Question

When 2.60 gof a substance that contains only indium and chlorine is dissolved in 50.0 gof tin(IV) chloride, the normal boiling point of the tin(IV) chloride is raised from 114.1⁰C to 116.3⁰C. if${\mathit{K}}_{\mathbf{\text{b}}}\mathbf{=}\mathbf{9}\mathbf{.}\mathbf{43}\mathbf{}\mathbf{\text{K}}\mathbf{}\mathbf{\text{kg}}\mathbf{}{\mathbf{\text{mol}}}^{\mathbf{-}\mathbf{1}}$for${\mathbf{\text{SnCl}}}_{\mathbf{4}}\mathbf{,}$what are the approximate molar mass and the probable molecular formula of the solute?

Short answer

The molar mass of the solute is$223.18{\text{gmol}}^{-1}$ and the molecular formula of solute is ${\text{InCl}}_3$.

Step-by-step solution

Given data.

$$\begin{gathered} {\text{T}}_{\text{1}}=114.1^0\text{C} \\ {\text{T}}_{\text{2}}{\text{= 116.3}}^0\text{C} \\ {K}_b=9.43KKgmo{l}^{-1} \end{gathered}$$

The concept of elevation of boiling point

When the boiling point of a solution exceeds the boiling point of a pure solvent, it is known as boiling point elevation.

Formula of elevation of boiling point

The formula of elevation of boiling point can be shown as:

$K_b=\frac{∆T_b}{m}$ ……. (i)

role="math" localid="1663705924696" $∆T_b$is the elevation of boiling point, m is molality of the solution and ${\text{K}}_{\text{b}}$is the boiling point elevation constant.

Determination of elevation of boiling point

The elevation of the boiling point can be determined by the formula,

$∆T=T_2-T_1$ ……. (ii)

Substituting the value of $T_1$and $T_2$in equation (ii),

$$\begin{gathered} ∆T_b=116.3-114.1 \\ =2.2 \end{gathered}$$

Calculation of Kb (molal boiling point constant)

Calculate the molarity of the solution with the help of equation (i)

$m=\frac{∆T_b}{K_b}$

Puts the value of given data in equation (i).

$$\begin{gathered} m=\frac{∆T_b}{K_b} \\ =\frac{2.2\text{K}}{9.43\text{K}/{\text{kgmol}}^{-1}}m \\ =0.233{\text{molkg}}^{-1} \end{gathered}$$

Calculation of $n_2$is shown as

$$\begin{gathered} n_2=\left(0.233{\text{molkg}}^{-1}\right)\times (0.050\text{kg}) \\ {n}_2=0.01165\text{mol} \end{gathered}$$

Calculation of M2

The value of$M_2$ can be determined by use the formula,

$M_2=\frac{m_2}{n_2}$ ……. (iii)

Puts the value of$m_2$ and$n_2$ in equation (iii)

$$\begin{gathered} M_2=\frac{2.60\text{g}}{0.01165\text{mol}} \\ =223.18{\text{gmol}}^{-1} \end{gathered}$$

Determination of molecular formula of solute

The formula of solute can be determined by as follows,

$\text{mass} \text{of} \text{chlorine} \text{=} \text{total} \text{mass} \text{-} \text{mass} \text{of} \text{indium}$

$$\begin{gathered} =223.18 \text{g}-114.82 \text{g} \\ =108.36 \text{g} \end{gathered}$$

data-custom-editor="chemistry" $$\begin{gathered} \text{Number of chlorine atoms}=\frac{108.36}{35.5} \\ =3 \end{gathered}$$

It can be seen that three atoms of chlorine is present, hence the molecular formula of solute will be${\text{InCl}}_3$ .