Q101P - Chemistry: Molecular Nature Of Matter And Change

Question

The freezing point of benzene is 5.5^oC. What is the freezing point of a solution of 5.00 g of naphthalene (C₁₀H₈) in 444 g of benzene (of benzene = 4.90^oC/m)?

Step-by-Step Solution

Answer

The freezing point of the given solution is 5.07^oc.

Definition

The temperature at which the vapor pressure of a solution is equal to that of a pure solvent is known as the freezing point of a solution.

 

Concept: For finding the freezing point we will use the equations below.

 

$$\begin{gathered} ∆T_f=∆k_{f}m \\ ∆T_f-the freezing point of depression \\ {k}_f-the mola drop of the freezing point cons\tan t \\ m- is the solution molality \end{gathered}$$

Further solution

Given information: 

The freezing point of benzene$= 5.5{}^{°}C$

The naphthalene in solution's mass = 5.00g

mass of the solvent of benzene = 444g

                                                      = 0.44 kg

$k_f$ for benzene $=4.90 {}^{°}C/m$

$$\begin{gathered} \mathrm{Molality} \left(\mathrm{m}\right) \mathrm{of} \mathrm{the} \mathrm{solution}=\frac{\mathrm{moles} \mathrm{of} \mathrm{solute} \left(\mathrm{mol}\right)}{\mathrm{mass} \mathrm{of} \mathrm{solvent} \left(\mathrm{kg}\right)} \\ \mathrm{Moles} \mathrm{of} \mathrm{solute}=\frac{\mathrm{mass} \mathrm{of} \mathrm{solute}}{\mathrm{molar} \mathrm{mass} \mathrm{of} \mathrm{solute}} \\ \mathrm{m}=\frac{0.039}{.444} \\ =0.087\frac{\mathrm{mol}}{\mathrm{kg}}. \end{gathered}$$

$$\begin{gathered} \mathrm{m}=\frac{0.039}{.444} \\ =0.087\frac{\mathrm{mol}}{\mathrm{kg}} \\ {\mathrm{\Delta T}}_{\mathrm{f}}={\mathrm{k}}_{\mathrm{f}}\mathrm{m} \\ =4.90\times 0.087 \\ =0.426 \\ =0.{43}^{\mathrm{o}}\mathrm{c}. \\ {\mathrm{\Delta T}}_{\mathrm{f}}={\mathrm{T}}_{\mathrm{f}}\left(\mathrm{solvent}\right)+{\mathrm{T}}_{\mathrm{f}}\left(\mathrm{solution}\right) \\ {\mathrm{T}}_{\mathrm{f}}\left(\mathrm{solution}\right)={\mathrm{T}}_{\mathrm{f}}\left(\mathrm{solvent}\right)-\mathrm{\Delta }{\mathrm{T}}_{\mathrm{f}} \\ =5.5-0.43 \\ =5.{07}^{\mathrm{o}}\mathrm{c}. \end{gathered}$$