Question

Solubility of a solute is S. Find its percentage by weight:
A. $\dfrac{{200S}}{{S + 100}}$
B. $\dfrac{{50S}}{{S + 100}}$
C. $\dfrac{{100S}}{{S + 100}}$
D. None of these

Answer 1

Hint: Solubility of a solute is given by S. It means that S g solute is present in 100 g solution. The total mass of the solution gives how much solute is dissolved in a certain amount of solvent.

Complete answer:
Solubility is a property referring to the ability for a given substance, the solute, to dissolve in a solvent. The mass/mass percent (% m/m) is defined as the mass of a solute divided by the mass of a solution times 100. It is measured in terms of the maximum amount of solute dissolved in a solvent at equilibrium. The relation between the solute and solvent is very important in determining solubility. Strong solute-solvent attractions equate to greater solubility while weak solute-solvent attractions equate to lesser solubility. polar solutes tend to dissolve best in polar solvents while non-polar solutes tend to dissolve best in non-polar solvents.
If the solubility is $S$ , there are $S$ g solute in $100g$ Solvent.
Total mass of solution $ = (S + 100)g$
$\% \,by \,mass = \dfrac{{mass \,of \,solute}}{{mass \,of \,solution}}\times100\% $
$ = \dfrac{{Sg}}{{(S + 100)g}}\times100$
% by mass $ = \dfrac{{100S}}{{100 + S}}$

Therefore the correct option is option C.

Note:
A concentrated solution is one in which there is a large amount of solute in a given amount of solvent. A dilute solution is one in which there is a small amount of solute in a given amount of solvent. At a given temperature the solubility product is constant. Lesser the value of solubility product indicates lower solubility and higher value of solubility product indicates greater solubility.