Electrochemistry Part 2: Getting quantitative and looking at electrochemical cells in action Everything we want to learn in the way of quantitative information about electrochemistry can be found in the familiar diagram below: • The e- e- e- e- is the amount of charge, q, and can be related to mass through a simple stoichiometry problem • The potential hill, E, is the value on your battery—it depends on the half cell potentials and the concentrations • Thermodynamic values like w and DG are realized from q times E. −−−−−eeeee These three general categories of calculations are examined in order on the following pages: E(V) (this is the voltage (V) difference measured by a voltmeter) This is the number of charges, as per unit time, the current. 1. For electrochemistry to do much work, the size of the hill (V) and the amount of charge (q) both need to be large. 2. Oh, this must mean work= w= qVEverything you wanted to know about measuring charge: basic stuff they should have told you in your high school physics class Electrical Charge. The fundamental unit of charge, q, is measured in Coulombs. One electron has a charge of 1.602 x 10-19 Coulombs (C). Therefore, one mole of electrons has a special amount of charge F= Faraday (Coulombs/mole) = q (Coulombs) / n (moles) F = 9.649 x 104 C/mole So q = nF So electrons are our currency for electrochemical measurements in the same way that protons were our currency for acid/base reactions. A Faraday is simply an amount of charge in the same way a dozen is an amount of eggs and we can do routine stoichiometry calculations with this charge to mole conversion factor. Example: In a redox reaction involving the reduction of Fe+++ to Fe++, a total of 9.649 x 103 C are used up. How much Fe+++ was reduced? 1mole Fe+3 1mole Fe+2 55.85g (9.649 x 103C)(⎯⎯⎯⎯⎯⎯⎯ ) ( ⎯⎯⎯⎯ ) ( ⎯⎯⎯⎯ ) = 5.585g Fe+3 9.65 x 104C/mol 1mole Fe+3 1mole Fe+2 Note that for this reaction, a single electron is transferred from the Fe+2 to the Fe+3. This is analogous to a single H+ transfer in a monoprotic acid.Adding time to the equation and get CURRENT. The measure of current as a function of time is the ampere: One Ampere = one Coulomb/second Having current measured as a function of time means we can talk about a rate of reaction (kinetics stuff, something we haven’t considered since we started equilibrium.) Example: What is the current measured in a circuit involving the half cell reaction Sn+4 + 2e- ⇔ Sn+2 which is occurring at a rate of 4.2 x 10-3 mole/hr? 1hr 2 mole e- 9.65 x 104C i = (4.24 x 10-3mole/hr) (⎯⎯⎯)(⎯⎯⎯⎯⎯)(⎯⎯⎯⎯⎯) = 0.227A 3600s 1 mole Sn+4 mole e- By the way, what do you think about this magnitude of current? Will it kill you? Will it power a small city or a small toy? I’d say, that’s a pretty nasty shock—right at the edge of where a DC voltage can kill you.Standard Potentials. You will recall from our brief detour into physics that you need the difference between TWO potentials to do work. A single half cell reaction is only a figment of your imagination (or an incorrect answer on an exam.) The only value of interest to interest to us is this difference, this CHANGE IN POTENTIAL. Now here is the problem, do you know how many half cell reactions there are in the world? Well a lot, since every chemical reaction can be described as an oxidation or reduction. So what do we do? We create a STANDARD REFERENCE POTENTIAL (Eo) to which we arbitrarily assign a number. Then all the other half cell reactions can be compared to the reference and through that reference, to each other. Let’s let our STANDARD REFERENCE POTENTIAL for a half cell reaction be equal to 0 V, so we can do the math in our head. Now, let’s choose a half cell to be our reference AGAINST WHICH ALL OTHERS THINGS ARE MEASURED!!! Let’s choose THE STANDARD HYDROGEN ELECTRODE (SHE). E1/2o = 0 assigned to 1/2 H2(gas, PH2 = 1) ⇔ H+(1M, ie.pH = 0) + e- Now looking at this half cell, it doesn’t seem to have a lot going for it. To build one you need to have a gas bulb filled with an explosive gas, AND a solution that is at pH = 0. But we don’t get to pick, it was already chosen for us. Fortunately we don’t have to use this half cell in the lab, we just use it to make the table of standard half cell reactions. In the lab we will use something else as a reference cell, like a STANDARD CALOMEL ELECTRODE (SCE) and we will simply note the difference between the SCE and the SHE when we do our calculations.TABLES OF STANDARD HALF CELL REACTIONS. Let’s go in the lab, pull out a standard hydrogen electrode, and hook it up in a cell like the one below. Now let’s hook up all the half cell reactions in the world and obtain standard reference potentials ( Eo)—in the case above we started with a zinc solution that was lying around. But a couple of things to consider before we get too far along…. First, electrochemistry is just thermodynamics, and you may recall from thermodynamics that things like concentration and temperature matter, so we need some standard concentrations and a standard temperature so that our electrochemistry friends can pitch in and help. How about we choose the following standard conditions: • all reactants and products must be at 1 atm or 1M• a standard temperature like 298K. Reduction potentials: One more thing. We need to either write our half reactions as either oxidations or reductions. (We can’t switch back and forth or we get our signs mixed up.) Now this may seem no big deal to you, but it sure was worth fighting over among electrochemists. For example, famous UT electrochemists like Al Bard and former Presidernt Larry Faulkner were big on writing everything as an oxidation half reaction. But they lost the This means the electrons will appear on the left side of the equation. Anyway, here it is, our very abbreviated table: Notice in my small table that the SHE sits pretty much in the middle of things. Half of the reactions when written as reductions are spontaneous (Eo is positive) and half are not spontaneous (Eo is negative).There is a much bigger collection of standard reduction potentials half reactions in the appendix of your text. Spend
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