Вплив концентрації на електричний потенціал

Let's say we want to construct a voltaic cell. What happens if each electrode is the same metal? Your immediate reaction might be, "that's a stupid question! It wouldn't do anything!" When we started studying redox reactions, we talked about what causes current. Do you remember? It's the difference between the cathode's and anode's potential energies. Different metals have different potentials. But, the same metal should have the same potential. What if there was a way to create a potential difference?

Do you remember the units for voltage? It's joules per coulomb. That's energy per unit charge. Could we create a charge difference between the two half-cells? But how?! Remember, each half-cell contains the electrode and the ion solution. What if our solutions were different concentrations? The lower concentration half-cell would have fewer ions. So, it has less charge. We would expect the voltages to be different. Voltaic cells made from the same electrode but different ion concentrations are concentration cells.

Standard Reduction Potential of a Concentration Cell

What's the standard reduction potential of a concentration cell? It's zero. Why? Because both electrodes are under standard conditions. What's the concentration for each half-cell? One molar! So, there is no concentration gradient!

To prove the point, let's do the calculation. Let's say we made a concentration cell with two zinc electrodes. What's the cell's standard electrode potential?

First, let's write the half-reactions.

$Zn^{2+}+ 2e^{-} \rightarrow Zn_{(s)} \,E^{o}=-0.76V$

$Zn^{2+}+ 2e^{-} \rightarrow Zn_{(s)} \,E^{o}=-0.76V$

Now, we can plug the values into our cell potential equation.

$E_{cell}^{o}=E_{cathode}^{o}-E_{anode}^{o}=-0.76-(-0.76)=0$

We see that the standard cell potential is zero. So, nothing happens. What tool do we have that uses concentration difference? The Nernst equation! We learned it when we studied electric potential under non-standard conditions.

Nernst Equation and Concentration Cells

A concentration cell is still a redox reaction. But, which half-cell is the anode and cathode? Oxidation will always occur in the cell with the lower ion concentration. Why? The two cells want to be in equilibrium. We reach equilibrium when the concentrations are equal. So, the solid metal needs to enter the aqueous phase by losing electrons. That will increase the ion concentration. The dilute solution is the anode. That means the cathode is the concentrated solution. It needs to lower its concentration. So, its ions precipitate.

So how would we write the half-reactions? Let's use zinc as our example again.

$Anode:\,Zn_{(s)} \rightarrow Zn_{dilute}^{2+}+ 2e^{-}$

$Cathode:\,Zn_{concentrated}^{2+}+ 2e^{-} \rightarrow Zn_{(s)}$

How does the Nernst equation help us with concentration cells? Let's look at the equation.

$E=E^{o} - \frac{2.303RT}{nF}\log{(Q)}$

Remember, we can simplify the equation more when our temperature is $298.15K$.

$E=E^{o} - \frac{0.0592}{n}\log{(Q)}\, when\, T=298.15K$

Each form of the equation has the reaction quotient. Remember we write it, $Q=\frac{[Products]}{[Reactants]}$. But which is the product or the reactant? Let's look at the half-reactions. The anode is producing ions. So, the dilute concentration is the product. The cathode is consuming ions. So, the concentrated solution is the reactant.

Let's consider a zinc concentration cell. Let's say our starting concentrations were 0.25M and 0.10M. What is the voltage at $298.15K$?

$E=E^{o} - \frac{0.0592}{n}\log{(Q)}= 0.0V-\frac{0.0592}{2}\log{(\frac{0.10}{0.25})}=0.0V-(0.0298\times-.398)=0.012V$

What happens if we have a more significant difference in concentration? Let's say our concentrations were 0.50M and $1\times10^{-3}M$.

$E=E^{o} - \frac{0.0592}{n}\log{(Q)}= 0.0V-\frac{0.0592}{2}\log{(\frac{1\times10^{-3}}{0.50})}=0.0V-(0.0298\times-2.70)=.080V$

We see that a more extensive concentration difference generates a higher voltage. But, how do the voltages compare to other voltaic cells we've seen. In both cases, the voltages are minuscule! So, a concentration gradient creates only a minimal voltage.

Applications of Concentration Cells

You might be wondering, "what's the point of a concentration cell?" The voltages are so low that they're unhelpful for batteries. But you already know of a concentration cell. When we studied acids and bases, we learned about pH. How do we measure pH? With a pH meter! A pH meter is a type of concentration cell.

How does a pH meter work? Both the electrodes have a chloride ion solution. One of the electrodes is glass. What happens when the glass electrode enters an acidic solution? There is an electrostatic interaction between the hydrogen ion and chloride ions. The electrostatic interactions change the potential energy. A voltmeter measures the change in potential between the electrodes. The meter's computer component converts the voltage change to a pH.

(Video) 19.5b Concentration Cells | General Chemistry

by Chad's Prep

In this video, Chad talks about concentration cells. He starts by describing how concentration cells work. Then, you'll learn how to apply the Nernst equation to them. Finally, Chad walks you through an example problem. This video is an excellent explanation of concentration cells!