Question

A solution is prepared by dissolving 10 g of non-volatile solute in 200 g of water. It has a vapour pressure of 31.84 mm Hg at 308 K. Calculate the molar mass of the solute.
(Vapour pressure of pure water at 308 K = 32 mm Hg).

Answer 1

Hint- In order to deal with this question first we will state Raoult's law then with the help of given data we will calculate the molar mass of the solute by using the formula of Raoult's law.

Complete answer:
Formula used- $\dfrac{{{p^0} - p}}{{{p^0}}} = \dfrac{{w \times M}}{{m \times W}}$
In Raoult 's theorem, the partial vapor pressure of a solvent in a solution (or mixture) is equal to or equivalent to the vapor pressure of the pure solvent measured in the solution by the mole fraction.
Given that
Vapour pressure of pure water = 32 mm Hg
Vapour pressure of solvent= 31.84 mm Hg
Weight of solute = 10g
Molecular weight of solute (water) = 18g
Weight of solvent = 200g
According to raoult's law formula,
$\dfrac{{{p^0} - p}}{{{p^0}}} = \dfrac{{w \times M}}{{m \times W}}$
Here,
${p^0}$ is the vapour pressure of pure water.
$p$ is the vapour pressure of solvent.
$w$ is the weight of solute.
$m$ is the molecular weight of solute.
$M$ is the molecular weight of solvent
$W$ is the weight of solvent.
So let us substitute all the values in the above formula to find the molecular weight of solute.
$
  \because \dfrac{{{p^0} - p}}{{{p^0}}} = \dfrac{{w \times M}}{{m \times W}} \\
   \Rightarrow \dfrac{{32 - 31.84}}{{32}} = \dfrac{{10 \times 18}}{{m \times 200}} \\
   \Rightarrow m = \dfrac{{10 \times 18 \times 32}}{{\left( {32 - 31.84} \right) \times 200}} \\
   \Rightarrow m = \dfrac{{0.9}}{{0.005}} \\
   \Rightarrow m = 180gm \\
 $

Hence, the molar mass of the solute is 180 g.

Note- A solution is formed, when one substance dissolves into another. A solution is a homogeneous mixture consisting of a solvent-dissolved solution. The solute is the dissolved material while the dissolving medium is the solution. The molar mass, also known as molecular weight, is the measure of the total mass of all the atoms in grams that make up a molecule with a given molecule. The measurement unit is grams by mole.