Cell Notation: Videos & Practice Problems

An electrochemical cell can be succinctly represented using cell notation, which outlines the redox reaction without the need for elaborate diagrams. The cell notation consists of phase boundaries, indicated by a single line, and a physical boundary, represented by two lines, separating the anode and cathode. The anode, where oxidation occurs, is the site where electrons are lost, while the cathode is where reduction takes place, gaining electrons. For instance, in a galvanic cell with a chromium anode and a copper cathode, the half-reactions are combined to yield the overall redox reaction. The cell notation follows the pattern of placing lower oxidation states at the ends and higher oxidation states in the middle, with the anode (A) and cathode (C) components separated by the physical boundary (B). This method provides a quick and efficient way to communicate the essential details of an electrochemical cell to others in the field.

Cell Notation

Now here we're going to say that our sub notation, also called our cell diagram, is a quicker method to describe the overall redox reaction in an electrochemical cell. Now here we're going to have two types of boundaries involved. We have our phase boundaries and then we have our physical boundaries. Our phase boundaries represent a solid line going up. Here we're going to say this is the condition where two phases of the same substance can coexist at equilibrium. Our physical boundary is shown as two solid lines going up. This is the physical space that separates the anode and the cathode of your electrochemical cell.

So when we're talking about a cell notation or cell diagram, we're referring to this portion here. Now, within this cell diagram or cell notation, we can plug in different elements, different types of ions, different types of compounds. So how exactly do we do that? Well, here, let's take a look at our electrochemical cell. In this electrochemical cell, we have the anode on the left and we have the cathode on the right. Here we're going to assume that we're dealing with a spontaneous electrochemical cell, otherwise known as the galvanic or voltaic cell. That means that our anode will be negatively charged and our cathode positive.

Remember, the anode is the site of oxidation and the cathode is a site of reduction. Remember oxidation? We're losing electrons, so electrons will be leaving. Here we have a chromium electrode. It'd be leaving and heading towards the cathode. The voltmeter would just register the amount of electricity being generated by the transferring of electrons from the anode to the cathode. Here we know that the copper electrode is gaining these electrons. Now if we think about this reaction in terms of half reactions, we're going to say here canceling out the intermediates gives the overall reaction.

Now in the cathode compartment, what's going on, we know reduction is occurring. If reduction is occurring, the electron is reacted. So if we look at the cathode compartment, we have Cu2+ ions and the copper neutral form. So here we have Cu2+. It will gain two electrons and that will create our Cu neutral form. In the anode compartment, more oxidation is occurring. With oxidation, remember electrons are products. We have the chromium electrode and the Cr2+ ions within the solution. So here we have Cr solid. This is solid here and this is aqueous here. So we have Cr solid being oxidized to give us Cr2+ aqueous, and here go the two electrons we're producing.

Over here are intermediates. Your electrons must always be intermediates and they have to be the same number: two electrons, two electrons, they cancel out. What's left at the end is our overall redox reaction. So that gives us Cu2+ aqueous plus Chromium solid gives us Cu solid plus Cr2+ aqueous. We have our half reactions. We cancel out the intermediates. Now we have our overall reaction.

Now we go to the cell notation portion. Remember the cell notation portion is a quick way of drawing or describing what's happening here in the electrochemical cell. You don't have time to draw this for another chemist, so you quickly write it down in cell notation form. Now memory tool: here cell notation is as easy as ABC. That's because we have a phase boundary here which is A. We have our physical boundary which is B. And here we have our next phase boundary which is C. A is for anode. So this portion here represents the anode compartment. B is the physical break, so the physical space between my two half-cell containers, and then C, you probably guessed it, is the cathode. So this portion represents the cathode.

Now when it comes to the cell notation, we'd say that the lower oxidation states or lower oxidation numbers will be found on the ends on both sides, and then the higher oxidation numbers will be found inside. With this information, we can write our cell notation here based on what's going on in this electrochemical cell. So in the anode compartment, we have chromium neutral and chromium 2+. Chromium neutral has an oxidation number of 0. Chromium 2+ has an oxidation number of 2+. So the lower oxidation number is on the end, so Cr solid, higher oxidation number in the center, Cr2+.

