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Introduction
Figure 1: Lithium on the Periodic Chart. (Source)
Most of the products that I work on are powered by lithium batteries. Lithium batteries are popular today because they have excellent energy density but there are safety concerns with using them because there have been issues with battery fires. These fires have caused the shipping industry to impose special labeling and packaging information on their transport. I recently have needed to consider shipping batteries on airplanes, so I have been looking at the International Air Transport Association (IATA) shipment guidance for lithium-ion batteries. These rules require knowing the amount of total amount of lithium mass present in a lithium-ion battery. This is not a number that is easy to get from the manufacturers, though I do have a number from one vendor.
As usual, I started by googling for a way to estimate the amount of lithium in a battery. I soon came upon a formula used by FedEx (Figure 2).
Figure 2: FedEx Guideline for Calculating Lithium Content in a Lithium Battery. (Source)
I decided that I needed to derive this relationship to understand it, which is the topic of this post. For the rest of this post, I will be working with a single cell. This post will focus on the amount of lithium in a single cell; a battery is just a bunch of cells in a serial and parallel configuration.
Background
A Little Chemistry
There are many different lithium-ion chemistries. A common one uses lithium cobalt oxide and Equation 1 shows the chemical formula for this discharge reaction. Observe that 1 electron is transferred for each atom of lithium reacted.
| Eq. 1 |  |
Equation 1 tells us that one mole of lithium will product 1 mole of electrons.
Alternate Forms of This Relationship
I actually found a number of different relationships online. While their units were all different, they are based on the same principles. One assumption I have made is that the nominal lithium cell voltage is 3.3 V, which allows me to convert between Amp-hours (A-hr) and Watt-hours (W-hr).
| Eq. 2 |  |
| Eq. 3 |  |
| Eq. 4 |  |
Analysis
Derivation
Figure 2 shows how to derive Equations 2 through 4. I obtain the atomic mass of lithium from the periodic chart symbol shown in Figure 1.
Figure 2: Derivation of Lithium Content Rules of Thumb.
Example with Known Lithium Content
I know the lithium content of one battery. Figure 3 shows a comparison between an equation from Figure 3 and the real value. At least for this case, approximation and reality are within 10%.
Figure 3: Comparison of Formula Estimates with Actual Value.
Conclusion
I expect to be using the FedEx approximation in Figure 2 for some battery packaging design in the next few months.
Appendix A: Great Lithium-Ion Safety Infographic
Chemical & Engineering News has a done a superb job of summarizing the fire issues associated with Lithium-ion batteries (Figure 4). Please check out their website for the reference material used in creating it.
Figure 4: Lithium-Ion Battery Infographic. (Source)