Find moles of $\mathrm{BaSO_4}$

Given mass of barium sulphate: $m(\mathrm{BaSO_4}) = 0.752\ \text{g}$ Molar mass: $M(\mathrm{BaSO_4}) = 233\ \text{g mol}^{-1}$

So, moles of $\mathrm{BaSO_4}$ formed are: $n(\mathrm{BaSO_4}) = \frac{0.752}{233}$ $n(\mathrm{BaSO_4}) \approx 0.003227\ \text{mol}$

Relate this to sulfur present

In Carius estimation, all sulfur in the organic compound is converted to sulfate and finally precipitated as $\mathrm{BaSO_4}$.

Since 1 mole of $\mathrm{BaSO_4}$ contains 1 mole of sulfur, $n(S) = n(\mathrm{BaSO_4}) = 0.003227\ \text{mol}$

Mass of sulfur in the sample: $m(S) = 0.003227 \times 32$ $m(S) \approx 0.1033\ \text{g}$

Use percentage of sulfur in the compound

The compound contains $51.6\%$ sulfur by mass.

Let mass of compound be $m$ g. Then: $0.516\,m = 0.1033$

Hence, $m = \frac{0.1033}{0.516}$ $m \approx 0.200\ \text{g}$

Match with the required form

The question asks for: $\underline{\hspace{1cm}} \times 10^{-1}\ \text{g}$

Since, $0.200\ \text{g} = 2.00 \times 10^{-1}\ \text{g}$

Nearest integer $= 2$.

Final answer

$\boxed{2}$