Question

Calculate the boiling point elevation for a solution prepared by adding $10gram$ of calcium Chloride to $200gm$ of water. (${{K}_{b}}$ for water = $0.512Kkgmo{{l}^{-1}}$, Molar mass of $CaC{{l}_{2}}mo{{l}^{-1}}$)

Answer 1

Hint:
-Boiling point elevation is a phenomena which occurs when a non-volatile solute, which means a solute which does not evaporate easily, is added to a solvent.
-Degree of dissociation of a solute is one in case of solutes which don't dissociate when they are added to water, and more than one in case of ionic solutes, the exact value depends on which solute we are considering.
Formula used:
$\vartriangle {{T}_{b}}=\dfrac{i\times {{K}_{b}}\times {{W}_{B}}}{{{M}_{b}}\times {{W}_{A}}}$
Where $\vartriangle {{T}_{b}}$ denotes the value of elevation in boiling point, ${{K}_{b}}$ is molal elevation constant and $m$ is the molality, $i$ is the degree of dissociation, ${{W}_{B}}$ is the mass of solute and ${{W}_{A}}$ is the mass of solvent, and ${{M}_{b}}$ is the molar mass of solute.

Complete step by step answer:
Boiling point elevation can be defined as the increase in the boiling point of a solvent under observation, when solute is added to it. When a non-volatile solute, that means a solute which does not evaporate easily, is added to a preferred solvent, the solution as a result has a higher boiling point as compared to that of the pure solvent. For instance, the boiling point of a solution which consists of sodium chloride and water is greater than the boiling point of the pure water.
Elevation of boiling point is one of the four colligative properties of matter, meaning, it is a property which is dependent on the ratio of solute-to-solvent but not on the identity of the solute. In other words we can say that the elevation in the boiling point of a solution is dependent on the amount of solute which is being added to it, and not the nature of that solute. The greater the concentration of solute in the solution, the higher will be the boiling point elevation.
In the given question we have to calculate the elevation in boiling point of a solution, whose molal elevation constant value is given to us along with the amount of water and calcium chloride.
The formula used to calculate the boiling point is,
$\vartriangle {{T}_{b}}=i\times {{K}_{b}}\times m$
Where $\vartriangle {{T}_{b}}$ denotes the value of elevation in boiling point, ${{K}_{b}}$ is molal elevation constant and $m$ is the molality, $i$ is the degree of dissociation.
The calcium chloride dissociates in water to form calcium and chloride ions. The reaction is shown below, $CaC{{l}_{2}}\to C{{a}^{2+}}+2C{{l}^{-}}$
Since three ions are produced by one mole of calcium chloride, the value of $i$ will be $3$.
We will write this equation in a modified form where we will write the molality equation in terms of given mass and molar masses.
$\vartriangle {{T}_{b}}=\dfrac{i\times {{K}_{b}}\times {{W}_{B}}}{{{M}_{b}}\times {{W}_{A}}}$
Where ${{W}_{B}}$ is the mass of solute which is given as $10g$ and ${{W}_{A}}$ is the mass of solvent which is given as $200g$, and ${{M}_{b}}$ is the molar mass of solute which we know $110gmo{{l}^{-1}}$
Substituting these values in the above equation we get,
$\vartriangle {{T}_{b}}=\dfrac{3\times (0.512Kkgmo{{l}^{-1}})\times 10g}{(110gmo{{l}^{-1}})\times (0.2kg)}$
So the value of $\vartriangle {{T}_{b}}$ came out to be $0.69K$.

Note:Since calcium chloride is an ionic molecule, so when it is dissolved in water as a solute, it dissociates into its constituent ions, which are calcium and chloride. Since, two chloride ions and one calcium ion is produced by one mole of calcium chloride, so the value of degree of dissociation becomes three.
-Molality of a solution is the number of moles of solute present per kilogram of solvent, and in this case the mass of solvent and solute were given to us, so it was easier to calculate the number of moles using that.