We are always hearing about the superiority of East Asian students in mathematics and accumulating evidence shows this is not just a stereotype. Shanghai topped the PISA ratings back in 2013, with the UK coming 26th. Earlier this year, the BBC reported that Asian students had once again trounced their global competitors, with Singapore, South Korea and Taiwan taking the top 3 spots. Vietnam was ranked 12th, ahead of the UK in 20th place. (Should we be proud of jumping up 6 places in the intervening years? It might be comparing apples with oranges.) I’m always sceptical of such comparisons, in terms of both validity and value. I hasten to add that I mean I’m sceptical because I have not yet familiarised myself with the nitty gritty of how the studies are conducted. However, my recent experience of a chemistry question from a Vietnamese text book has shown me there just might be something in these claims.

I was having a particularly egregious Monday when one of my students innocently asked me how to complete a question from his Vietnamese text book. I’m not willing to disclose the actual number of hours it took me, but suffice it to say that the remaining 10 minutes of the lesson did not suffice to find the answer.

Now obviously I blame the egregiosity of the week’s commencement for the fact not only that it took me so long to do, but also that for about half that time I hadn’t realised that I’d already found the right answer. Looking back, the question was loaded with flashing beacons, all brazenly hinting at the solution. Anyway, without further ado, here is the question:

Based on observations in the laboratory, a student writes the following unbalanced equation to describe the reduction of an unidentified metal oxide.

R_{x}O_{y} + CO --> R + CO_{2}

The mass of the metal oxide is 8g and the volume of carbon monoxide that reacts is 3.36dm^{3} (at STP, ie: molar volume = 22.4 dm^{3} mol ^{-1})

All of the resulting metal is then reacted with hydrochloric acid in a second reaction, according to the following equation:

2R +2nHCl --> 2RCln + nH_{2}

The volume of HCl reacted is 200cm^{3}, and the concentration is 1 mol dm^{-3}.

Identify the metal R.

Flashing beacon number 1 is that the classic metal to undergo reduction by carbon monoxide is iron, which turns out to be the answer. If the question is phrased *show that R is iron*, it doesn’t become that much easier. In fact, for me it made it much harder because I inadvertently confused two of the relevant equations.

I was very impressed by the thinking the question demanded about gases. Given a volume of gas in a question about moles, the obvious thing to do is divide it by molar volume to deduce the number of moles. I have not experienced a question in the UK syllabus that requires students to do what I found necessary in this case, which is to convert the subsequent amount of substance (n) into a mass of carbon monoxide. A key misconception, not only from scientific history but also in the modern day science class, is that gases have no mass. Based on that misconception, how counter-intuitive to realise that calculating the mass of carbon monoxide gives the total mass of reactants, from which the mass of metal produced can be determined.

The next thing that wasn’t immediately obvious was that the coefficients for carbon monoxide and carbon dioxide must be equal. I can’t really put into words what I mean about this, but it puts me in mind of the great pioneers of modern day chemistry, Antoine Lavoisier and his contemporaries. Nowadays we know all about moles, masses, coefficients and amounts of substance, but all of this grew out of their early findings. Now we can take for granted that if we know the balanced equation, we can use the mass of one species to determine the theoretical masses of all the others. But Lavoisier and his peers did not have that luxury. These constrictions forced them to conceive imaginative experiments, such as the one in which the burning reactant consumed exactly one fifth of the gas in the sealed jar, showing that a fifth of air is oxygen by volume. At any rate, with no other carbon-containing species in the reactants or products, the number of moles of each must be identical, which unlocks the masses of each product. This in turn points to flashing beacon number 2. The mass of metal is 5.6g, exactly a factor of 10 smaller than the relative mass of iron.

Then came the fatal slip up. I trialled values of N in equation 2 from 1 to 4 to see what numbers came up. If N = 2 then the molar mass of the metal comes out at 56gmol^{-1} – flashing beacon number 3. Unfortunately, I fluffed the check. A great strength of the human brain is its ability to automate. We drive from the neck downwards, carefully indicating turns, checking mirrors, braking and accelerating as necessary, only very rarely diverting our incessant stream of consciousness into the conscious decision-making process. So familiar was I with a related equation of the process of iron reduction that I mistakenly checked my answers according to this incorrect equation:

2Fe_{2}O_{3} + 3C --> 4Fe + 3CO_{2}.

After messing around with other values of N and then checking all my other deductions and calculations, I got thoroughly stressed. My department head gave me the sensible advice to go home, during which cycle ride the answer came to me.

Educationally speaking, this question really demands a strong understanding of chemistry and simply cannot be solved with formulaic approaches. In the UK, questions are broken down into steps, which guide students through the process of determining the amount of substance for one species, using the ratio of coefficients to determine the amount of substance of another species, and then converting that value of n into a mass or volume. However, this question demands the application of chemical knowledge to what I would consider a higher level than has typified AS questions in recent years. Unofficial data in support of this view was provided by one of the student’s classmates. She was determined to solve it by herself but was yet to achieve it by the end of the class. The next week I asked her how she’d got on with it. Not only could she not answer it, but neither could the A2 students that she’d asked in the year above her.

My frustration mellowed into inspiration. Having cracked the beast, I set out to write some questions of my own with which to challenge the student. The result was my

*Putting the Me in Moles*activity, in which students answer questions about the numbers of atoms of each different elements in their own bodies. I was able to write questions that were challenging, but I just didn’t feel they matched the elegance of the Vietnamese problem. Although this charming question caused a not inconsiderable amount of frustration, ultimately I’m very glad to have discovered it.

We have been warned that AS chemistry is going to be 20% more mathematical than its predecessors, so I am planning to generate a collection of head-scratchers. The above question is obviously the first addition, closely followed by the

*Putting the Me in Moles*activity. But just as I’ve been writing this, I got waylaid for another few hours finding an answer to a question I thought of myself. I think maths aficionados will find it suitably challenging….

*By how much would the atomic radii of the relevant elements have to expand in order for a fingernail to grow large enough to cover the surface of the earth?*

If you know any tricky questions, feel free to leave them in the comments section. Meanwhile, subscribe to rhymingchemist.com for updates on new questions as they roll in.