Question

Insulin contains 3.4% sulphur. Calculate minimum molecular weight of insulin .
A) $614.27$
B) $941.17$
C) $841.27$
D) $714.17$

Answer 1

Hint: Mass by mass percent of sulphur is given and for minimum mass at least one mole of sulphur has to be present in insulin. Keeping these points in mind, we will use the formula for mass by mass percent of solute and solution.

Complete answer:
Here, sulphur acts as a solute and insulin acts as a solution. The things that have been given to us are :
Mass by mass percentage of a solution (sulphur) $=3.4\mathrm{\%}$
Molar mass of sulphur $=32g$
Here, for minimum mass at least one mole has to be present, so mass of solute= molar mass of sulphur.
Mass of solute (one mole) $=32g$
We know the mass by mass percentage of a solution is given by $={\displaystyle \frac{mass(solute)}{mass(solution)}}$

Mass of the solution is unknown , that is what has been asked in the question. Let the mass of the solution ( insulin) be $x$.
Then,
$$\begin{gathered} \Rightarrow 3.4={\displaystyle \frac{32}{x}}\times 100 \\ \Rightarrow 3.4x=3200 \\ \Rightarrow x={\displaystyle \frac{3200}{3.4}} \\ \therefore x=941.176 \end{gathered}$$
The mass of the insulin is $941.17g$ .Hence, the correct option is (B).

Note: The one point that should be kept in mind that here we have assumed the mole is sulphur as unity and that is why the mass of solute is equal to the molar mass of sulphur. If the number of moles were to be given something else, the mass of the solute would have been different.