Breathe With Me

Breathe is a song by the Prodigy in which their vocalist Keith Flint calls upon us to "Breathe with me". Flint died in 2019, and this made me wonder, do I still breathe with him in a way?

Flint died at age 49. Assuming he breathed at the same rate as an average human, he took around 350 million breaths in his life1. The volume of a regular breath is about 500mL of air2, so Flint breathed 175 million litres of air overall, or about 215 tonnes3. Since the total mass of the atmosphere is \(5.15 \times 10^{18}\) kg, about one part in every \(2 \times 10^{13}\) parts of the atmosphere has been in Flint's lungs4.

In order to find out whether a breath of ours contains some part that has been in Flint's lungs, we need to see how many molecules of air we breathe. If its greater than \(2 \times 10^{13}\), we know that each breath contains at least one molecule of air that has been in Flint's lungs. We find that, with an average molar mass of 0.029 kg/mol, we breathe about \(10^{23}\) molecules of air per breath5, that's nearly 5 billion molecules that were once in Flint's lungs with every single breath we take.

This is wild. Each time you breathe, you are breathing air that has been breathed by every person that has ever lived. "Breathe with me," indeed.

Footnotes

1 According to Wikipedia, an adult typically breathes for about 12-15 breaths per minute. Children breathe more often, but also take smaller breaths, so I'm going to assume Flint breathed like an adult for his entire life. He lived for 18,065 days, so he breathed \(18,065 \times 24 \times 60 \times 13.5 \approx 3.5 \times 10^{8}\) times. ↩
3 Air weighs about 1.225 kg/m^3. So \(0.5 \times 351,183,600 \times 10^{6} \mathrm{L} \times 1.225 \mathrm{kg}/\mathrm{m}^3 \approx 215,100 \mathrm{kg}\). ↩
4 \(215,100/(5.15 \times 10^{18}) \approx 4.18 \times 10^{−14}\), which is the fraction of the atmosphere that has been in Flint's lungs. The reciprocal of that, \(1 / 4.18 \times 10^{-14} \approx 2.39 \times 10^{13}\) means "one in every \(2.39 \times 10^{13}\) atmospheric parts has been in Flint's lungs". This makes the perhaps unrealistic assumption that each breath is a totally new volume of air in our atmosphere. In reality our number will be lower, but not orders of magnitudes lower. ↩
5 Using a density of 1.225 kg/m^3, each breath weighs \(500 \mathrm{mL} \times 1.225 \mathrm{kg}/\mathrm{m}^3 = 0.0006125\mathrm{kg}\). So, each breath contains \(0.0006125 \mathrm{kg} / (0.0289652 \mathrm{kg}/\mathrm{mol}) \times \mathrm{avogadro} \approx 1.27 \times 10^{23}\) molecules. ↩
6 At sea level, air weighs 1.225kg/m^3 ↩