### Richard A. Paselk

Chem 110

General Chemistry

Summer 2006

Lecture Notes::Lec 8_8 June

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# Keq and Temperature

In Chem 109 we used le Chatelier's Principle to predict the effects of changes in temperature on reaction equilibria. Thus, for example, for an exothermic reaction, if T increases heat must have been added, therefore the reaction will use up some of the extra heat, driving the reaction to the left and lowering the temperature back toward its original value. With our new thermodynamic knowledge we can determine this relationship quantitatively.

deltaG° = - RT ln K

and

deltaG° = deltaH° -Tdelta

Substituting we can say

- RT ln K = deltaH° -Tdelta

dividing by - RT:

ln K = (-deltaH°/R)(1/T) + deltaS°/R

Assuming deltaH° and deltaS° are constants (a reasonable approximation if deltaT is not large) this is now in the form of the equation of a straight line:

y = ax + b where ln K and 1/T are variables.

Plotting:

So we can find both deltaH and deltaS (as seen in the lab).

We can also find these values non-graphically by looking at a system at two different temperatures and doing a bit of algebra:

ln K1 = (-deltaH°/R)(1/T1) + deltaS°/R)

ln K2 = (-deltaH°/R)(1/T2) + deltaS°/R

Subtracting (2) from (1) we get:

ln K1 - ln K2= (-deltaH°/R)(1/T1) + deltaS°/R -[(-deltaH°/R)(1/T2) + deltaS°/R]

ln K1 - ln K2 = (-deltaH°/R)(1/T1-1/T2)

And using log rules:

ln (K1/K2) = (-deltaH°/R)(1/T1-1/T2)

the van't Hoff Equation

Another common form of the van't Hoff Equation is:

ln (K1/K2) = (deltaH°/R)[(T1-T2)/(T1)(T2)]

# Free Energy and Work

Reversible vs. irreversible processes. In order for a process to be completely efficient we say it must be reversible - that is we can get back to the starting point without energy loss. At the microscopic level (atoms and molecules or smaller) processes are frequently reversible. However at the macroscopic level there are inevitably heat losses due to friction etc.

For real processes a further complication arises in that the only energy available is the Free Energy, so we measure the efficiency of a process by how much of the free energy (deltaG) is captured.

As state above, in real processes some energy is lost to the environment as heat. Folks often lament this loss because it appears to be wasted - wouldn't it be better to capture all the deltaG to do work? If so why hasn't nature done so? After all life on Earth has had somewhere around 3.5 x 109 years to get it right, and glycolysis still "wastes" about 40% of the available deltaG. Why? Unfortunately in order to capture the maximum amount of deltaG we have to accomplish things in very small equilibrium steps. Very highly simplified, if you're very efficient, its hard to generate enough working energy, and you get eaten! For human designed processes you have to be somewhat inefficient to get anything done during your lifetime.

So like many things we have to compromise and try to optimize the process between speed and completion versus efficiency. The challenge is to reach this optimum, which generally changes with circumstance -life's tough!

# Introduction to Electrochemistry

Why do we care? Examples of electrochemistry all around us (batteries, plating, corrosion, fuel cells, manufacture etc.)

Electrochemistry is the interchange of electrical and chemical energy.

First let's review Redox chemistry.

Terms: Look briefly at some terms used in redox/electrochemistry.

• Oxidation: electrons are removed (note oxidation is what oxygen does).
• Reduction: electrons are gained (reduce ores to metals).
• Oxidizing agent/oxidant: takes electrons in reaction (acts like oxygen).
• Reducing agent/reductant: provides electrons in chemical reaction.

Note that in any chemical redox reaction that oxidation and reduction are always coupled getting an exchange of status:

oxidant1 + reductant1 reductant2 + oxidant2

Balancing Half-Reactions. In electrochemistry we separate a redox reaction physically into half-reactions. Thus we need to be able to separate a redox reaction into half-reactions and to balance them, as we did in Chem 109. So let's review redox balancing by the half-reaction method. In the half-reaction method what we do is first break an equation into two parts and then balance the parts individually. We will just review the method for reactions in acid solution. But remember the same method works for basic solutions as well with a few additional steps.

Presented step wise for Acid Solution:

• Separate the reaction into two half-reactions.
• Balance each half-reaction separately:
1. Balance atoms other than O & H by inspection.
2. Balance O by adding H2O to the opposite side.
3. Balance H by adding H+ as appropriate.
4. Balance the charge by adding electrons (e-) - add to same side as excess of positive charge, or opposite side if excess negative charge.
5. Balance the charges of the two half-reactions by multiplying appropriately.
• Cancel items appearing on both sides.

