Question

Molarity and molality of a solution of a liquid (mol wt = 50) in aqueous solution is 9 and 10 respectively. What is the density of solution?
(A)- 1 g/cc
(B)- 0.95 g/cc
(C)- 1.05 g/cc
(D)- 1.35 g/cc

Answer 1

Hint: Density of a solution is a measure of its mass present per unit volume. It is given as
     \[\text{Density = }\frac{\text{mass of solution}}{\text{volume of solution}}\]
Density is generally expressed in g/cc (or g /ml). Its S.I unit is kg/${{m}^{3}}$.
Molality of a solution gives the mass of the solute present in one kg of the solvent. It is calculated as
\[\text{Molality (m) = }\frac{\text{no}\text{. of moles of solute}}{\text{weight of solvent (in kg)}}=\frac{\text{mass of solute (in g)}}{\text{molar mass of solute}}\times \frac{1000}{\text{weight of solvent (in g)}}\]
Molarity of a solution is the mass of the solute present in per liter of the solution. It can be calculated using the following relation
     \[\text{Molarity}=\frac{\text{number of moles of solute}}{\text{volume of solution (in L)}}=\frac{\text{mass of solute (in grams)}}{\text{molar mass of solute}}\times \frac{1000}{\text{volume of solution (in mL)}}\]


Complete step by step solution:
We have been given the molar mass of the liquid dissolved in the aqueous solution = 50 g
To find the density of the solution we require the total mass and total volume of the solution, i.e.
Total mass of the solution, m = mass of the solute + mass of the solvent
Total volume of the solution, V = volume of the solute + volume of the solvent
We know that molality of a solution is the number of moles of solute dissolved in per kg of the solvent.
Given molality of the aqueous solution = 10 mol $k{{g}^{-1}}$.
10 molal solution means that 10 moles of the given liquid are dissolved in 1000 g (1 kg) of the solvent. Then, 1 mole of the liquid solute will be present in $\frac{1000}{10}$= 100 g of the solvent.
Thus, we have the mass of solvent = 100 g.
Now we already know that the mass of one mole of the liquid solute = 50 g.
Hence, the total mass of the solution (m) will be = 50 g + 100 g = 150 g.
Since molarity is the number of moles of a solute dissolved in one liter of solution. Given molarity of the aqueous solution = 9 mol $li{{t}^{-1}}$
9 molar solution contains 9 moles of the solute in 1000 ml (1 liter) of the solution, then 1 mole of the solute will be present in $\frac{1000}{9}$= 110 ml of the solution.
Therefore, we obtain the total volume of the solution (V) = 110 ml.
Let us now find the density of the solution.
     \[\text{Density = }\frac{\text{mass of solution (m)}}{\text{volume of solution (V)}}\]
Substituting the value of total mass of the solution, m = 150 g and volume of the solution, V = 110 ml in the above equation, we get
     \[\text{Density = }\frac{\text{150 g}}{\text{110 ml}}\text{=1}\text{.35}\]g/ml = 1.35 g/cc.

Hence, the correct option is (D).

Note: Note that 1 millimeter = 1 cubic centimeter. Do not get confused between molality and molarity. Molality does not involve the volume but mass of the solvent. Volume of the solution is obtained from the molarity.