Cell Potential: The Nernst Equation - Video Tutorials & Practice Problems
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concept
The Reaction Quotient
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Now, before we can talk about cell potential and its connection to the nerd equation, it's important to revisit the idea of our reaction potion. Now recall that the reaction potion which uses the variable Q is a ratio of product reacting concentrations at a particular time. And we're gonna say it can be calculated by setting up an expression and ignoring solids and liquids. Remember like your equilibrium constant K, we only care about gaseous and aqueous aqueous species. Now how does this relate to electro chem? Well, we're gonna say here that for electrochemical cells, it helps to find the max potential at the exact moment. The cell circuit is connected because as we know over time, our voltage is gonna decrease as our battery as our electrochemical cell over all the grades, right? So this is where the reaction quotient comes into play. It helps us to find that exact moment in which our voltage is going to be at its highest.
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example
The Reaction Quotient Example
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Here, it says what is the reaction quotient for the fog redox reaction with the given concentrations? All right. So here we have lead two ion reacting with two moles of potassium solid to produce one mole of lead solid plus two moles of potassium ion. Here, we're going to say that the concentration of let two ion and potassium ion are given as these molarity. Now remember that your reaction quent cue can be solved by setting up its expression and Q equals products overreact its. Now remember with this expression, we ignore solids and liquids. So the solids we're going to ignore. So it basically becomes the concentration of K positive. And remember because there's a two here that becomes our exponent. So K positive squared divided by PB two plus. Here we plug in the values for each one. So potassium ion, it's 0.0015 which will be squared divided by 0.0880. When we punch this into our calculators, we get 2.6 times 10 to the negative five. So this represents the value for a reaction quotient Q
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concept
The Nernst Equation
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Now recall that our standard cell potential is calculated when ions in half cells have values of one molar, one atmosphere and a ph equal to seven. Now, the nerds equation is used to find the cell potential when ion concentration or concentrations do not equal one molar. So that's why we're gonna use our nerd equation because it's going to help us to calculate non-standard cell potentials. Now, here, the nerd equation formula is we're gonna say E cell E sub cell here represents our non-standard cell potential and it equals our standard cell potential which is E knot sub cell minus 0.05916 over N times log of QN equals the moles of electrons that are transferred between our species within our redox reaction. And Q is just our reaction quotient. So here this represents our N equation formula. Again, it helps us to determine our non-standard cell potentials when ion concentrations are not equal to one molar.
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example
The Nernst Equation Example
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Here, it says to calculate the cell potential for reaction at 25 °C. When given the following ionic concentrations and standard reduction potentials. Here, we're given the overall redox reaction as this. We were given the concentrations of our ions of Cobalt three ion and magnesium ions as one molar and 0.0033 molar respectively. In addition to this, we're given the standard reduction potentials in the form of these half reactions. Now notice they ask us to determine cell potential, not standard cell potential, there is a difference. So to find our non-standard cell potential, we use the nerds equation. So that's going to be cell potential, which is E sub cell equals standard cell potential, which is E not sub cll minus 0.05916 over N times log of Q. Here we're going to find out what cu was. First, remember Q equals products over reactants. It ignores solids and liquids. So here it would equal MG two plus cubed because of the three divided by co three plus squared because of the two. Here we plug in the value. So this is 0.0033 cubed divided by one molar squared here that gives me a Q of 3.5937 times 10 to the negative eight. Here, I'm not rounding until I get my final answer at the end. So we find out what Q is now, what do we have to find next? Uh Let's try to find out what, what N is N is the number of multiple electrons transferred. Remember the mole electrons have to match in both half reactions. This one here has three and this one here has two. Their lowest common multiple is six. OK. So it's six electrons that have been transferred. This would also explain our coefficients here. Those coal fishes came into play because we had to multiply this by two to give us six electrons. And we had to multiply this by three to give us six electrons here. This will be log of 3.5937 times 10 to the negative eight. Now remember multiplying your half reactions does nothing to our standard reduction potentials. They stay those numbers because those values are based on the identity of the elements being reduced, not on the amounts of them. OK. So I can multiply these by a million, these reduction potentials stay the same. So we found out almost everything. The only piece that's missing is our standard reduc is our standard cell potential. Remember standard cell potential which is ee knot sub cll equals cathode minus a node. Cato remember that's a sign of reduction. A node is a sign of oxidation. If we look at the overall redox reaction, that will help us determine what's been oxidized and what's been reduced. Cobalt three has an oxidation number of plus three because its charges plus three and it goes to zero, its oxidation number has been reduced. Therefore, it is, the cathode magnesium goes from zero to plus two, its oxidation ever increased. So it's been oxidized. So now we can do cathode minus a node. So that'd be cathode is 1.82 volts minus a minus 2.37 volts. Now remember a minus of a minus really means that we're adding them together. That comes out to 1.82 volts plus 2.37 volts. So that comes out to 4.19 volts. That'd be our standard cell potential. So now we do 4.19 volts minus 0.05916 divided by six times log of RQ value. When you punch this into your calculator, you'll go, you'll get back 4.26 volts. So this would represent our regular non-standard self potential. So that would be our final answer.
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Problem
Problem
If [Br–] = 0.010 M and [Al3+] = 0.022 M, predict whether the following reaction would proceed spontaneously as written at 25ºC:
Al (s) + Br2 (l) ⇌ Al3+ (aq) + Br– (aq)
Standard Reduction Potentials
Al3+ (aq) + 3 e– → Al (s) E°red = –1.66 V
Br2 (l) + 2 e– → Br– (aq) E°red = +1.09 V
A
2.90 V
B
2.60 V
C
3.03 V
D
2.75 V
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Problem
Problem
Determine [Fe2+] for the following galvanic cell at 25ºC if given [Sn2+] = 0.072 M, [Fe3+] = 0.0219 M, and [Sn4+] = 0.00345 M.