CHEMISTRY 2000 Topic #3: Thermochemistry and Electrochemistry – What Makes Reactions Go? Spring...

CHEMISTRY 2000

Topic #3: Thermochemistry and Electrochemistry – What Makes Reactions Go?

Spring 2008Dr. Susan Lait

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Electrochemical Cells

An electrochemical cell consists of: Two physically separated half-cells (one for each half-

reaction), An external circuit via which electrons generated by the

oxidation half-cell can travel to the reduction half-cell, A salt bridge (or equivalent) to allow ions to move between

the two half-cells so that charge doesn’t build up in them. (That would stop the flow of electrons, rendering the cell useless.)

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So that we don’t have to draw a picture every time we want to describe an electrochemical cell, there is a standard notation:

With the anode (where electrons are generated) at the left, we describe the relationships between each phase in the cell.

A single bar represents two phases in direct contact. e.g. an electrode immersed in a solution

A double bar represents two phases indirectly connected. e.g. two solutions connected by a salt bridge.

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If the overall reaction in an electrochemical cell is spontaneous, energy is released. This energy is measured in relation to the number of electrons involved in the reaction, giving a potential. When 1 Joule of energy is released by an electrochemical reaction involving electrons with 1 Coulombe of charge, the potential is 1 Volt:

A cell’s potential can be measured by applying an external voltage opposing the current flow. When the external voltage has exactly the right energy to stop the reaction but not reverse it (i.e. to make the system be at equilibrium), that external voltage is termed the electromotive force (emf). Since the electromotive force must be exactly equal to the potential produced by the cell, the following terms are often used interchangeably:

Voltage (or potential) Electromotive force (or emf) Electric potential difference

C10 1.602176- of charge a has electron 1 where CJ

1 V 1 19-

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Cell Potential and Gibbs Free Energy

Recall that changes to internal energy occur via heat and work. The reaction in an electrochemical cell is a reversible process, so we can clarify that both the heat and work are reversible.

Let us assume that the electrochemical cell is operating at constant pressure and temperature (so that qrev = H and S = H/T).

We can also divide the work into pressure-volume work (i.e. expansion (wrev,PV = -PV)) and non-pressure-volume work

revrev wqU

PVnonrev

PVnonrevPVrevrev

wVPSTU

wwqU

,

,,

)(

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Cell Potential and Gibbs Free Energy

This rearranges to give:

When we defined enthalpy, we defined H = U + PV…

This equation is starting to look very familiar…

The maximum work that can be done on the system is rG. Since rG < 0 for a spontaneous reaction, a spontaneous reaction can do work on the surroundings. The maximum amount of non-PV work that can be done on the surroundings is equal to -rG!

STVPUw PVnonrev ,

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The Nernst Equation

So, the free energy change is equal to the work done on the electrons (charge = q) as they travel through a potential difference (cell potential = E):

The charge of the electrons will be negative with a magnitude equal to the # moles of electrons (n) multiplied by the charge of 1 mole of electrons (F = Faraday’s constant = 96485 C/mol):

Usually, we work in terms of molar free energy change. When we divide both sides of the equation by moles of a product (or reactant), n is converted to the stoichiometric coefficient of the electrons in the overall redox reaction (e):

qEGw rPVnonrev ,

For a spontaneous reaction, rG <0 therefore E >0!!!

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The Nernst Equation

This equation can, of course, be used under standard conditions (among others), so we can say:

Recall that:

Rearrangement gives us the Nernst equation:

and

QRTGG omrmr ln

QF

RTEE

e

ln

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Half-cells and Standard Reduction Potentials

It’s impossible to directly measure the potential for a half-cell since there would be no current and therefore no voltage. Instead, cell potential is measured against an arbitrary zero reference point, the standard hydrogen electrode (SHE):

As it does for H, S, and G, reversing the reaction reverses the sign of E˚; therefore, we can also say that:

The standard hydrogen electrode (shown at the left) is an electrode in which hydrogen gas is bubbled over a platinum electrode in the presence of 1 M H+

(aq).

2(g)(aq) H2e2H VE 0

2e2H H (aq)2(g) VE 0

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Half-cells and Standard Reduction Potentials

Like enthalpies, entropies and free energies, cell potentials are additive.e.g.

