Question

In a gas, S and O are 50% by mass. Hence, their molar ratio is:
A. $1:1$
B. $1:2$
C. $2:1$
D. $3:1$

Answer 1

We have to calculate the moles of sulfur and oxygen using the molar mass of sulfur and oxygen. From the moles of sulfur and oxygen, we can determine the molar ratio.

Complete step by step answer:
Given data contains,
Mass percent of sulfur is 50%.
Mass percent of oxygen is 50%.
This means that,
Mass of sulfur is 50g.
Mass of oxygen is 50g.
From the mass percent of sulfur and oxygen, we can calculate the moles of sulfur and oxygen using their respective molar masses.
We know that the molar mass of sulfur is $32.06g/mol$.
We know that molar mass of oxygen is $16.00g/mol$.
We have to calculate the moles of the elements by dividing the mass of elements to their respective molar mass. We can write the formula to calculate the moles as,
Moles$= \dfrac{{{\text{Mass}}}}{{{\text{Molar mass}}}}$
Let us now calculate the moles of sulfur from the mass percent of sulfur and molar mass of sulfur. We can write the formula to calculate the moles of sulfur as,
Moles of sulfur$= \dfrac{{{\text{Mass of sulfur}}}}{{{\text{Molar mass of sulfur}}}}$
Let us now substitute the values of mass of sulfur and molar mass of sulfur.
Moles of sulfur = $\dfrac{{50g}}{{32.06gmo{l^{ - 1}}}}$
Moles of sulfur = $1.56mol$
We have calculated the moles of sulfur as $1.56mol$.
Let us now calculate the moles of oxygen from the mass percent of oxygen and molar mass of oxygen. We can write the formula to calculate the moles of oxygen as,
Moles of oxygen$= \dfrac{{{\text{Mass of oxygen}}}}{{{\text{Molar mass of oxygen}}}}$
Let us now substitute the values of mass of oxygen and molar mass of oxygen.
Moles of oxygen = $\dfrac{{50g}}{{16.00gmo{l^{ - 1}}}}$
Moles of oxygen = $3.125mol$
We have calculated the moles of oxygen as $3.125mol$.
We can see that moles of oxygen are twice those moles of sulfur. Therefore, their molar ratio is $1:2$.

Therefore, the option (B) is correct..

Note:
From the molar ratio, we can write the empirical formula of the compound. We have to divide by lowest molar quantity to get the empirical formula of the compound. In this case, we have calculated the moles of sulfur and oxygen as $1.56mol$ and $3.125mol$ respectively. The lowest molar quantity here is sulfur. So let us divide by sulfur to get the empirical formula.
$S\dfrac{{1.56mol}}{{1.56mol}}O\dfrac{{3.125mol}}{{1.56mol}} = S{O_2}$
Therefore, $S{O_2}$ is the empirical formula of the compound.