Example. Balance the following equation as it occurs in acid solution:

MnO4- + Cl- Mn2+ + Cl2

First break the equation into two half reactions, one for Mn and one for Cl, then follow the steps above for each:

 MnO4- Mn2+ MnO4- Mn2+ MnO4- Mn2+ + 4 H2O 8 H+ + MnO4- Mn2+ + 4 H2O 5 e- + 8 H+ + MnO4- Mn2+ + 4 H2O 10 e- + 16 H+ + 2 MnO8- 2 Mn2+ + 8 H2O Cl- Cl2 2 Cl- Cl2 ... ... 2 Cl- Cl2 + 2 e- 10 Cl- 5 Cl2 + 10 e-

Finally, combine half reactions and cancel terms:

10 e- + 16 H+ + 2 MnO4- + 10 Cl- 2 Mn2+ + 8 H2O + 5 Cl2 + 10 e-

16 H+ + 2 MnO4- + 10 Cl- 2 Mn2+ + 8 H2O + 5 Cl2

Consider a simple Redox system consisting of a beaker full of copper sulfate and a zinc strip as an example:

When we place the zinc strip into the Cu2+ solution we will observe a gradual darkening of the zinc strip while the solution gradually goes from light blue to colorless. (you may recall doing this this reaction in the Ionic Reactions lab in Chem 109).

So what's going on?

• The loss of the blue color indicates that the Cu2+ is being lost from the solution, being converted to Cu metal.
• Of course something must replace the Cu2+ and its charge. There are no bubbles or other indications of solution reactions, so the most likely reactant is the zinc going to Zn2+.
• This is reinforced by the appearance of the black coating on the zinc strip where it contacts the solution. Since finely divided metals in general are black, this coating is apparently the deposited copper metal, picking up electrons from zinc as it is oxidized on the surface.
• Thus we postulate the following reactions to explain the phenomena:

Cu2+ + 2 e- Cu

Zn Zn2+ + 2 e-

Cu2+ + Zn Zn2+ + Cu

# Galvanic Cells

What we'd really like to do is capture the energy of this redox reaction as a flow of electrons. After all our half-reactions tell us electrons are being exchanged. So how do we do this? We can separate the reaction into its two half-reactions by putting the components of each half reaction into its own container. We then have:

1. A beaker filled with Zn2+ (for example, 1 M zinc sulfate solution) with a zinc strip immersed in the solution.
2. A beaker filled with Cu2+ (for example, 1 M copper sulfate solution) with a copper strip immersed in the solution.

If we now connect the two metal strips in our set-up with a wire with a meter on it what will occur?

Before we go further, we need to understand the units and instruments for measuring electricity. These are discussed in the box below.

 Measuring electricity Electrical units. There are four different units we need to be familiar with: Volt (J/C) - This is the unit of electrical potential difference. It is analogous to height in a gravitational field. It is the potential difference needed for the flow of one coulomb (C) of charge to produce one joule (J) of work. Coulomb (C = As) - This is the unit of electrical charge. There are 9.65 x 104 coulombs (one Faraday's constant) in one mole of electrons. Ampere (amp, A) - This is the unit of electrical current. It is the SI base unit for electricity (all other electrical units may be constructed from the amp and other SI base units). An amp is equal to the flow of one coulomb of electrons in one second. Ohm (W) - This is the unit of electrical resistance. It is defined as the amount of resistance which will require one volt of potential to give a current of one amp. Measuring devices. Electrical "meters" are commonly used to measure volts and amps. The difficulty in measuring voltage is that any flow of current during the measurement process will lower the voltage! Since the common mechanical meter (a D'Arsonval meter) relies on the production of a force due to a flow of current though a coil in a magnetic field, they generally do not give a high accuracy measurement. The quality of such meters is commonly given as xxx W/V, since the greater the resistance the lower the current flow and thus the more accurate the meter. For much of the past century or so the best voltages were thus measured with a potentiometer and null meter arrangement in which measurements were made under conditions where no current flows. These devices give very precise voltages, but are inconvenient and require trained users. Fortunately, modern electronics have enabled the creation of volt meters based on solid state devices (such as FETs) that have input resistances of millions of ohms and greater. Digital meters can thus give very accurate voltages with virtually no current loss.
Let's go back to our two containers each with its own half-reaction and connect them with a wire. What happens? If we watch very carefully with a sensitive current meter we should see a pulse of electricity followed by a return to zero.

Why does the current not continue? The problem is that the charges in the two beakers quickly build up until the free energy of the redox reaction is not sufficient to over come the work needed to move the charges against the potential gradients.

So what can we do to allow the flow of electrons to continue? We need to connect the solutions in the beakers so that the charges can be neutralized with a counter flow of ions. The connecting ionic fluid is referred to as a salt-bridge, as seen in the figure. Other arrangements are possible such as semi-permeable membranes etc. Such an arrangement is called a Galvanic cell.

Galvanic cells (or Voltaic cells) are cells in which the overall redox reactions occur spontaneously (equilibrium favors products) as written. They can serve as a source of electric power (as a battery).

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