Physics: Electrochemistry (Galvanic & Electrolytic Cells)

Cell Potentials

Electrolytic Cells

Electromotive Force and Thermodynamics

Equation: Combining the Gibbs Free Equation ΔG° = -nFE°cell = -RT ln Keq so nFE°cell = RT ln Keq

Equation: Standard Change in Free Energy from Equilibrium Constant: ΔG° = -RT ln Keq ΔG° = standard change in free energy (J) R = ideal gas constant (8.314 m3Pa/molK or 8.314 lkPa/molK or 0.082 Latm/molk) T = absolute temperature Keq = equilibrium constant for the reaction

Galvanic (Voltaic) Cell

Rechargeable Cells/Battery

Shorthand Notation for Electrochemical Galvanic/Voltaic Cell Example Zn(s) I Zn2+ (1M) II Cu2+ (1M) I Cu(s) The following rules are used in constructing a cell diagram: 1. The reactants and products are always listed from left to right in this form: anode I anode sol'n (concentration) II cathode sol;n (concentration) I cathode 2. A single vertical line indicates a phase boundary 3. A double vertical line indicates the presence of a salt bridge or some other type of barrier

How does the current (I) move in electrochemical cells? A. From cathode to anode B. From cathode to cathode C. From anode to cathode D. from anode to anode

A. From cathode to anode For all electrochemical cells, the current (I) runs from cathode to anode.

Which of the following statements regarding electromotive force (emf) is true? A. If the emf is positive, the cell must absorb energy (ΔG > 0), which means it is nonspontaneous. If the emf is negative, the cell is able to release energy (ΔG < 0), which means it is spontaneous. B. If the emf is positive, the cell is able to release energy (ΔG < 0), which means it is spontaneous. If the emf is negative, the cell must absorb energy (ΔG > 0), which means it is nonspontaneous. C. If the emf is positive, the cell must absorb energy (ΔG > 0), which means it is spontaneous. If the emf is negative, the cell is able to release energy (ΔG < 0), which means it is nonspontaneous. D. If the emf is positive, the cell is able to release energy (ΔG > 0), which means it is spontaneous. If the emf is negative, the cell must absorb energy (ΔG < 0), which means it is nonspontaneous.

B. If the emf is positive, the cell is able to release energy (ΔG < 0), which means it is spontaneous. If the emf is negative, the cell must absorb energy (ΔG > 0), which means it is nonspontaneous. The electromotive force corresponds to the voltage or electrical potential difference of the cell.

What is the change in free energy for an electrolytic cell? A. ΔG < 0 B. ΔG > 0 C. ΔG = 0 D. It depends on the reaction that occurs in the cell

B. ΔG > 0 The change in free energy for an electrolytic cell is positive because electrolytic cells house nonspontaneous reactions that require the input of energy to proceed. This type of oxidation-reduction reaction driven by an external voltage source is called electrolysis, in which chemical compounds are decomposed. For example, nonspontneous decomposition of water into oxygen and hydrogen gas. -the half reactions do not need to be separated into different compartment because the desired reaction is nonspontaneous **look at page 402 of the general chemistry Kaplan book for the diagram

Which of the following statements is true? A. For galvanic cells, the difference of the reduction potentials of the two half-reactions is negative, for electrolytic cells, the difference of the reduction potentials of the two half-reactions is positive B. For galvanic cells, the difference of the reduction potentials of the two half-reactions is negative, for electrolytic cells, the difference of the reduction potentials of the two half-reactions is negative C. For galvanic cells, the difference of the reduction potentials of the two half-reactions is positive, for electrolytic cells, the difference of the reduction potentials of the two half-reactions is negative D. For galvanic cells, the difference of the reduction potentials of the two half-reactions is positive, for electrolytic cells, the difference of the reduction potentials of the two half-reactions is positive

C. For galvanic cells, the difference of the reduction potentials of the two half-reactions is positive, for electrolytic cells, the difference of the reduction potentials of the two half-reactions is negative Standard electromotive force (emf or E°cell) of a reaction is the difference in potential (voltage) between two half-cells under standard conditions (25°C (298K), 1 atm pressure, and 1M concentration). -the emf of a reaction is determined by calculating the difference in reduction potentials between the two half-cells

How do electrons move in electrochemical cells? A. From cathode to anode B. From cathode to cathode C. From anode to cathode D. from anode to anode

C. From anode to cathode For all electrochemical cells, the movement of electrons is from anode to cathode. Mnemonic Electron flow in an electrochemical cell: A ---> C (order in the alphabet) Electrons flow from Anode to Cathode in all types of electrochemical cells.

