Question

A compound contains $8\% $ sulphur by mass. The minimum molecular weight of the compound is:
A. $100$
B. $200$
C. $350$
D. $400$

Answer 1

Hint: We are given that sulphur constitutes $8\% $ of the compound’s mass. In the bare minimum case, the compound will have only one sulphur atom in it. As we know the molar mass of sulphur as $32g/mol$, in the minimum case, the $8\% $ sulphur can be equated to this weight. In other words, $8\% $ of the compound’s molecular mass will be $32g$ and this will be the minimum molecular mass required to constitute at least one sulphur atom.

Complete step by step answer:
We are given that sulphur constitutes $8\% $ of the compound’s total mass. Thus, in order to find the minimum molecular weight in which this can happen, we have to consider the case where only a single atom of sulphur is present in the entire compound. We know that the molar mass of a sulphur atom is $32g/mol$. Thus, we should find the weight of the compound which will have exactly $32g$ of sulphur in its molecular mass. It is given that the compound contains $8\% $ sulphur by mass. What this means is that in $100g$ of the compound, we will have $8g$ of sulphur. Now all we have to do is find the weight of the compound which will have $32g$ of sulphur. Let us denote the overall mass of the compound as $x$. Therefore:

Mass of sulphur in compound ($grams$)	Total mass of compound ($grams$)
$8$	$100$
$32$	$x$

Using cross multiplication, we have:
$8x = 100 \times 32$
On rearranging, we get:
$x = \dfrac{{100 \times 32}}{8} = 400g$
Hence, the minimum molecular mass of the compound which will contain $8\% $ sulphur by mass is $400g$.

So, the correct answer is Option D .

Note: Note that the minimum molecular weight is calculated usually using the empirical formula of the compound, which is the simplest positive integer ratio of the atoms present in that compound. Also, note that sulphur is quantitatively estimated using the Lassaigne’s test in the laboratory. Here we have computed the mass taking molecular mass of the compound as our unit. It can also be done by taking the atomic mass unit ($amu$), in which case also the answer will be the same, only the unit remaining different. What the minimum molecular mass from this compound indicates is that there can be no compound in this universe of molecular mass under $400g$ which can have $8\% $ or more sulphur by mass.