In the cathode compartment, over here, what are the two species interacting with each other that are the same substance? We have copper 2+ ion and just copper neutral. Their higher oxidation state is copper 2+, which would be in the interior and then copper solid here on the end. So basically this cell notation or cell diagram is equivalent to me drawing this entire electrochemical cell, at least in its basic design. Well, we're not talking about the ions in the salt bridge. We're just talking about, OK, we have an anode compartment, these are the species involved, we have our cathode compartment and then these are the species involved and how they interact with each other. So just from this information, we don't need to draw an entire electrochemical cell. So that's the beauty of our cell notation or cell diagram.

Cell Notation Example

Here it says consider an electrochemical cell where the following reaction takes place from this overall redox reaction. It asks what is the subnotation for this cell, or remember some notation. We're going to have a phase boundary, a physical boundary and another phase boundary. Some notation is easy as ABC, where A represents our anode, B is our physical break between both half cell compartments or containers, and C is our cathode.

Remember that our lower oxidation numbers are on the ends and then our higher oxidation states or numbers are in the interior or inside. So here if we take a look at our overall reaction, we have Sn2 going to Sn neutral. Its oxidation number goes from +2 to 0. Its oxidation number was reduced, therefore it represents the cathode. So here it d be in the cathode compartment. Which is this portion here?

Remember the higher oxidation state is on the interior, so that the Sn2+(aq), and then the lower one is on the end. So that'd be Sn. Solid aluminum goes from zero to +3. Its oxidation number went up, so it's been oxidized and therefore represents the anode. Again, the higher oxidation states on the interior, so Al3+(aq), and the lower oxidation state is on the end Al salt. So this here would represent our cell notation or cell diagram for the following electrochemical cell.

Write the half reactions as well as the overall net ionic equation for the following line notation: 
                     Fe (s) | Fe²⁺ (aq) || Mg²⁺ (aq) | Mg (s)

• A. Anode: Fe (s) → Fe²⁺ (aq) + 2e^-Cathode: Mg²⁺ (aq) + 2e^- → Mg (s)Overall: Fe (s) + Mg²⁺ (aq) → Fe²⁺ (aq) + Mg (s)
• B. Anode: Fe (s) → Fe²⁺ (aq) + 2e^-Cathode: Mg²⁺ (aq) + 2e^- → Mg (s)Overall: Fe²⁺ (aq) + Mg (s) → Fe (s) + Mg²⁺ (aq)
• C. Anode: Fe (s) → Fe²⁺ (aq) + 2e^-Cathode: Mg (s) → Mg²⁺ (aq) + 2e^-Overall: Fe (s) + Mg²⁺ (aq) → Fe²⁺ (aq) + Mg (s)
• D. Anode: Fe²⁺ (aq) + 2e^- → Fe (s)Cathode: Mg²⁺ (aq) + 2e^- → Mg (s)Overall: Fe (s) + Mg²⁺ (aq) → Fe²⁺ (aq) + Mg (s)

Answer: (A)

The cell notation for a redox reaction is given as the following at (T= 298 K). Calculate the cell potential for the reaction at 25ºC.
Zn (s) | Zn²⁺ (aq, 0.37 M) || Ni²⁺ (aq, 0.059 M) | Ni (s)
Standard Reduction Potentials
Zn²⁺ (aq) + 2 e^–  →. Zn (s)            E°_red = - 0.7621
Ni²⁺ (aq) + 2 e^–­  →  Ni (s)             E°_red = - 0.2300

• A. 0.3130 V
• B. 0.4033 V
• C. 0.5085 V
• D. 0.1199 V

Answer: (C)

What is the [Cu²⁺] for the following cell notation diagram if the cell potential is 0.4404 V?
Cu | Cu²⁺ (aq, ? M) || Ag⁺(aq, 0.50 M) | Ag
Standard Reduction Potentials
Cu²⁺ (aq) + 2 e^–  →. Cu (s)               E°_red = + 0.3394
Ag⁺ (aq) + e^–­  →  Ag (s)                    E°_red= + 0.8000

• A. 0.87 M
• B. 1.20 M
• C. 3.32 M
• D. 0.11 M

Answer: (B)

Here’s what students ask on this topic:

How do you write cell notation?