If a reaction in galvanic cells (aka voltaic cells) is spontaneous then... A. The free energy change is negative and the electromotive force is also negative B. The free energy change is positive and the electromotive force is also positive C. The free energy change is negative and the electromotive force is positive D. The free energy change is positive and the electromotive force is negative

C. The free energy change is negative and the electromotive force is positive If a reaction in galvanic cells (aka voltaic cells) is spontaneous, this means that the reaction's free energy is decreasing (ΔG < 0) as the cell releases energy to the environment. By extension, if the free energy change is negative for these cells, their electromotive force (Ecell) must be positive. -the free energy change and electromotive force always have opposite signs.

Concentration Cells -Are a specialized form of a galvanic cell in which both electrodes are made of the same material. -Rather than a potential difference causing the movement of charge, it is the concentration gradient between the two solutions

In a galvanic/voltaic cell which way do the anions and cations from the salt bridge flow? A. The anions from the salt bridge diffuse into the solution on the cathode side, and the cations of the salt bridge flow into the solution of the cathode side. B. The anions from the salt bridge diffuse into the solution on the anode side, and the cations of the salt bridge flow into the solution of the anode side. C. The anions from the salt bridge diffuse into the solution on the cathode side, and the cations of the salt bridge flow into the solution of the anode side. D. The anions from the salt bridge diffuse into the solution on the anode side, and the cations of the salt bridge flow into the solution of the cathode side.

D. The anions from the salt bridge diffuse into the solution on the anode side, and the cations of the salt bridge flow into the solution of the cathode side. For example, while the anions from the salt bridge (Cl-) diffuse into the solution on the anode side (ZnSO4) to balance out the charge of the newly created Zn2+ ions (via oxidation of Zn), the cations of the salt bridge (K+) flow into the solution on the cathode side (CuSO4) to balance out the charge of the sulfate ions left in solution when the Cu2+ ions are reduced to Cu and precipitate onto the electrode. - This precipitation process onto the cathode itself can also be called plating or galvanization Example galvanic cell setup and reaction: Electrons flow from the zinc anode through the wire and to the copper cathode. Therefore the zinc is oxidized and the copper is reduced. The anions (Cl-) flow externally from the salt bridge into the ZnSO4 solution at the anode side, and the cations (K+) flow externally from the salt bridge into the CuSO4 solution on the cathode side.

Equation: Combining the Gibbs Free Equation ΔG° = -nFE°cell = -RT ln Keq so nFE°cell = RT ln Keq n = number of moles of electrons exchanged F = Faraday constant expressed in coulombs (J/V) (96,500C or 10^5C) R = ideal gas constant (8.314 m3Pa/molK or 8.314 lkPa/molK or 0.082 Latm/molk) T = absolute temperature Keq = equilibrium constant for the reaction *You will probably not need to know this equation for the MCAT, just understand what it means: For equilibrium constants less than 1 (equilibrium state favors the reactants), the E°cell will be negative because the natural log of any number between 0 and 1 is negative -This is characteristic of electrolytic cells which house nonspontaneous oxidation-reduction reactions For equilibrium constants greater than 1 (equilibrium state favors the products), the E°cell will be positive because the natural log of any number greater than 1 is positive -This is characteristic of galvanic/voltaic cells which house spontaneous oxidation-reduction reactions If the equilibrium constant is equal to 1 (concentrations of the reactants and products are equal at equilibrium), the E°cell will be equal to zero. *If E°cell is positive, ln Keq is positive. This means that Keq must be greater than one and that the equilibrium lies to the right (product are favored). This means the reaction is spontaneous.

