A Chemistry Puzzle

In this month’s blog posting, I thought I would pose a question that I (and many other Oxbridge applicants) faced in our interviews. But before posing the question to you, I thought I would introduce why this question is so important.

When applying to do Natural Sciences at Cambridge or Biochemistry at Oxford, many students already have a keen idea about what particular area of science interests them most. Especially among the Natural Sciences applicants, there is a pretty clear split between the biologists at one end and the physicists at the other. However, one A-level nearly all these students share in common is Chemistry. Given that their main interest often lies outside the focus of Chemistry, this doesn’t mean that the interviewers will not touch upon the subject – in fact, quite the opposite! Given that it is an A-level shared by nearly all applicants, whom are being compared against each other in the competition to gain a place at the college, posing some chemistry questions in the interview is a good way to compare directly nearly all the students, regardless of whether they are leaning more towards the biological or physical sciences.

As such, the question I shall pose below was one given to all Natural Sciences applicants the year I replied. Not only did it test simple AS-level Chemistry knowledge, but it also allows the applicant a chance to demonstrate their ability to tackle an unusual question and show clearly their thought process in generating a clear and easy to follow solution to the problem.

The Question

So the question! Imagine yourself across a table from your interviewer who you have just sat down with. After some initial pleasantries, your interviewer offers you a glass of water which he pushes in front of you:

As you reach to take a sip, the interviewer stops you and asks “Before you take a drink, please calculate for me the number of hydrogen atoms that are in the water inside the glass.”

Now, when posed with such an unusual question, always remember Occam’s Razor – the simplest solution is usually the correct one. The first thing to do is determine how much water you have. You can either ask, approximate or (my preferred approach) use algebra. As such, let us say we have x millilitres of water.

Given that this is a chemistry question, its a good guess that we should be trying to figure out how many moles of water we have. To do this, it is easiest to convert the volume of water that we have into grams. Hopefully from your GCSE years you will remember that pure water has a density of 1gram/ml meaning that x millilitres is equal to x grams. Then, as we know that the molecular weight of water is 18 (oxygen = 16, two hydrogens = 2), then we know that the number of moles of water is [x/18].

So, knowing that we have [x/18] moles of water, how do we figure out how many hydrogen atoms are present? First, we should work out how many water molecules there are. Given we know the number of moles, if we multiply this by the 

Avogadro constant (A) (which is defined as the number of constituent particles in one mole of a given substance), we will work out the number of water molecules:

Number of water molecules: A[x/18]

As we know that for every molecule of water, there are two hydrogen atoms, the final answer will be:

Number of hydrogen atoms: 2A[x/18]

The Principle

Having completed this puzzle successfully, you can now take a well deserved sip of that water! The science knowledge required for this problem is quite basic, nothing beyond AS-level. However, the unusual presentation of the problem, combined with the pressure of an interview situation, can make this quite a challenging question to many interviewees and can leave them rather flustered! What is most important is to take your time to structure you answer clearly and logically. Do ask for a minute before responding if you need a little time to compose your thoughts (or remember your mole equations!). If you ever do get stuck, the trick is not to panic and start rambling, but voice to the interviewer that you are unsure of a certain step and explain what you think the solution might be. This shows the interviewer that when you face a problem, you remain ‘teachable’ and undaunted by a challenge!

This question comes in various flavours (how many molecules in a watermelon, how many atoms in an elephant), but the principle remains the same for all of them! Do practise some more on your own – its revision time well spent!