Question

A solution of urea in water is 3000ppm by weight. if the density of this solution is 1.04 g/ ml. What is the molar strength of the solution?

Answer 1

Molarity is also known as molar strength and is defined as the number of moles of solute present in one litre of solution. Mathematically it is given as:
$Molarity = \dfrac{{{\text{no}}{\text{.of moles of solute}}}}{{{\text{volume of solution}}}}$

Complete step by step answer:
As we know ppm stands for parts per million. Mathematically it is represented as:
$ppm = \dfrac{{{\text{Mass of the component}}}}{{{\text{mass of the solution}}}} \times {10^6}$
The density of a solution is related to mass and volume and the formula for density is given as:
$Density = \dfrac{{Mass}}{{Volume}}$
On putting the given value of density and volume we can calculate the mass of solution as:
$1.04 = \dfrac{{Mass}}{{1000}}$
$\Rightarrow 1.04 \times 1000 = {\text{Mass of the solution}}$
$\Rightarrow {\text{Mass of the solution = }}1040g$
As per the question, it is given that solution of urea in water is 3000ppm by weight, then the mass of the urea is calculated as:
$3000 = \dfrac{{{\text{Mass of the component}}}}{{140}} \times {10^6}$
$\Rightarrow \dfrac{{3000 \times 1040}}{{{{10}^6}}} = {\text{Mass of the component}}$
$\Rightarrow {\text{Mass of the component = 3}}{\text{.12g}}$
Since the molar strength (molarity) is given as:
$Molarity = \dfrac{{{\text{no}}{\text{.of moles of solute}}}}{{{\text{volume of solution}}}}$
Number of moles of solute (urea) = given mass/ molecular mass
Number of moles of urea = $\dfrac{{3.12}}{{60}}$
And the volume of the solution is 1 litre, then the Molarity is calculated as:
$Molarity = \dfrac{{3.12}}{{60 \times 1}}$
Hence, the Molar strength of the solution is 0.052M

Additional Information:
Apart from Molarity, we have other concepts also that relate to the concentration of a solute in a solvent. They are:
Molality: It is defined as the number of moles of solute in one kg of solution.
Weight percent: It is defined as the ratio of the mass of solute to the mass of solution multiplied by 100 is represented as w/w %. It is also known as Mass per Cent.

Note: We use molar concentration instead of molecular concentration as the number of molecules in a solution will be high as per the definition of a mole; it is equal to the gram-equivalent weight of the Avogadro's number of molecules, i.e. $6.023 \times {10^{23}}$. So it will be simpler to represent the concentration in terms of moles per litre.