Equation: Electrodeposition Equation mol M = It/nF M = amount of metal ion being deposited at a specific electrode I = current t = time n = numder of electron equivalents for a specific metal ion F = Faraday constant (1F = 96,485 C or 10^5 C/mol e- rounded up) This equation helps determine the number of moles of element being deposited on a plate. It can also be used to determine the amount of gas liberated during electrolysis. Mnemonic Calculating Moles of Metal, It is Not Fun mol M = It/nF

Equation: Free Energy Change (nonstandard condition) ΔG = ΔG° + RT ln Q ΔG = free energy change under nonstandard conditions ΔG° = free energy change under standard conditions R = ideal gas constant (8.314 m3Pa/molK or 8.314 lkPa/molK or 0.082 Latm/molk) T = temperature Q = reaction quotient Use this equation to solve for Gibbs free energy (spontaneity) under nonstandard conditions (standard conditions = 25°C (298K) 1 atm pressure, and 1 M concentrations).

Equation: Gibbs Free Energy in relation to Electromotive Force (emf) ΔG° = -nFE°cell ΔG° = standard change in free energy (J) n = number of moles of electrons exchanged F = Faraday constant expressed in coulombs (J/V) (96,500C or 10^5C) E°cell = emf of the cell under standard conditions The change in Gibbs free energy, ΔG, is the change in the amount of energy available in a chemical system to do work. *If ΔG is positive, the reaction is nonspontaneous; if ΔG is negative, the reaction is spontaneous. --- The same goes for ΔG°. *Note the significant of the negative sign on the right of the equation. ΔG° and E°cell will always have opposite signs. Therefore, galvanic cells have negative ΔG° and positive E°cell values; electrolytic cells have positive ΔG° and negative E°cell values.

Equation: Moles of electrons transferred during reduction and Faraday's Laws M^n+ + ne- ---> M(s) According to this equation, one mole of metal M(s) will be produced if n moles of electrons are supplied to one mole of M^n+. Faraday's laws states that the amount of chemical change induced in an electrolytic cell is directly proportional to the number of moles of electrons that are exchanged during the oxidation-reduction reaction. To determine how many moles are in an electron, multiply the charge of an electron (1.6 x 10^-19 C) by Avogadro's number (6.02 x 10^23) = 96485 C/mol e- - This numder (96,485 C/mol e-) is the Faraday constant and one faraday (F) is equivalent to the amount of charge contained in one mole of electrons (1F = 96,485 C) - On the MCAT round Faraday's constant up to 10^5 to make calculations easier

Equation: Nerst Equation When conditions deviate from standard conditions (25°C (298K) 1 atm pressure, and 1 M concentrations), use the Nerst equation: Ecell = E°cell - RT/nF lnQ Ecell = emf of the cell under nonstandard conditions E°cell = emf of the cell under standard conditions R = ideal gas constant (8.314 m3Pa/molK or 8.314 lkPa/molK or 0.082 Latm/molk) T = temperature in kelvins n = number of moles of electrons F = Faraday constant (96,500C or 10^5C) Q = reaction quotient for the reaction at a given point in time If T = 298, the equation can be simplified to: Ecell = E°cell - 0.0592/n logQ Remember that the reaction quotient, Q, for a general reaction aA + bB ---> cC + dD has the form: Q = {[C]^c[D]^d} / {[A]^a[B]^b} *Only calculate for aqueous terms of the reaction (only the species in solution. For example, of the Daniell cell, only the concentrations of zinc and copper ions are considered: Zn(s) +Cu2+(aq) ---> Zn2+(aq) + Cu(s) Q = [Zn2+]/[Cu2+]

Equation: Nerst Equation When conditions deviate from standard conditions (25°C (298K) 1 atm pressure, and 1 M concentrations), use the Nerst equation: Ecell = E°cell - RT/nF lnQ Ecell = emf of the cell under nonstandard conditions E°cell = emf of the cell under standard conditions R = ideal gas constant (8.314 m3Pa/molK or 8.314 lkPa/molK or 0.082 Latm/molk) T = temperature in kelvins n = number of moles of electrons F = Faraday constant (96,500C or 10^5C) Q = reaction quotient for the reaction at a given point in time If T = 298, the equation can be simplified to: Ecell = E°cell - 0,0592/n logQ Remember that the reaction quotient, Q, for a general reaction aA + bB ---> cC + dD has the form: Q = {[C]^c[D]^d} / {[A]^a[B]^b} *Only calculate for aqueous terms of the reaction (only the species in solution. For example, of the Daniell cell, only the concentrations of zinc and copper ions are considered: Zn(s) +Cu2+(aq) ---> Zn2+(aq) + Cu(s) Q = [Zn2+]/[Cu2+]

