Question

A $1.24M$ aqueous solution of $KI$ has density of $1.15g/c{m^3}$ . What is the percentage composition of solute in the solution?
A. \[17.89\]
B. \[27.89\]
C. \[37.89\]
D. \[47.89\]

Answer 1

Hint:In this question we have to calculate weight by weight percentage composition. We will calculate the weight of the solute and the solution and get their ratio multiplied by \[100\] to get the answer. Also molar mass of $KI$ is $166g/mol$ .
Formula used:
$M = ({n_b}/V) \times 1000$
Where, $M$ is the molarity
${n_b}$ is the number of moles of solute
And $V$ is the volume of the solution in $ml$ or $c{m^3}$
Percentage composition of solute in solution
 $\% (w/w) = ({W_b}/{W_{solution}}) \times 100$
 $w = $ weight
 ${W_b} = $ weight of solute
 ${W_{solution}} = $ weight of solution

Complete step by step answer:
In the question, the following information and values are given:
Molarity is given to be $1.24M$
Since we know that molarity is the number of moles of solute present in one litre of the solution , we can say that
$1l$ of the solution ( $1000ml$ ) has $1.24mol$ of $KI$
Hence, $1l$ of the this solution will have $1.24 \times 166g$ of $KI$ $ = 205.84g$ (this is the weight of the solute or ${W_b}$ )
[we know that, $\text{number of moles} = \dfrac{Given weight}{molecular weight}$
Hence, given weight of $KI$ $ = 1.24 \times 166g$ ]
Density of the solution is given to be $1.15g/c{m^3}$
This means that in $1c{m^3}$ volume, we have $1.15g$
Thus in $1000c{m^3}$ we will have $1.15 \times 1000g$
Or we can say that $1l$ has $1150g$ (weight of the solution or ${W_{solution}}$ )
Thus, now we will use the percentage composition formula
$\% (w/w) = ({W_b}/{W_{solution}}) \times 100$
Putting all the values, we will have
$
  \% (w/w) = (205.8/1150) \times 100 \\
   \Rightarrow \% (w/w) = 17.89\% \\
 $
Thus the answer is Option A .

Additional Information: Molarity is defined as the number of moles of solute which are present in one litre of a solution. It is a concentration term, other concentration terms could be normality which is the number of gram equivalent of a solute present in one litre of a solution. Molality is also a widely used concentration term which means number of moles of a solute present in one kilogram of a solvent.

Note:
Percentage composition means the parts of solute which are there per 100 parts of the solution ( mass of solution is a sum of the mass of the solute and the mass of the solvent).