As such, when a cell is constructed under standard conditions with a standard hydrogen electrode as the anode, the measured cell potential will be equal to the standard reduction potential for the other half-cell.

(s)(aq) AgeAg

2e2H H (aq)2(g) VE o

HH0

/2

(s)2(aq) Cu2eCu VE o

CuCu340.0

/2

2eZn Zn 2(aq)(s) VE o

ZnZn763.02/

VE 800.0

o

AgAgE

/

Because E is measured in J/C, it DOES NOT CHANGE when the reaction equation is multiplied by a coefficient!

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Electrochemical Cells Under Nonstandard Conditions

We can also use a hydrogen electrode (standard or nonstandard) to measure reduction potentials of half-cells under nonstandard conditions. To do this, we must know the exact activities of each species so that we can determine Q and use the Nernst equation:

The cell below has a potential (aka emf) of -1.425 V at 25 C.

Write balanced equations for each half-cell and an overall chemical equation.

QF

RTEE

e

ln

)()(3)()(2)( )00100.0()00.5()00.1( saqaqgs AlMAlClpHHbarHPt

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Knowing that E = -1.425 V, calculate E for the cell in the previous example.

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Finally, use E for the cell to determine the standard reduction potential of the Al3+/Al half-cell.

As noted previously, potentials can be added and subtracted but, because they are intensive properties (do not depend on quantity), they are never multiplied or divided by reaction coefficients.

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Finally, we can use the standard potential for an electrochemical cell to determine the standard free energy of formation for one of the reactants/products. This is a convenient method to measure fG for new compounds/ions.e.g. Use the information from the previous example to determine fG for Al3+

(aq).

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If we can use cell potential to determine free energies then it follows that we can use free energies to determine cell potential.

e.g. We wish to know whether the reaction described by the cell below is spontaneous and, if so, what is its

potential.

We can look up the standard reduction potential for a Cl2/Cl- half-cell, but there is no standard reduction potential listed for a S2O3

2-/HSO4- half-cell. We can, however, look up standard

free energies of formation for each species in the reaction…

)()(2)()()(42

)(32)( )35.0()038.0()5.1(),044.0(),0083.0( sgaqaqaqaqs PtbarClMClpHHMHSOMOSPt

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So, we’ll start by calculating the standard free energy change for this reaction…

mol

kJClG

mol

kJHSOG

mol

kJOHG

mol

kJOSG

aq

aq

l

aq

2.131)(

7.755)(

1.237)(

5.522)(

)(f

)(4f

)(2f

2)(32f

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At this point, we can take one of two paths: Calculate the standard potential for the cell (E) then use the

Nernst equation to find E. Calculate the free energy change under the actual

conditions then use G=eFE to find E.

Either way, we get the same answer and, either way, we need to find Q to get from standard conditions to actual conditions.

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Finally, we calculate E. Is this reaction spontaneous?

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Using Electrochemistry to Measure Ksp Values

Ksp values for relatively insoluble solids are tiny.

e.g. Iron(III) hydroxide has a Ksp of 410-38. That means that, at pH 7, you could dissolve 4 fg of Fe(OH)3 in 1 L water.

To analyze a solution this dilute, we can’t just titrate!

We can, however, measure the Ksp of an ionic solid electro-chemically if we can find half-reactions that add up to the desired solubility equilibrium expression. Often, this means that one of the electrodes will consist of the ionic solid coated on the corresponding metal.

Once we have constructed the electrochemical cell, we can: Measure the cell potential (E) Use the cell potential to find the standard free energy change

(rG) Use the standard free energy change to find the equilibrium

constant (Ksp)

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Let’s say that we can’t find the Ksp value for silver(I) iodide:

We can obtain this net reaction using a Ag/Ag+ anode and a AgI cathode:

The value for the electron coefficient (e) is _______ and the standard cell potential (E) is _____________.


VE

VE

oAgI

o

AgAg

1518.0

7991.0/

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This allows us to calculate the Ksp for AgI:


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Batteries

Electrochemical cells produce a voltage, so they can be used to power electrical devices. The voltage produced depends on:

Standard cell potential (due to half-cells) Concentrations of reactants and products (Q in Nernst

equation) Temperature (T in Nernst equation)

The voltage does not depend on the size of the cell – that just determines the quantity of available reactants (i.e. how long the cell can run before the concentration of reactants is too low for the reaction to be spontaneous).