Equation: Standard Electromotive Force (emf or E°cell) Standard electromotive force (emf or E°cell) of a reaction is the difference in potential (voltage) between two half-cells under standard conditions (25°C (298K), 1 atm pressure, and 1M concentration). -the emf of a reaction is determined by calculating the difference in reduction potentials between the two half-cells E°cell = E°red,cathode - E°red,anode The emf of a cell can also be measured with a voltmeter.

Example Galvanic/Voltaic Cell: Daniell Cell -In this galvanic cell, zinc is the anode and copper is the cathode -A zinc electrode is placed in an aqueous ZnSO4 solution, and a copper electrode is placed in an aqueous CuSO4 solution -The anode of this cell is the zinc bar where Zn(s) is oxidized to Zn2+(aq) -The cathode is the copper bar, and it is the site of the reduction of CU2+(aq) to Cu(s) -The half cell reactions are written: Oxidation: Zn(s) ---> Zn2+(aq) + 2e- Ered = -0.762 V Reduction: Cu2+(aq) + 2e- ---> Cu(s) Ered = +0.340 V The net reaction is Zn(s) + Cu2+ (aq) ---> Zn2+(aq) + Cu(s) Ecell = +1.102V

Example Galvanic/Voltaic Cell: Daniell Cell -In this galvanic cell, zinc is the anode and copper is the cathode -A zinc electrode is placed in an aqueous ZnSO4 solution, and a copper electrode is placed in an aqueous CuSO4 solution -The anode of this cell is the zinc bar where Zn(s) is oxidized to Zn2+(aq) -The cathode is the copper bar, and it is the site of the reduction of CU2+(aq) to Cu(s) -The half cell reactions are written: Oxi: Zn(s) ---> Zn2+(aq) + 2e- Ered = -0.762 V Red: Cu2+(aq) + 2e- ---> Cu(s) Ered = +0.340 V The net reaction is Zn(s) + Cu2+ (aq) ---> Zn2+(aq) + Cu(s) Ecell = +1.102V

True or False: A less positive E°red means a greater relative tendency for reduction to occur, while a more positive E°red means a greater relative tendency for oxidation to occur.

False. E°red = standard reduction potential. Therefore, a more positive E°red means a greater relative tendency for reduction to occur, while a less positive E°red means a greater relative tendency for oxidation to occur. Standard reduction potential (E°cell) is measured under standard conditions (25°C (298K), 1 atm pressure, and 1 M concentrations). The relative reactivities of different half-cells can be compared to predict the direction of electron flow. * The greater (higher) the E°red, the more it wants to be reduced.

True or False: For all electrochemical cells, the electrode where oxidation occurs is called the cathode, and the electrode where reduction occurs is called the anode.

False. For all electrochemical cells, the electrode where oxidation occurs is called the anode, and the electrode where reduction occurs is called the cathode. *Think AN OX and a RED CAT The ANode is the site of OXidation REDuction occurs at the CAThode

True or False: For all electrochemical cells, the movement of electrons is from cathode to anode, and the current (I) runs from anode to cathode.

False. For all electrochemical cells, the movement of electrons is from anode to cathode, and the current (I) runs from cathode to anode. Electrons move through an electrochemical cell opposite to the flow of current (I). *Think of current as having a theoretical flow of positive charge. *Think that electrons want to flow from the negative anode to the positive cathode and that current wants to flow from the positive cathode to the negative anode. -oxidation occurs at the anode because the electrons are moving out and current is moving in -reduction occurs at the cathode because the electrons are moving in and current is moving out Mnemonic Electron flow in an electrochemical cell: A ---> C (order in the alphabet) Electrons flow from Anode to Cathode in all types of electrochemical cells.

