Ask Dr. Universe: Use stoichiometry to count the atoms in a leaf

Washington State University

Dr. Universe: How many atoms are in a leaf? – Lily, 8, Georgia

Dear Lily,

I love thinking about things I can’t see with just my eyes. Like the atoms that make up everything.

I asked my friend Fred Gittes how to figure out the number of atoms in a leaf. He’s a physicist at Washington State University.

He showed me a worksheet he gives his students. It included a question exactly like yours!

“It’s a question I assign college students for fun,” Gittes said.

So, you’re in great company when you ponder big questions like this.

We decided to use stoichiometry to find the answer. That’s a kind of math that scientists do to understand chemical reactions.

To get started, I picked an oak leaf off a tree in my yard. It weighed 0.95 grams.

Then I called my friend Henry Adams. He’s a tree scientist at Washington State University.

He told me how much of each element make up the average plant.

It turns out a plant is mostly carbon, oxygen and hydrogen. It contains some nitrogen, potassium, calcium, magnesium, phosphorous, sulfur and silicon, too. Together, that’s 99.6% of a plant.

Then it was math time.

First, I multiplied the weight of the leaf by the percentage of each element. That told me how many grams of each element we have in our leaf.

Next, I pulled out a periodic table. That’s a chart of all the elements we know about. It usually shows a number for each element–called atomic weight or molar mass. One thing that number tells us is how many grams there are in one mole of that element.

A mole is a non-numerical number–like a dozen. When you order a dozen donuts, everyone knows you mean exactly 12 donuts. If you order a mole of donuts, scientists know you mean exactly 602,214,076,000,000,000,000,000 donuts.

You’ll probably need to call ahead to order that many.

Scientists use moles when they’re working with super tiny things–like atoms.

To figure out how many moles of each element were in my leaf, I divided the weight of each element by the number from the periodic table.

Then, I multiplied the moles of each element in our leaf by 602,214,076,000,000,000,000. Remember that’s the number of things in one mole. For us, those “things” are atoms. That number is also called Avogadro’s number.

That told me how many atoms of each element we have in our leaf.

I repeated all those steps for each element. Finally, I added together the number of atoms for each element. That told me the total number of atoms in our leaf. I got 72,530,943,200,000,000,000,000 atoms. That’s about 72 sextillion atoms.

That’s a low estimate. We only looked at 99.6% of the elements in a plant. Plus, we’re guessing that our oak leaf exactly matches an average plant.

We could send our leaf to a lab for elemental analysis. That would tell us the exact amount of each element so our math would be precise.

If you do that and wind up with exact numbers, let me atom. I just love real-life word problems.

Sincerely,

Dr. Universe

Adults can help kids submit a question at askdruniverse.wsu.edu/ask.