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# How many grams of solute should be added in $100 g$ water to get a solution of density $1.2$ $g/mL$ and strength 5%(w/v)?

Last updated date: 20th Jun 2024
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Answer
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Hint: The question talks about two measurements; one is density and the other is mass concentration. Density is a general formula; however mass concentration requires a specific mass of solute to be dissolved in the given volume of solution. So, keep both these conditions in mind, while adding solute particles as both of them have to be satisfied.

Complete step by step solution:
Density or volumetric mass density is defined as the mass per unit volume of a given substance. Density is often expressed in terms of g/L or g/mL. The most common symbol of density is the Greek symbol rho. Along with that, the capital letter D is also used in some places.
The formula is given below:
$\rho \text{ = }\dfrac{m}{V}$
Where,
$\rho$ stands for a density
m denotes the mass of solute
V is the volume of solution.
We have the following values given to us:
$\rho$ = 1.2 g/mL
Mass of water = 100 g
5% (w/v) by definition means that 5 grams of solute per 100 grams of solution present.
We have the density, so we can find the volume occupied by 100g of water.
$\implies 100\times \dfrac{1}{1.2}\text{ = 83}\text{.33 mL}$
We will now substitute the values to obtain the mass of the solute.
$\implies 83.33\times \dfrac{5}{100}\text{ = 4}\text{.17 g}$
Thus, the amount of solute to be added in 100 g water to get a solution of density 1.2 g/mL and strength 5%(w/v) is 4.17 g.

Therefore, the correct answer is option (C).

Note: Do not confuse density with molarity. Molarity is related to moles of solute and volume of solution. However, density is related to the mass of solute dissolved and the volume of solution. The formula for density is mentioned in the solution for your better understanding.