True or False: Whereas galvanic cells house nonspontaneous oxidation-reduction reactions that generate electrical energy, electrolytic cells house spontaneous reactions.

False. Whereas galvanic cells house spontaneous oxidation-reduction reactions that generate electrical energy, electrolytic cells house nonspontaneous reactions that require the input of energy to proceed.

True or False: For galvanic cells, the electrode with the more positive reduction potential is the anode, and the electrode with the less positive reduction potential is the cathode.

False: For galvanic cells, the electrode with the more positive reduction potential is the cathode, and the electrode with the less positive reduction potential is the anode. Because the species with a stronger tendency to gain electrons (that wants to gain electrons more) is actually doing so, the reaction is spontaneous and ΔG is negative.

Fill in the blanks: For galvanic cells, the anode is __________ (negatively or positively) charged and the cathode is __________ (negatively or positively) charged. For electrolytic cells, the anode is __________ (negatively or positively) charged and the cathode is __________ (negatively or positively) charged.

For galvanic cells, the anode is negatively charged and the cathode is positively charged. For electrolytic cells, the anode is positively charged and the cathode is negatively charged. This is because an external source is used to reverse the charge of an electrolytic cell. However, in both types of cells, reduction occurs at the cathode, and oxidation occurs at the anode (electrons always flow through the wire from the anode to the cathode and current flows from cathode to anode); cations are attracted to the cathode, and anions are attracted to the anode. In a galvanic cell, electrons flow from the anode to the cathode, which is why the anode is considered the negative electrode - because it is the source of electrons. In an electrolytic cell, the anode is considered positive because it is attached to the positive pole of the external voltage source and attracts anions from the solution. The cathode of an electrolytic cell is considered negative because it is attached to the negative pole of the external voltage source and attracts cations from the solution.

Lead-Acid Batteries - A lead-acid battery, aka lead storage battery, is a type of rechargeable battery - When discharging, consists of Pb anode and a PbO2 cathode in a concentrated sulfuric acid solution -When fully discharged, it consists of two PbSO4 electroplated lead electrodes with a dilute concentration of H2SO4 -The battery acts as a galvanic/voltaic cell when fully charged and is discharging -When charging, the PbSO4-plated electrodes are dissociated to restore the original Pb and PbO2 electrodes and concentrate the electrolyte - this is done by an external source (reversing the electroplating process and concentrating the acid solution) -When charging, the lead-acid cell is part of an electrolytic circuit -These cells have low energy densities - Energy density - a measure of a battery's ability to produce power as a function of its weight - the amount of energy a cell can produce relative to the mass of battery material -Lead-acid batteries, therefore, require a heavier amount of battery material to produce a certain output as compared to other batteries. The net equation for a discharging lead-acid battery: Pb(s) + PBO2(s) + 2H2SO4(aq) ---> 2PbSO4(s) + 2H20 E°cell = 1.685 - (-0.356) = 2.041 V

Lead-Acid Batteries - A lead-acid battery, aka lead storage battery, is a type of rechargeable battery - When discharging, consists of Pb anode and a PbO2 cathode in a concentrated sulfuric acid solution -When fully discharged, it consists of two PbSO4 electroplated lead electrodes with a dilute concentration of H2SO4 -The battery acts as a galvanic/voltaic cell when fully charged and is discharging -When charging, the PbSO4-plated electrodes are dissociated to restore the original Pb and PbO2 electrodes and concentrate the electrolyte - this is done by an external source (it reverses the electroplating process and concentrates the acid solution) -When charging, the lead-acid cell is part of an electrolytic circuit -These cells have low energy densities - Energy density - a measure of a battery's ability to produce power as a function of its weight - the amount of energy a cell can produce relative to the mass of battery material -Lead-acid batteries, therefore, require a heavier amount of battery material to produce a certain output as compared to other batteries. The net equation for a discharging lead-acid battery: Pb(s) + PBO2(s) + 2H2SO4(aq) ---> 2PbSO4(s) + 2H20 E°cell = 1.685 - (-0.356) = 2.041 V

