Oxford Biochemistry Interview: Atoms in Water

Lauren A. · Biochemistry (Oxford)

Hi, I'm Lauren, a fourth-year biochemist at Oxford University. When I applied in 2013 I was asked a range of questions, on everything from DNA bases and amino acids to genetic diseases. In this post I want to work through one of my favourites, because it shows how to handle a question that looks impossible the moment you hear it: how many hydrogen atoms are there in a glass of water?

The question that sounds unanswerable

At first this sounds absurd. You obviously can't count them, so how could you possibly answer? That reaction is exactly what the question is designed to provoke, and getting past it is half the test. This is an estimation question, sometimes called a Fermi problem, and the interviewer isn't looking for a precise figure. They want to see whether you can take something overwhelming and break it into a sequence of small, manageable steps. The best thing you can do is think aloud and tackle it one stage at a time.

Step one: estimate the volume of the glass

Start by estimating the size of the glass. A reasonable everyday glass might be around 750 cubic centimetres in volume. You won't be exact, and that genuinely doesn't matter, but state your assumption clearly so the interviewer can follow it, and step in if they want to. Naming a rough number confidently is far better than freezing because you don't know the "right" one.

Step two: turn volume into mass

Because the density of water is about 1 gram per cubic centimetre, 750 cubic centimetres of water has a mass of roughly 750 grams. This is a lovely step to say out loud, because it shows you know a useful fact about water and can use it to move from something you estimated, the volume, to something you can actually calculate with, the mass.

Step three: from mass to moles

Next, convert that mass to moles using the molecular weight of water, which is about 18 grams per mole. So 750 grams divided by 18 grams per mole gives roughly 42 moles of water. Moles are the bridge between the everyday scale of a glass and the atomic scale of individual particles, which is why this step is really the heart of the problem.

Step four: from moles to atoms

Now apply Avogadro's constant, about 6 times 10 to the 23 particles per mole, to turn moles of water molecules into a number of molecules. Then account for the fact that each water molecule contains two hydrogen atoms, so you multiply by two. Working it through, you land on an answer on the order of 5 times 10 to the 25 hydrogen atoms in the glass of water. That's how you estimate it, and notice the answer is an order of magnitude, not a precise count.

Why interviewers love estimation questions

Estimation questions are popular because they reveal how you think under uncertainty. There's no memorised answer to fall back on, so the interviewer sees your reasoning laid bare: your assumptions, the facts you reach for, and how you chain them together. What matters is:

• breaking a huge problem into small, ordered steps
• stating your assumptions openly rather than agonising over precision
• leaning on a few reliable anchors, here the density and molar mass of water and Avogadro's constant
• getting the method and the order of magnitude right, not the exact number

Common mistakes to avoid

The classic errors are all avoidable. Freezing because you can't recall an exact volume, when a sensible estimate is all that's wanted. Hiding your assumptions instead of saying them out loud. Forgetting a step, such as multiplying by the two hydrogens per water molecule. And going silent while you calculate, when the interviewer needs to hear the working to help you.

Final thoughts

Practise Fermi-style questions until breaking a big number into steps feels natural, keep a few anchors in mind like the density and molar mass of water and Avogadro's constant, and always tidy your final answer so it's clean and easy to interpret. If you'd like support preparing for an Oxford Biochemistry interview, Oxbridge Solution can help.