Writing cell notation involves representing the components of an electrochemical cell and the direction of electron flow. Here's how you do it:

1. Anode to Cathode: Write the anode (oxidation half-cell) on the left and the cathode (reduction half-cell) on the right. The vertical line, "|", represents a phase boundary, and the double vertical line, "||", represents the salt bridge or a porous membrane separating the two half-cells.
2. Anode Half-Cell: Start with the anode material (the solid electrode), followed by the phase boundary line. Next, write the anode's aqueous ions with their concentration in parentheses. If there's a solid and a gas involved, write the gas before the solid.
3. Cathode Half-Cell: After the double line for the salt bridge, write the cathode's aqueous ions and their concentration, followed by the phase boundary line, and then the cathode material (the solid electrode).
4. Electron Flow: Electrons flow from the anode to the cathode, but in cell notation, you don't explicitly write the direction of electron flow.

For example, for a cell with zinc and copper:

$\mathrm{Zn}\left(s\right)\left|{\mathrm{Zn}}^2\right(\mathrm{aq})||{\mathrm{Cu}}^2(\mathrm{aq}\left)\right|\mathrm{Cu}\left(s\right)$

How do you read cell notation?

Cell notation, also known as line notation, is a shorthand way to represent the components of an electrochemical cell. Here's how to read it:

1. Anode and Cathode: The anode (negative electrode where oxidation occurs) is written on the left, and the cathode (positive electrode where reduction occurs) is on the right.
2. Electrode Material: The material of the electrode is written first, typically a metal.
3. Ion Concentration: After the electrode material, the concentration of the ions in solution is given in parentheses.
4. Double Vertical Lines: These represent a salt bridge or a porous membrane, which separates the two half-cells.
5. Single Vertical Lines: These denote a phase boundary within a half-cell, such as between a solid electrode and an aqueous solution.

For example, in the cell notation:

$\mathrm{Zn}\left(s\right)\left|{\mathrm{Zn}}^{\mathrm{2+}}\right(\mathrm{aq},1M)||{\mathrm{Cu}}^{\mathrm{2+}}(\mathrm{aq},1M\left)\right|\mathrm{Cu}\left(s\right)$

Zinc is the anode, and copper is the cathode. The zinc electrode is solid, as denoted by (s), and it's in a 1M solution of Zn²⁺ ions. The double vertical lines indicate the separation between the anode and cathode half-cells, and the copper cathode is solid, as denoted by (s), and it's in a 1M solution of Cu²⁺ ions.

What is the correct line notation for the following voltaic cell?

To write the correct line notation for a voltaic cell, you'll need to know the specific details of the cell's components, such as the anode and cathode materials, and the electrolytes involved. However, I can give you a general format for a voltaic cell's line notation:

Anode | Anode Ion (Concentration) || Cathode Ion (Concentration) | Cathode

Here's how to break it down:

1. Start with the anode (the electrode where oxidation occurs) on the left.
2. Separate the anode material and its aqueous ions with a single line (|), which represents a phase boundary.
3. Use a double line (||) to represent the salt bridge or membrane that separates the two half-cells.
4. After the double line, list the cathode ion and its concentration.
5. End with the cathode material (the electrode where reduction occurs) on the right.

For example, if you have a zinc-copper voltaic cell with Zn as the anode and Cu as the cathode, and both are in solutions of their respective sulfates, the line notation would be:

$\mathrm{Zn}\left(s\right)\left|{\mathrm{Zn}}^{\mathrm{2+}}\right(\mathrm{aq})||{\mathrm{Cu}}^{\mathrm{2+}}(\mathrm{aq}\left)\right|\mathrm{Cu}\left(s\right)$

Remember to include the physical state of the materials (s for solid, aq for aqueous).