Nickel-Cadmium Batteries -Are rechargeable cells, so function both as a galvanic/voltaic cell as well as an electrolytic cell -When discharging (galvanic/voltaic cell process), consist of a Cd anode and a NiO(OH) cathode in a concentrated KOH solution -When charging (electrolytic cell process), the Ni(OH)2- and Cd(OH)2-plated electrodes are dissociated to restore the original Cd and NiO(OH) electrodes and concentrate the electrolyte -Have a higher energy density than lead-acid batteries Net equation for a Ni-Cd battery: 2NiO(OH)(s) + Cd + 2H2O ---> 2NI(OH)2(s) + Cd(OH)2(s) E°cell = 0.49 - (-0.86) = 1.35 V *Nickel-metal hydride (NiMH) batteries have more or less replaced Ni-Cd batteries because they have higher energy density, are more cost effective, and are significantly less toxic.

True or False: A rechargeable cell or rechargeable battery is one that can function as both a galvanic and electrolytic cell.

True. A rechargeable cell or rechargeable battery is one that can function as both a galvanic and electrolytic cell. Rechargeable batteries are electrochemical cells that can experience charging (electrolytic) and discharging (galvanic) states.

True or False: For electrolytic cells, the electrode with the more positive reduction potential is the anode, and the electrode with the less positive reduction potential is the cathode.

True. For electrolytic cells, the electrode with the more positive reduction potential is forced by the external voltage source to be oxidized and is, therefore, the anode. The electrode with the less positive reduction potential is forced to be reduced and is, therefore, the cathode. Because the movement of electrons is in the direction against the tendency or desired of the respective electrochemical species, the reaction is nonspontaneous and ΔG is positive. *Remember that electrolytic cells are nonspontaneous and are opposite to galvanic/voltaic cells.

True or False: Galvanic cells and concentration cells house spontaneous reactions, whereas electrolytic cells contain nonspontaneous reaction.

True. Galvanic cells and concentration cells house spontaneous reactions, whereas electrolytic cells contain nonspontaneous reaction. All three types contain electrodes where oxidation and reduction take place.

True or False: The two separate compartments of a galvanic/voltaic cell are called half-cells.

True. In a galvanic/voltaic cell, two electrodes of distinct chemical identity are placed in separate compartment, which are called half cells. The two electrodes are connected to each other with a conductive material (copper wire). Surrounding each of the electrodes is an aqueous electrolyte solution composed of cations and anions. Connecting the two solutions is a structure called a salt bridge, which consists of an inert salt (KCl or NH4NO3) that will not react with the electrodes or with the ions in solution.

True or False: To determine the oxidation potential, you can reverse the sign of the reduction potential.

True. Reduction and oxidation are opposite processes. Therefore, to obtain the oxidation potential of a given half-reaction, both the reduction half-reaction and the sign of the reduction potential are reversed. For example: The reduction potential for Ag is given as: Ag+ + e- ---> Ag(s) E°red = +0.80 V To get the oxidation potential, just reverse everything: Ag(s) ---> Ag+ + e- E°ox = -0.80

True or False: Surge currents are period of large current (amperage) early in the discharge cycle.

True. Surge currents are period of large current (amperage) early in the discharge cycle. Surge current is an above-average current transiently released at the beginning of the discharge phase; it wanes rapidly until a stable current is achieved

True or False: The more positive the reduction potential, the greater the tendency to be reduced.

True. The more positive the reduction potential, the greater the tendency to be reduced - the more it wants to be reduced. -The species in a reaction that will be oxidized or reduced can be determined from the reduction potential of each species. -Reduction potential is defined as the tendency of a species to gain electrons and to be reduced. A reduction potential is measured in volts (V) and defined relative to the standard hydrogen electrode (SHE), which is given a potential of 0V by convention. Oxidation is the loss of electrons, gain of oxygen or loss of hydrogen. Reduction is the gain of electrons, loss of oxygen or gain or hydrogen.

True or False: The purpose of the salt bridge is to exchange anions and cations to balance, or dissipate, newly generated charges.

True. The purpose of the salt bridge is to exchange anions and cations to balance, or dissipate, newly generated charges.

Physics: Electrochemistry (Galvanic & Electrolytic Cells)

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