Question

How many grams of solute should be added in 100g water to get a solution of density 1.2g/ml and strength 5% (w/v)?
(A) 5g
(B) 6g
(C) 4.17g
(D) 4.35g

Answer 1

Hint: Density is defined as mass per unit volume so, 1.2 grams of solution weighs 1ml. And also the strength is 5% (w/v) means 5 grams per 100 grams of solution. The volume can be found from the given values of density and strength and then the mass of solution is calculated.

Complete step by step answer:
Let us first calculate the volume of 100g solution. We know that the density is mass per volume by definition.
Given that 1.2g/ml is the density which means 1.2g in 1ml of solution.
So for 100g of solution, the volume would be calculated by cross multiplication of the values.
1.2g - 1ml
100g - ? so, upon cross multiplication we get,
$
  100 \times \dfrac{1}{{1.2}}
   = 83.33 ml
 $

Now, to know the amount of solute to be dissolved in 83.33ml of water, the strength of the given solution has to be considered. The strength is given as 5% (w/v), this implies 5 grams mass of solute is dissolved in 100ml volume of solvent. So in 83.33 ml of the solvent the solute mass would be obtained again by cross multiplication of the values we have.
100ml – 5gm
83.33ml – x gm. So, upon cross multiplication, we get
$
  \dfrac{{83.33 \times 5}}{{100}}
   = 4.1665 \simeq 4.17
 $gm.
Therefore the amount of solute should be added in 100g of water to get a solution of 1.2 g/ml density and the strength of 5% (w/v) is 4.17 g.
So, the correct answer is “Option C”.

Note: When a solution is given in mass (g) to convert into volume (ml), the mass is converted to volume by using the density formula provided the density of the given solution is provided. The density will be always provided in the solutions. The strength is mentioned in percentage weight by volume indicates x grams of solute dissolved in 100ml of solvent.