Animated Solution for Chemistry - Organic Chemistry: In the sulphur estimation, $0.471\text{ g}$ of an organic compound gave $1.44\text{ g}$ of barium sulphate. The percentage of sulphur in the compound is ......... %. (Nearest integer) (Atomic mass of $\text{Ba}=137\text{ u}$)

Imagine you are standing in a chemistry laboratory, tasked with finding out exactly how much sulphur is hidden inside an unknown organic compound. This is where the elegance of quantitative analysis, specifically the Carius Method, comes into play.

In this method, we take a known mass of our organic compound—in this case, $0.471\text{ g}$—and subject it to rigorous oxidation using fuming nitric acid. This intense reaction ensures that every single atom of covalently bonded sulphur is oxidized into sulphate ions (${\text{SO}}_4^{2-}$).

Once the sulphur is in the form of sulphate, we introduce barium ions (usually from barium chloride). The magic happens instantly: a heavy, white precipitate of barium sulphate (${\text{BaSO}}_4$) forms. We filter, dry, and weigh this precipitate, which turns out to be $1.44\text{ g}$.

To find out how much sulphur is locked inside that $1.44\text{ g}$ of ${\text{BaSO}}_4$, we first need to look at the molar mass of the precipitate.

Notice the beautiful stoichiometry here: one molecule of ${\text{BaSO}}_4$ contains exactly one atom of sulphur. This means that out of every $233\text{ g}$ of barium sulphate, exactly $32\text{ g}$ is pure sulphur.

We can use this ratio, known as the gravimetric factor, to find the mass of sulphur in our specific sample:

Now that we know the mass of the sulphur, finding its percentage in the original organic compound is a straightforward calculation. We simply divide the mass of the extracted sulphur by the total mass of the starting organic compound, and multiply by $100$.

I know this expression looks a bit dense, but let's take a breath and evaluate it carefully.

Since the question explicitly asks for the nearest integer, we round our result to $42\%$.

Why do we go through all this trouble to form barium sulphate? The answer lies in its extreme insolubility in water ($K_{sp}\approx 10^{-10}$). This ensures that virtually no sulphur is lost during the washing and filtration process, making our gravimetric analysis incredibly accurate.