use it, we must separate the place where oxidation is occurring from where reduction is occurring

• Anode is oxidized

• Cathode is reduced

Electrochemical cells

• Oxidation and reduction half-reactions are kept separate in half-cells of an electrochemical cell

• Electrons flow through a wire along with ions (electrolyte) flowing through a solution via the salt bridge

• The flow of e- requires as conductive solid electrode to allow the transfer of electrons either through an external circuit or metal/graphite electrode

• An electrochemical cell requires the exchange of ions between the two half cells of the system via a salt bridge

Voltage and current

• Voltage is the difference in potential energy between the reactants and products, also called the potential difference.

  • 1 V = 1 J/C (C=Coulomb, charge of e-)

• The amount of force pushing the e- through the wire is called the electromotive force, emf

• Current is the number of electrons that flow through the system per second

  • Unit= ampere

  • 1 A of current = 1 coulomb of charge flowing per second

• Electrode surface area dictates the number of electrons that can flow

  • Larger batteries produce larger currents

Cell potential

• The difference in potential energy between the anode and the cathode in a voltaic cell is called the cell potential.

• The cell potential depends on the relative ease with which the oxidizing agent is reduced at the cathode and the reducing agent is oxidized at the anode

• The cell potential under standard conditions is called the standard emf, E°_cell

  • 25 C, 1 atm for gases. 1 M conc for solutions

• E°_cell = E°_ox + E°_red

• Electrons flow from the anode to the cathode

• When two half cells are connected, the electrons will flow so that the half reaction with the stronger tendency will occur

Electrodes of an Electrochemical Cell

Anode:

• Electrode where oxidation occurs

• Anions attracted to it

• Connected to a positive end of a bettery in a electrolytic cell

• Loses weight in electrolytic cell

Cathode:

• Electrode where reduction occurs

• Cations attracted to it

• Connected to negative end of battery in an electrolytic cell

• Gains weight in an electrolytic cell

An inert electrode doesnt participate in the reaction, but just provides a surface for the transfer of e- to take place on

Cell Notation

• Shorthand description is a voltaic cell is

  • electrode I electrolyte II electrolyte II electrode

• oxidation is on the left, reduction is the right

Standard reduction potential

• The standard half reaction for the reduction of H+ to H₂ is assigned a potential difference of 0 V

• The standard hydrogen electrode, SHE

Half cell potentials

• SHE is 0 V

• Half reactions with a stronger tendency toward reduction than the SHE have positive E°

• Half reactions with a stronger tendency toward oxidation than the SHE have negative E°

• Cell potential for any electrochemical cell is

  • E°_cell = E°_ox + E°_red

• Cell potential is positive for spontaneous reactions and negative for nonspontaneous reactions

Cell