Typical cell potentials are ~1V. If we want/need a larger potential, we must connect multiple cells in series, producing a battery:

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Batteries

In theory, any battery can be recharged – just apply an external potential to force the reverse reaction to occur, “pushing the electrons backwards”.

In practice, this isn’t always easy (or safe!) In some batteries, the electrodes can be damaged during

discharge In some batteries, the electrodes get coated with resistive

products which cause heating when current is passed through them.

In some batteries, the desired “reverse reaction” is not the one that occurs when recharging is attempted – generally because there is something else that is more easily oxidized or reduced. A common example is the electrolysis of water – used to make pastes in many batteries.

A reliable battery is a good battery. Many batteries contain a paste so that the solutes are always saturated in the small amount of water available. This keeps the solute concentration constant – thereby keeping Q and E constant.

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Alkaline Batteries

An alkaline battery has a zinc anode and a manganese(IV) oxide cathode. As the name implies, it operates under basic conditions:

Because there are no solutes in the overall reaction equation, Q ≈ 1 and E ≈ E, giving a constant voltage.

Outer steel jacket

Plastic sleeve

Inner steel jacket

(-)

(+)

Cathode(+): paste containingMnO2, graphite, and water

Anode(-): Paste containingpowdered zinc, KOH, and water

Brass collector

Cell base

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Lead-Acid Batteries

An lead-acid battery has a lead anode and a lead(IV) oxide cathode. As the name implies, it operates under acidic conditions (HSO4

-(aq)):

The cell potential is ~2 V. To get a 12 V car battery, six cells are connected in series.

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Fuel Cells

We know that burning a fuel releases energy as heat. This energy is more efficiently harnessed if it is produced by oxidizing the fuel electrochemically – as in a fuel cell. It also causes less pollution!

A lot of research is currently being done to develop a practical hydrogen fuel cell – which would be a very environmentally friendly power source as the only waste product would be water:

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Fuel Cells

Since fuel cells always involved oxidation of a fuel (hydrogen, methane, methanol, etc.), the reaction at the cathode is always the same: reduction of oxygen to either water or hydroxide:

What is the reaction at the anode in a hydrogen fuel cell? Assume basic conditions.

The major difference between a battery and a fuel cell is that the reactions in a fuel cell cannot be reversed, so it cannot be recharged. Instead, the fuel must be replenished

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Membrane Potential

Biological membranes have transport systems that facilitate the movement of some species more than others. For example, they tend to be relatively permeable to K+ but relatively impermeable to Na+ and Cl-.

Cells use energy to maintain a high internal concentration of K+ but, due to the permeable nature of cell membranes, some K+ will always leak out:

The free energy change associated with this process is:

Because the internal concentration of K+ is maintained to be higher than the external concentration of K+, this process has a negative Gm and is therefore spontaneous.

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Membrane Potential

Since the K+ ions are charged, an electochemical potential is established, and we get a relationship similar to the Nernst equation:

where z is the charge of the ion (+1 for K+)

As K+ travels through the membrane without the accompaniment of any anions to balance its charge, a charge imbalance builds up across the cell membrane. This generates an opposing potential called the transmembrane potential ():

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Membrane Potential

The transmembrane potential of most cells stays relatively constant. For example, [K+] inside a mammalian muscle cell is 155 mmol/L while [K+] outside the cell is 4 mmol/L, giving a transmembrane potential of -94 mV at 37 C (calculated using the formula on the previous page).

Neurons are an important exception to this rule. They transmit information by means of changes in the transmembrane potential. The transmembrane potential is normally about -90 mV for K+ (as for the muscle cell above); however, an external stimulus can cause ion channels to open, allowing some Na+ ions into the neuron and some K+ ions out. This increase in membrane permeability to those ions alters the transmembrane potential which can travel along the neuron until it reaches a synapse – where it stimulates the emission of neurotransmitters which stimulate opening of ion channels in the next neuron.

CHEMISTRY 2000 Topic #3: Thermochemistry and Electrochemistry – What Makes Reactions Go? Spring...

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