Chemistry question Olympiad

Please could I have some help with this question? I understand the first two part but not part iii. Thank you!

So the initial concentration of As2O3 before dilution throughout the question is assumed to be 20.6 g dm^-3 and part (iii) concerns use of D30 solution (i.e diluted by a scale of 10^30, as per the paragraph above the three parts of (c)).

So, from this, can you start by finding the concentration of the solution after diluting and then calculate how many grams of As2O3 are present in 1 dm^3?

Following on from this, now that you have the number of grams in 1 dm^3, can you now try calculating the moles of As2O3? The moles of As should be twice this number.

Now try using the equation N = n x Na (where N is the number of atoms, n is the number of moles and Na is avogadro’s constant) to find the number of atoms of arsenic in 1 dm^3.

Since the number of atoms of As in 1 dm^3 is much less than 1, we can estimate how much D30 solution is required to obtain 1 atom. It can be inferred that (volume needed) = (desired number of atoms)/(average number of atoms per unit volume).

Following on from this, convert the volume of solution needed into cm^3 and divide by 28 cm^3 (since there are 28 cm^3 in each bottle, as per the question). This is your answer.

Thank you for this very clear explanation! Please could you give me any tips on how to tackle these questions because I always find it difficult to get the answers?

It’s difficult to give good advice you probably haven’t heard yet for complex calculations.

Usually, you want to start by underlining/highlighting any important details given earlier in the question (or alternatively, copy them down onto a separate piece of paper). This helps you keep track of important numbers you may be required to use in your calculations.

Using this end point to the question, you should think about possible calculations you may need to find that particular thing. You can then reverse-engineer the process.

In the case of this particular question, it was clear that you’d have to calculate the number of atoms somewhere down the line, as it asked how many bottles were needed to find 1 atom of arsenic.

To find the number of atoms, you need to use N = n x Na (an equation taught at both GCSE and A level). But for that to work, you would need the number of moles of arsenic. You can work out moles from the given concentration of the solution and you can use the Mr of As2O3 (calculated using the relative masses on the periodic table) to convert it to the appropriate units.

Since the initial concentration is given and it tells you how to find the concentration once the solution is diluted, you can find a value of n (and hence, N) for a particular volume of the solution.

The method chosen to be shown in the solutions estimates the number of atoms of arsenic per dm^3, but I’d be more inclined to find the moles of arsenic per bottle, since they state the volume of 1 bottle (28 cm^3) in the question.

So, here’s how I’d go about that question after showing you how I’d reverse-engineer the calculation (note my last post was explaining the horrible method used in the solutions that I never would have attempted in an exam situation):

(1: Find the Mr of As2O3.

(2: Convert 20.6 g dm^-3 to mol dm^-3 of As2O3

(3: Use the instructions in the question to find the diluted concentration of As2O3

(4: Since the question asks for the number of bottles needed to find one atom of arsenic, double the answer to (3, since that will be the diluted concentration of arsenic atoms.

(5: Use the equation conc = mol/volume to find the moles of arsenic atoms in 1 bottle, where the volume used is the volume of 1 bottle (28 cm^3, which should be converted to 0.028 dm^3 first).

(6: Since we have a value for n, now use N = n x Na to find the number of arsenic atoms per bottle

(7: Take the reciprocal of your answer to (6, since 1 atom divided by the number of atoms per bottle = the number of bottles needed to contain 1 atom.