Question

What is the Molarity of 1 M solution ${\text{NaN}}{{\text{O}}_{\text{3}}}$ , if the density of the solution is 1.25 g/ml
1. 0.8 m
2. 0.858 m
3. 1.6 m
4. 1 m

Answer 1

Molarity of a solution can be defined as the number of moles of solute present in per kilogram of a solvent, and the density of a solution tells us about the Mass of the solution present in per volume of the solution.

Formula used:
a. ${\text{Molality}} = \dfrac{{{\text{no}}{\text{. of moles of solute}}}}{{{\text{Mass of solvent in kg}}}}$
b. ${\text{Density = }}\dfrac{{{\text{ Mass}}}}{{{\text{volume}}}}$

Complete answer:
Since the molarity of the solution is 1 M, we can say that 1 mole of solute is dissolved in 1 litre of the solution.
We can calculate the Mass of the solution by using the density formula, since the unit of density is given in g/ml, we have to convert the given 1 litre volume into ml
$\Rightarrow 1{\text{L = 1000 mL}}$
$\Rightarrow$ ${\text{Density = }}\dfrac{{{\text{ Mass}}}}{{{\text{Volume}}}}$
$\Rightarrow$ Mass = Volume $\times$ Density
$\Rightarrow$ Mass = 1000 $\times$ 1.25
$\Rightarrow$ Mass = 1250 g
1250g is the Mass of the solution we have to subtract the Mass of ${\text{NaN}}{{\text{O}}_{\text{3}}}$solute, to get the Mass of the solvent,
$\Rightarrow$ Mass of solvent (${{\text{H}}_{\text{2}}}{\text{O}}$) = 1250 – 84 = 1166g
Since the formula of Molality has a Mass of solvent in kg, we have to change the unit of 1166g to kilogram,
$\Rightarrow$ 1166 = 1.166 kg ( using the knowledge that 1kg = 1000g)
We can now calculate the Molality of the solution;
$\Rightarrow$ ${\text{Molality}} = \dfrac{{{\text{no}}{\text{. of moles of solute}}}}{{{\text{Mass of solvent in kg}}}}$
$\Rightarrow$ Molality = $\dfrac{1}{{1.166}}$ ( 1 mole of ${\text{NaN}}{{\text{O}}_{\text{3}}}$ is dissolved in 1 litre of a solution)
$\Rightarrow$ Molality = 0.8576 m
Therefore, the Molality of the solution is 0.8576 m, rounding off this value will give
$\Rightarrow$ Molality = 0.858 m

**Hence, the correct answer is option (2) i.e., 0.858

Note:**
There are multiple numbers of times we have changed the units of the quantities, thus it is important to carefully notice the units and bring changes when required, also we had to look at up to 3 decimal value in this question, as 1st option i.e., 0.8 could have been correct, if 2nd option did not exist.