An organic compound contains C, H and S. The minimum molecular weight of the compound containing 8% Sulphur is

We are told that the compound contains carbon, hydrogen and sulphur, and that the percentage by mass of sulphur in the compound is 8 %. Our aim is to find the smallest (minimum) molecular mass that is consistent with this percentage.

First recall the general definition of mass percent. For any element present in a compound, the percentage by mass is given by the formula

$$\text{Mass percent of an element} \;=\; \frac{\text{Mass of that element in one mole of the compound}}{\text{Molar mass of the compound}}\times 100.$$

Applying this to sulphur, we have

$$\text{Percentage of S}=\frac{\text{Mass of S present in one mole}}{\text{Molar mass of compound}}\times 100.$$

We know the percentage of sulphur is 8, so

$$8=\frac{\text{Mass of S in one mole}}{\text{Molar mass}}\times 100.$$

For the minimum molecular mass we must take the smallest integer number of sulphur atoms that can appear in an actual molecule. The least possible is one atom of sulphur. The atomic mass of sulphur is $$32\ \text{g mol}^{-1}.$$ Hence the mass of sulphur present in one mole of the compound, when only one sulphur atom is present, is $$32\ \text{g}.$$

Substituting this value into the percentage expression, we get

$$8=\frac{32}{\text{Molar mass}}\times 100.$$

Now we solve for the molar mass step by step. First divide both sides by 100 to remove the factor of 100:

$$\frac{8}{100}=\frac{32}{\text{Molar mass}}.$$

This simplifies to

$$0.08=\frac{32}{\text{Molar mass}}.$$

Next, cross-multiply (i.e. multiply both sides by the molar mass and by 1):

$$0.08\times \text{Molar mass}=32.$$

Now divide both sides by $$0.08$$ to isolate the molar mass:

$$\text{Molar mass}=\frac{32}{0.08}.$$

Carrying out the division, we have

$$\text{Molar mass}=400\ \text{g mol}^{-1}.$$

This is the smallest possible molecular weight consistent with exactly one sulphur atom providing 8 % of the total mass. Any molecule containing two or more sulphur atoms would necessarily have a higher molecular mass, so 400 g mol$$^{-1}$$ is indeed the minimum.

Hence, the correct answer is Option C.