ELECTROCHEMISTRY Chapter 14

Basic Concepts: Overview of Electrochemical Process at Constant

T

,

P

(

= welec (maximum)

= ‒ qE = ‒ ItE (exp)

(Eintensive parameter, q extensive) = ‒ nFE (theory)

or rearranging to the Nernst equation E = Eo

‒ (RT

/

= Eo

‒ (0.02569

/

/

electric charge electric current

electrical work

1. n determined by balancing redox equation

2. Eo _{determined by E}o _{of species being oxidized and E}o _{of species being reduced (standard}

reduction potentials)

3. therefore only Q (reaction quotient) can change the voltage

Oxidation - Reduction Reactions

oxidation reduction

André-Marie Ampère Michael Faraday Note: I below

stands for current in amperes

Balancing Redox Equations

oxidation numbers, ON (in order of priority)

1. Sum of the oxidation numbers of atoms in a neutral species is zero; in an ion the sum equals the ion charge.

2. Alkali metals (Group I) ON = 1, alkaline earth metals (Group II) ON = 2, Group III usually have ON = 3.

3. Fluorine ON = -1 always. Other halogens usually have ON = -1 except in compounds with oxygen or other halogens when the oxidation number can be positive (follows the trend in electronegativity).

4. Hydrogen has ON = 1 except in metal hydrides when the oxidation number is negative.

5. Oxygen usually has ON = -2 except in compounds with fluorine when the oxidation number can be positive and in compounds containing the O-O bond. For peroxides ON = -1 and for superoxides (e.g., NaO) ON = - 1_/

2.

Steps in Balancing Oxidation-Reduction Equations by Half-Reaction Method (Appendix D)

(use oxidation numbers and include electrons in half-reactions)

(omit step d if oxidation numbersused with electrons)

*for basic react-ions neutralize

H+ _{with OH}-

*for basic react-ions neutralize

H+ _{with OH}-

*include these steps for a basic reaction

Basically two ways to balance:

1. start with electrons in

half-reactions determined from oxidation numbers

OR

2. use electrons to balance charge after all elements are balanced

Galvanic Cells, 14-2

FIG I - Terms Used in a Galvanic (Voltaic) Cell

half-cells electrodes anode cathode electrolyte salt bridge

EX 1. Balance in acidic solution

MnO4-_{(aq) + Fe(s) → Mn}2+_{(aq) + Fe}2+_(aq)

EX 2. Balance in basic solution

types of electrochemical cells

ΔG = welec(max) = ‒ nFE 1. spontaneous: ΔG < 0, E > 0

2. nonspontaneous: ΔG > 0, E < 0 FIG II - Electrochemical Cells

a) spontaneous: galvanic (voltaic) b) nonspontaneous: electrolytic

electrochemical cell notation (line notation or cell diagram) OXIDATION half-reaction: Sn(s) → Sn2+_{(aq) + 2e}- REDUCTION half-reaction: Cu2+_{(aq) + 2e}- _{→ Cu(s)} OVERALL: Cu2+_{(aq) + Sn(s) → Cu(s) + Sn}2+_(aq) OXIDATION half-reaction: Cu(s) → Cu2+_{(aq) + 2e}- REDUCTION half-reaction: Sn2+_{(aq) + 2 e}- _{→ Sn(s)} OVERALL: Sn2+_{(aq) + Cu(s) → Sn(s) + Cu}2+_(aq)

Luigi Galvani Alessandro Volta

Cell Diagram or Line Notation for Galvanic Cells half-cell notation

different phases separated by vertical lines species in same phase separated by commas

types of electrodes

• active electrode – involved in electrode half-reaction (most metal electrodes)

ex: Zn2+_{/Zn metal electrode}

Zn(s) → Zn2+ _{(aq) + 2e}- _(oxidation)

notation: Zn|Zn2+

• inert electrode – not involved in electrode half-reaction (inert solid conductors which serve to contact solution with external electrical circuit)

ex: Pt electrode in Fe3+_/Fe2+ _solution

Fe3+_{(aq) + e}-_{→ Fe}2+_{(aq) (reduction)}

notation: Fe3+_{, Fe}2+_|Pt

• electrodes involving metals and their slightly soluble salts

ex: Ag/AgCl electrode

AgCl(s) + e- _{→ Ag(s) + Cl}-_{(aq) (reduction)}

notation: Cl-_|AgCl|Ag

• electrodes involving gases – a gas is bubbled over an inert electrode

ex: H2 gas over Pt electrode

H2(g) → 2H+(aq) + 2e- (oxidation)

notation: Pt|H2|H+ cell notation

anode half-cell written to left of cathode

half-cell (ordered way spontaneous reaction goes) electrodes appear on the far left (anode) and far right (cathode) in notation

salt bridges represented by double vertical lines

ex: Zn|Zn2+ _{and Fe}3+_{, Fe}2+_{|Pt half-cells}

Zn(s) → Zn2+_{(aq) + 2e}- _{(anode, oxidation)}

Fe3+_{(aq) + e}-_{→ Fe}2+_{(aq) [×2] (cathode, reduction)}

Zn + 2Fe3+_{→ Zn}2+ _{+ 2Fe}2+

coulombs, current, and quantity of reaction

Standard Potentials, 14-3

standard states – stable form (allotrope) at P = 1 atm and specified T (usually 25°C)

pure solid pure liquid

gas – ideal gas behavior

1 molar (1 M) solution – ideal solution behavior

standard cell potential, Eo _{– there is no way to separately} measure the potential of an oxidation or reduction half-reaction so conveniently define a zero for the scale

standard reduction potential, Eo _{– by international} con-vention, Eo _{for the reduction of H}+_{(aq) to give H}

