Mole Day Fun: A Mole of Heartbeats

I have to disclose that the original idea for this activity was not mine. It was a question on a worksheet I inherited as a graduate teaching assistant about 20 years ago. If you do a Google search for “mole of heartbeats” you will get lots of results and lots of different ways to ask a related question, but I find this formulation to be especially effective.

Start with a class of students who have been introduced to the mole concept. They know Avogadro’s number and they can use it properly in conversions. Put them in pairs and then ask them this:

A mole of heartbeats most closely approximates which of the following:

The number of times your heart beats in one year.
The number of human heartbeats that occur in the United States in one year.
The number of human heartbeats that occur on Earth in one year.
The number of human heartbeats that have ever occurred on Earth.

Have them do calculations that justify their answer and refute the others. Let them whip out their cellphones and Google away! One of the great things about this exercise is that there are several different ways to go about it. Students will learn the scale of a mole and the value of using round numbers in “back of the envelope” type calculations. They’ll also learn a bit about human population growth.

The simplest way to do this calculation is find a good estimate for how many people have ever lived on Earth. Luckily, the folks at the Population Reference Bureau have done that for us. Their analysis is interesting and logical, but I find the number they report to have way too many significant figures, so I round it to 110,000,000,000. Yes that is 110 Billion.

After you get that figure, use a human lifespan and pulse rate, along with conversions of years to minutes and BOOM you have a number. I assume that all of those people lived to be 100 and that they all maintained a pulse rate of 100 bpm for their entire lives. Even with those crazy assumptions, the numbers show that there have only been 5.8 x10^20 human heartbeats in all of history! So, just under one millimole of heartbeats. In all of history!

I find this exercise more useful than calculating how long you would have to live to perform a mole of heartbeats, or how many people you would need to perform a mole of heartbeats, because neither of those numbers gives the kids a meaningful context of time to see just how long it would take.

I hope you like this activity and I’d love to hear more ideas on good Mole Day activities!

P.S. The above image of Amadeo Avogadro is public domain.