Question #a8780

May 13, 2016

$\text{CO"_2" : F"_2" : NH"_3" : He}$
$\text{ "3" : "2" : "4" : } 1$

Explanation:

In beginning to tackle this problem, we are given three crucial pieces of information in the question:

1. all flasks are to be filled separately to a volume of 1 litre,
2. all flasks are at the same temperature, and
3. all flasks are at the same pressure.

When we refer this information back to the ideal gas equation, which is itself derived from the Boyle's, Charles's, and Avogadro's Laws, we realise that the number of moles of gas will therefore be constant in each case.

$P V = n R T \to n = \frac{P V}{R T}$

Again, since the values of $P$, $V$, $R$, and $T$ are the same across all of the flasks, the number of moles of gas will be the same. This also means that the number of molecules of gas (if the gas is a molecule) will be constant.

We're looking at atoms, though, and that's where things are a bit different! Although we have appreciated that the number of instances of the species present in the flask is the same in all cases- though we do not know that value - we have not yet considered how many atoms constitute each individual species.

${N}^{o} \left({\text{atoms in 1 molecule of CO}}_{2}\right) = 3$
${N}^{o} \left({\text{atoms in 1 molecule of F}}_{2}\right) = 2$
${N}^{o} \left({\text{atoms in 1 molecule of NH}}_{3}\right) = 4$
${N}^{o} \left(\text{atoms in 1 atom of He}\right) = 1$

So all your ratio really boils down to is the number of atoms that constitutes each species, since filling to a constant volume under shared temperature and pressure conditions will always result in the same number of moles of gas present in a container.