Question

In a significant experiment performed many years ago, 5.6977 g of cadmium iodide in 44.69 g of water raised the boiling point 0.181 °C. What does this suggest about the nature of a solution of${\mathbf{C}\mathbf{d}\mathbf{I}}_2$?

Short answer

The actual increase in boiling point is 0.181°C.

Step-by-step solution

Boiling Point

At standard atmospheric pressure, the boiling may be defined as the temperature at which the liquid is converted into vapors.

The boiling point is:

$\begin{array}{r}\mathbf{\Delta }{\mathbf{T}}_{\mathbf{b}}\mathbf{=}\mathbf{K}\mathbf{b}\times \mathbf{m}\\ \mathbf{\Delta }{\mathbf{T}}_{\mathbf{b}}\mathbf{=}\mathbf{E}\mathbf{l}\mathbf{e}\mathbf{v}\mathbf{a}\mathbf{t}\mathbf{i}\mathbf{o}\mathbf{n}\mathbf{i}\mathbf{n}\mathbf{b}\mathbf{o}\mathbf{i}\mathbf{l}\mathbf{i}\mathbf{n}\mathbf{g}\mathbf{p}\mathbf{o}\mathbf{i}\mathbf{n}\mathbf{t}\\ \mathbf{K}\mathbf{b}\mathbf{=}\mathbf{E}\mathbf{b}\mathbf{u}\mathbf{l}\mathbf{o}\mathbf{s}\mathbf{c}\mathbf{o}\mathbf{p}\mathbf{i}\mathbf{c}\mathbf{c}\mathbf{o}\mathbf{n}\mathbf{s}\mathbf{t}\mathbf{a}\mathbf{n}\mathbf{t}\\ \mathbf{m}\mathbf{=}\mathbf{m}\mathbf{o}\mathbf{l}\mathbf{a}\mathbf{l}\mathbf{i}\mathbf{t}\mathbf{y}\mathbf{o}\mathbf{f}\mathbf{s}\mathbf{o}\mathbf{l}\mathbf{u}\mathbf{t}\mathbf{i}\mathbf{o}\mathbf{n}\end{array}$

Explanation

From the elevation of boiling point, determine the molarity expected,

$\begin{array}{r}\begin{array}{rl}\mathrm{M}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{C}\mathrm{d}{\mathrm{I}}_2& ={\displaystyle \frac{5.6977\mathrm{g}}{366.220\mathrm{g}\mathrm{m}\mathrm{o}\mathrm{l}{\mathrm{e}}^{-1}}}\\ \mathrm{M}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{C}\mathrm{d}{\mathrm{I}}_2& =0.015558\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\end{array}\\ \begin{array}{rl}\mathrm{M}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{y}\mathrm{o}\mathrm{f}\mathrm{C}\mathrm{d}{\mathrm{I}}_2& ={\displaystyle \frac{0.015558\mathrm{m}\mathrm{o}\mathrm{l}}{0.04469\mathrm{k}\mathrm{g}}}\\ \mathrm{M}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{y}\mathrm{o}\mathrm{f}\mathrm{C}\mathrm{d}{\mathrm{I}}_2& =0.3481\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{K}{\mathrm{g}}^{-1}\end{array}\end{array}$

The boiling point elevation expected if no ionization occurs is:

$\begin{array}{rl}\mathrm{\Delta }\mathrm{T}\mathrm{b}& =\mathrm{K}\mathrm{b}\times \mathrm{m}\\ \mathrm{\Delta }\mathrm{T}\mathrm{b}& =0{.512}^{\circ }\mathrm{C}{\mathrm{m}}^{-1}\times 0.3481\mathrm{m}\\ \mathrm{\Delta }\mathrm{T}\mathrm{b}& =0.178^{\mathrm{o}}\mathrm{C}\end{array}$

The actual boiling point increase is 0.181°C.

Nature of $\mathbf{C}\mathbf{d}{\mathbf{I}}_{\mathbf{2}}$ solution

After the addition of $\mathrm{C}\mathrm{d}{\mathrm{I}}_2$in water, it will increase the boiling point of water.

That means it releases the heat in the solution.