# How to calculate the number of atoms in a gas molecule?

$$\pu{20 mL}$$ of sulfur vapour at $$\pu{1000 °C}$$ reacts with $$\pu{40 mL}$$ of oxygen gas to form $$\pu{40 mL}$$ of sulfur dioxide gas. Determine the number of atoms in the molecule of sulfur in the vapour state at this temperature.

My working out is as follows:

$$\ce{\underset{\pu{20 mL}}{S(g)} + \underset{\pu{40 mL}}{O2(g)} -> \underset{\pu{40 mL}}{SO2(g)}}$$

I then used the formula $$n = m/M$$ to find the amount of substance.

$$n = m/M = 20/32.07 = x$$

Then, to find the number of atoms, I used the formula $$n = N/N_\mathrm{A}$$.

$$N = nN_\mathrm{A} = x\cdot\pu{6.022e23} = \pu{3.80e23}~\text{(atoms)}$$

However, I am uncertain as to whether this is correct as I did not utilize any of the gas laws. For this question, which of the gas laws should I have used?

• Welcome to our site! BTW I noticed that you used the volume $(20\pu{mL})$ of $\ce{S}$ in the place of mass "$m$". Are you sure you want it that way? – William R. Ebenezer Jul 18 '19 at 3:03
• @WilliamR.Ebenezer Should I be using one of the gas law equations to solve for "n" and then use the formula N=N/Na to solve for the number of atoms? – user77170 Jul 18 '19 at 4:16
• Instead of using any 'gas laws', why don't you just remember the equation $pV = nRT$? – Apoorv Potnis Jul 18 '19 at 9:47
• I'm afraid I misread the question, further fueled by seeing your usage of Avogadro's number. – William R. Ebenezer Jul 19 '19 at 3:54
• The question isn't about counting all the atoms of sulphur but the number of atoms of sulphur in a single molecule of sulphur vapour. This can be done with simple gas-law reasoning. – matt_black Jul 19 '19 at 23:31

Reason for rewrite: refer to edit summary.

From Wikipedia on Disulfur ($$\ce{S2}$$)

This violet gas is commonly generated by heating sulfur above 720 °C

Since the sulfur is well above $$720^\circ\pu{C}$$, it would most likely be in the diatomic state, more like an analogous structure to dioxygen ($$\ce{O2}$$).

We can also judge this from the molar ratios too, as rose22 has pointed out. Since it is given that $$40~\pu{mL}$$ of $$\ce{SO2}$$ is formed from $$20~\pu{mL}$$ of $$\ce{S_x}$$ (assuming the atomicity of $$\ce{S}$$ to be $$x$$ at this temperature) and $$20~\pu{mL}$$ of $$\ce{O2}$$, they must come to terms with a simple whole number ratio.

$$\ce{\underset{20~\pu{mL}}{S_x}+\underset{40~\pu{mL}}{xO2}->\underset{40~\pu{mL}}{xSO2}}$$

Statement 1: Since the ratio of volumes of gases at a particular temperature and pressure is equal to the ratio of amount of substance in moles, it is clear that:

$$1:x:x=20:40:40$$

That is to say, $$x=2$$, so the atomicity of sulfur here is $$2$$.

In the question, the OP said:

However, I am uncertain as to whether this is correct as I did not utilize any of the gas laws. For this question, which of the gas laws should I have used?

Statement 1 is a result from the universal gas law.

$$PV=n\text{R}T$$

When $$P$$ and $$T$$ are constant,

$$\frac{V_1}{V_2}=\frac{n_1}{n_2}$$

Some may argue that this relationship is called Avogadro law, but again, this law too is a gas law, evidently.

• @KarstenTheis If you're referring to the line "dead wrong to say that there are no gas laws involved", I was replying to question itself, which was(and is still) asking if gas laws were required or not. Not referring to the answer, sire. Anyway, I respect you for explaining your downvote. – William R. Ebenezer Jul 20 '19 at 5:55
• I did not realize until now that the question and the other answer were by the same person. You answer makes more sense to me know. I also appreciate the bit about properties of $\ce{S2}$ you included. – Karsten Theis Jul 20 '19 at 11:15

The question is (my emphasis):

20 mL of sulfur vapour at $$\pu{1000 ^\circ C}$$ reacts with 40 mL of oxygen gas to form 40 mL of sulfur dioxide gas. Determine the number of atoms in the molecule of sulfur in the vapour state at this temperature.

For this question, we must understand that the number of sulfur atoms in the sulfur molecule (the subscript in its chemical formula) is actually an integer ($$x$$). The volume ratios determine the mole ratios and thus, are able to determine the stoichiometry of the equation. From this stochiometry, the value of ($$x$$) can be determined.

The working out is as follows:

Let $$\ce{S_x}$$ be the formula of the molecule making up the sulfur vapour.

Volume ratios (Sx:O2:SO2) = 20:40:40 = 1:2:2 = mole ratios, so the chemical equation with stoichiometric coefficients is:

$$\ce{S_x + 2O2 -> 2SO2}$$

Thus $$x = 2$$ (to have a balanced equation).

Therefore, the molecule making up the sulfur vapour is $$\ce{S2}$$.

To conclude, there are 2 atoms of sulfur in this particular molecule of sulfur.

• I agree with the corrected statements made in your answer - however, what I meant was that no gas laws equations are required to solve this problem. Also, thank you very much for your additional information. – user77170 Jul 19 '19 at 7:56
• @rose22 Without using gas laws you wouldn't be able to use direct proportionality between gas volumes and the amounts of substances. It doesn't matter whether you write those down or not — they are the basis of your assumption. Also, note that this doesn't really answers your the question (where is the answer for the number of atoms?) and is more justified as an edit or a shortened comment. – andselisk Jul 19 '19 at 8:09
• @andselisk Okay, thank you for your input. I'll ensure that the answer is more coherent and distinguishable next time. – user77170 Jul 19 '19 at 8:21
• I am up-voting because the answer is correct, and the incorrect statement about not using the gas laws have been removed. – Karsten Theis Jul 19 '19 at 20:08
• @KarstenTheis I noticed that, but since OP initially attempted to find the total number of sulfur atoms, I thought there might be some incorrect translation of the question. Note that the first revision of William's answer also addresses this number, using an assumption about the composition of sulfur molecule (which, as it's turned out, should be the answer) as an aid to solve the problem. – andselisk Jul 19 '19 at 23:36