Question

What volume of `O_2(g)` at 350. `"^o`C and a pressure of 5.25 atm is needed to completely convert 10.0 g of sulfur to sulfur trioxide?

Sulfur trioxide, `SO_3`, is produced in enormous quantities each year for use in the synthesis of sulfuric acid.
`S(s) + O_2(g) -> SO_2(g)`
`2SO_2 (g) + O_2 (g) -> 2SO_3(g)`

Answer 1

We can use the stoichiometric equation: `S(s) + 3/2O_2(g) rarrSO_3(g)`. Approx. `5*L` dioxygen gas are required.

Explanation:

`"Moles of sulfur"` `=` `(10.0*g)/(32.06*g*mol^-1)=0.312*mol`.

Given the stoichiometry, we require `3/2xx0.312*mol` of dioxygen gas, i.e. `0.468*mol`.

And now we solve for volume in the Ideal Gas equation:

`V=(nRT)/P` `=` `(0.468*cancel(mol)xx0.0821*L*cancel(atm)*cancel(K^-1)*cancel(mol^-1)xx623*cancel(K))/(5.25*cancel(atm))` `~=` `5*L`.

Note (i) that we converted `"degrees Celsius"` to `"degrees Kelvin"`, and (ii) that we had to use an appropriate `"Gas constant, R"`. `"R"` with various units would be supplied as supplementary material in any exam. The fact that our equation gave units of volume, when a volume was sought in the problem, can help to convince us that we got the problem right (for once!!).