Question

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

Answer 1

A solution is a type of homogenous mixture which consists of two or more substances. In a solution, a solute is dissolved in another substance which is called the solvent.
Molarity is the most commonly used method of concentration. The concentration of a solution is commonly expressed by its molarity, defined as the amount of dissolved substance per unit volume of solution, for which the unit is used in moles per liter. The units of molarity are M or $mol/L$. A $1M$ solution is said to be “one molar.” It is expressed as the number of moles of solute dissolved in 1L of solution. For example, if $1.4 \times {10^{ - 4}}$ the moles per liter solution means $1.4 \times {10^{ - 4}}$ moles of $\left[ {{H_3}{O^ + }} \right]$ has been dissolved in one liter of solution.
SI unit of molarity is $mol/L$
Formula used:
$M = \dfrac{n}{V}$
where, $M =$ molarity , $n =$ number of moles and $V =$ volume of solution

Complete answer:
Let the volume of solution$= 1$ litre or $1000ml$
Mass of urea (solute) in solution $= 3000ppm$
$1ppm = \dfrac{{1mg}}{{litre}}$
So, using this we can say that
$3000ppm = \dfrac{{3000 mg}}{{1 litre}} = 3000mg$

We know,
$1g = 1000mg$
So, we can say that mass of the solution of urea $= 3g$
Given, Density of the solution$= 1.04g/ml$
We know the formula of finding density from mass and volume by the formula:
$Density = \dfrac{{mass}}{{Volume}}$
We know the values of volume and density, so we can find the mass of the solution:
Mass of solution $=$ volume of the solution $\times$ density
$\, = 1000ml \times 1.04g/ml\,$
$\, = 1040g\,$
Mass of solvent(in grams) $=$ mass of solution $-$ mass of solute
$\, = 1040 - 3\,$
$\, = 1037g\,$
Strength of a solution or its molarity is calculated by the formula
$M = \dfrac{n}{V}$
We know the volume of solution is $= 1$ litre.
$number\,of\,moles = \dfrac{\text{given mass}}{\text{molar mass}}$
Given mass of urea $= 3g$
Molar mass of urea can be calculated from its formula and it is $= 60g$
So,
No. of moles $= \dfrac{3}{{60}}$
$= 0.05mol$
Now, we calculate the molarity or the strength of the solution by substituting the values of number of moles and volume of solution in the molarity formula:
$M = \dfrac{{0.05}}{1}$
$\Rightarrow Molarity = 0.05M$
Hence the correct option is B.

Note:
-The molar mass of a compound is equal to the sum of the atomic masses of its constituent atoms in $g/mol$ .
-Even though there is no physical way of measuring the number of moles of a compound, we can relate its mass to the number of moles by using the compound’s molar mass as a direct conversion factor.
-To convert between mass and number of moles, one can use the molar mass of the substance.