What volume of O_2(g) at 350. "^oC 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)

1 Answer
Nov 5, 2016

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!!).