Calculate the vapor pressure of a solution containing equal masses of benzene and toluene at 313 K, if the vapor pressures of pure benzene and toluene are 160 mm and 60 mm, respectively, at 313 K.

Question

11-10-2023
Chemistry

High School

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Calculate the vapor pressure of a solution containing equal masses of benzene and toluene at 313 K, if the vapor pressures of pure benzene and toluene are 160 mm and 60 mm, respectively, at 313 K.

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Neetoo Neetoo · Answer 1 · 2024-01-05T03:04:53-05:00

The vapour pressure of the solution containing equal masses of benzene and toluene at 313 K is [tex]$ 110 \, \text{mm} $[/tex].

To find the vapor pressure of the solution, we can use Raoult's Law, which states that the partial vapor pressure of each component of an ideal mixture of liquids is equal to the vapor pressure of the pure component multiplied by its mole fraction in the mixture.

Given that equal masses of benzene and toluene are used, their mole fractions are equal. Let's denote the vapor pressure of benzene as [tex]$ P_B $[/tex], vapor pressure of toluene as [tex]$ P_T $[/tex], and the total vapor pressure of the solution as [tex]$ P_{\text{total}} $[/tex]. According to Raoult's Law,

[tex]\[ P_{\text{total}} = x_BP_B + x_TP_T \][/tex]

Since the masses are equal, the mole fractions [tex]($ x_B $[/tex] and [tex]$ x_T $)[/tex] for benzene and toluene are both ( 0.5 ). Substituting the given values, [tex]$ P_B = 160 $[/tex]mm and [tex]$ P_T = 60 $[/tex]mm, we get:

[tex]\[ P_{\text{total}} = (0.5 \times 160) + (0.5 \times 60) \]\[ P_{\text{total}} = 80 + 30 \]\[ P_{\text{total}} = 110 \, \text{mm} \][/tex]

Hence, the vapor pressure of the solution is [tex]$ 110 \, \text{mm} $[/tex].

The given statement "Calculate the vapor pressure of a solution containing equal masses of benzene and toluene at 313 K, if the vapor pressures of pure benzene and toluene are 160 mm and 60 mm respectively at 313 K" is true because it applies Raoult's Law to determine the total vapor pressure of the solution based on the vapor pressures and mole fractions of the pure components, which is a valid method in ideal solutions.