Question

What is the molecular weight of sulfur if $35.5$ grams of sulfur dissolve in $100.0$ grams of ${\mathrm{CS}}_2$ to produce a solution that has a boiling point of $49.48°\mathrm{C}$?

Answer 1

Step 1: Given,

$$\begin{gathered} \mathrm{Mass}\mathrm{of}\mathrm{sulfur}=35.5\mathrm{g} \\ \mathrm{Mass}\mathrm{of}{\mathrm{CS}}_2=100.0\mathrm{g}=0.1000\mathrm{Kg} \\ \mathrm{Boiling}\mathrm{point}\mathrm{of}\mathrm{solution}=49.48{}^{\mathrm{o}}\mathrm{C} \end{gathered}$$

Step 2: Expression for the calculation of elevation in boiling point is:

$$\begin{gathered} {\mathrm{\Delta T}}_{\mathrm{b}}={\mathrm{k}}_{\mathrm{b}}\times \mathrm{m} \\ {\mathrm{T}}_{\mathrm{b}}-{\mathrm{T}}_{\mathrm{b}}^{\mathrm{o}}=\frac{{\mathrm{k}}_{\mathrm{b}}\times {\mathrm{w}}_2}{\mathrm{M}\times {\mathrm{w}}_1(\mathrm{in}\mathrm{Kg})} \end{gathered}$$

Where,

• ${\mathrm{\Delta T}}_{\mathrm{b}}$ is change in boiling point or boiling point elevation
• ${\mathrm{T}}_{\mathrm{b}}^{\mathrm{o}}$ is boiling temperature of ${\mathrm{CS}}_2=46.2^{\mathrm{o}}\mathrm{C}$
• ${\mathrm{T}}_{\mathrm{b}}$ is boiling temperature of solution
• ${\mathrm{K}}_{\mathrm{b}}$ is boiling point constant for water $=2.37{}^{\mathrm{o}}\mathrm{C}.\mathrm{kg}.{\mathrm{mol}}^{-1}$
• $\mathrm{m}$ is molality
• ${\mathrm{w}}_1$ is mass of solvent ${\mathrm{CS}}_2$
• ${\mathrm{w}}_2$ is mass of solute (sulfur)
• $\mathrm{M}$ is molar mass of solute (sulfur)

Step 3: Calculation of molecular weight of sulfur.

$$\begin{gathered} {\mathrm{T}}_{\mathrm{b}}-{\mathrm{T}}_{\mathrm{b}}^{\mathrm{o}}=\frac{{\mathrm{k}}_{\mathrm{b}}\times {\mathrm{w}}_2}{\mathrm{M}\times {\mathrm{w}}_1(\mathrm{in}\mathrm{Kg})} \\ (49.48-46.2){}^{\mathrm{o}}\mathrm{C}=\frac{2.37{}^{\mathrm{o}}\mathrm{C}.\mathrm{kg}.{\mathrm{mol}}^{-1}\times 35.5\mathrm{g}}{\mathrm{M}\times 0.1000\mathrm{Kg}} \\ \mathrm{M}=256.51\mathrm{g}.{\mathrm{mol}}^{-1} \end{gathered}$$

Therefore, the molecular weight of sulfur is $\mathbf{256}\mathbf{.}\mathbf{51}\mathbf{}\mathbf{g}\mathbf{.}{\mathbf{mol}}^{\mathbf{-}\mathbf{1}}$.