2(g) is

taken to be zero at all temperatures:

2 H+(aq, 1 M) + 2 e- → H2(g, P = 1 atm)

RED: 2H+_{(aq) + 2e}- _{→ H}

2(g) => H+(aq, 1 M)|H2(g, 1 atm)|Pt

OX: H2(g) → 2H+(aq) + 2e- => Pt|H2(g, 1 atm)|H+(aq,1 M)

EX 3. A galvanic (voltaic) electrochemical cell whose overall reaction is

Cu(s) + 2 Ag+_{(aq) → Cu}2+_{(aq) + 2 Ag(s)}

oxidizes metallic copper at the anode dissolving the metal

Cu(s) → Cu2+_{(aq) + 2 e}

-and reduces silver ions in solution by plating them out as metallic silver at the cathode. Ag+_{(aq) + e}- _{→ Ag(s)}

a) The cell delivers 0.1 A. How long does it take to dissolve 5.00 g of copper at the anode? (MCu = 63.546)

b) An external power source is connected to the cell and the cell is run electrolytically. If the cell produces

FIG V – SHE/Silver

FIG IV – SHE/Zinc

Note use of activities A

rather than pressures or molarities.

EX 4. Will Ag+ _{oxidize Zn}

metal or will Zn2+ _oxidize

metallic silver? str en gth o f o xi di zi ng a ge nt stren gth o f r ed uc in g a ge nt

Nernst Equation

The Nernst Equation

E cell = Eocell ‒ (RT

/

_/

10Q at 25oC Half-Cells

EX 5. Determine Efor the hydrogen electrode: 2 H+ _{+ 2 e}- _{→ H} 2 a) [H+_{] = 0.00100 M, P} H2 = 0.500 atm b) H+ _{+ e}- _→ 1_/ 2 H2; [H+] = 0.00100 M, PH2 = 0.500 atm c) [H+_{] = 1.00 × 10}-14 _{M, P} H2 = 1.00 atm

d) rewrite hydrogen electrode equation in base, [OH-_{] = 1.00 M, P}

H2 = 1.00 atm

Eo _{and the Equilibrium Constant}

Reaction Parameters at Standard State ∆G° K E°cell Reaction at standard-state conditions < 0 = 0 > 0 > 1 = 1 < 1 > 0 = 0 < 0 spontaneous at equilibrium nonspontaneous

EX 7. If [Cu2+_{] = 0.10 M and [Ag}+_{] = 0.20 M, what is the voltage of an electrochemical cell based upon the}

couple: E o_(Cu2+_{|Cu) = 0.340 V and E} o_(Ag+_{|Ag) = 0.800 V?}

EX 8. An electrochemical cell is based upon the couple:

E o _(Cu2+_{|Cu) = 0.340 V and E} o _(Ag+_{|Ag) = 0.800 V. If the}

voltage of the cell were 0.448 V when [Cu2+_{] = 0.10 M,}

what is the silver ion concentration?

EX 9. If the cell voltage is 0.473 V what is the pH of the cathode compartment for the following cell where E o

(Zn2+_{|Zn) = - 0.7618 V?} Zn(s)|Zn2+_{(aq, 1.00 M)||H}+_{(aq, ? M)|H} 2(g, 1 atm)|Pt(s)

∆

_G°

E°

K

solubility product, Ksp

EX 10. If E o_(Cr3+_{|Cr) = -0.74 V and E} o_(Zn2+_{|Zn) = -0.7628 V what is the equilibrium constant for} 2 Cr3+_{(aq) + 3 Zn(s) → 2 Cr(s) + 3 Zn}2+_(aq)

EX 16. From the following reaction cell where Ecell= 0.397 V

Pt|H2(1 atm)|H+(1.00 M)||Cl-(l.00 × 10-3 M), Ag+(? M)|AgCl(s)|Ag(s) determine the value of Ksp(AgCl). Relevant standard

reduction potentials are 2 H+_{(aq) + 2 e}- _{→ H}

2(g) Eo = 0.0000 V Ag+_{(aq) + e}- _{→ Ag(s) E}o _{= 0.7996 V}

EX 11. Determine the value of Ksp(AgSCN) given that

AgSCN(s) + e- _{→ Ag(s) + SCN}-_{(aq) E} o _{= 0.0898 V}

Nerve Transmission

A nerve cell (neuron) can be likened to a receiver, transmitter, and transmission line between the two. Dendrites receive impulse signals from a neighboring neuron. Transmission of electrical signals within the receiving neuron proceeds from dendrites to synapse along the length of the axon. The signal is due to opening and closing of sodium channels in the axon’s membrane, allowing Na+ _{to enter or not enter the cell.}

Entering Na+ _{causes an increase in charge}

inside the cell.

At rest, the inside of a neuron is slightly negative (~ -70 mV) due to a higher concentration of K+

ions inside (concentration gradient balanced by a potential difference across the membrane,

Einside - Eoutside which can be calculated by modifying the Nernst equation)

E = constant + (0.05916

/

where n is the charge of the ion. An impulse opens Na+ _{channels. When stimulated past a}

threshold Na+ _{rushes into the axon, causing a region of positive charge (depolarization) within}

the axon and a potential of ~30 mV across the membrane. The channels open in one direction

along the axon as an opened channel needs a rest period before it can reopen. The region of positive charge causes nearby Na+ channels to close. Just after the Na+ channels close, K+ channels open and K+ _{exits the axon (repolarization). The membrane is brought back to its}

negative resting potential by Na+_/K+ _{pumps in the cell membrane. This process continues as a}

chain-reaction along the axon. The influx of sodium ions depolarises the axon, and the outflow of potassium ions repolarises it.

K+ _Na+

inside 20 x y outside x 10 y