when themixture of two immicible liquids(water+nitro benzene) boils at 372k and the vapour pressure at this temp. are 97.7kpa.(water)and 3.6kpa(nitro benzene). calcutate the wht. % of nitro benzene in the vapour?

To determine the weight percentage of nitrobenzene in the vapor above a mixture of water and nitrobenzene at a boiling point of 372 K, we can use Dalton's Law of Partial Pressures along with the concept of vapor pressure. Let's break this down step by step.

Understanding the Components

We have two immiscible liquids: water and nitrobenzene. At 372 K, the vapor pressures are given as:

• Vapor pressure of water (P_w) = 97.7 kPa
• Vapor pressure of nitrobenzene (P_nb) = 3.6 kPa

Calculating Total Vapor Pressure

The total vapor pressure (P_total) above the mixture can be calculated by summing the individual vapor pressures:

P_total = P_w + P_nb = 97.7 kPa + 3.6 kPa = 101.3 kPa

Finding Mole Fractions

Next, we need to find the mole fractions of each component in the vapor phase. The mole fraction of each component in the vapor can be calculated using the formula:

X_component = P_component / P_total

For water:

X_w = P_w / P_total = 97.7 kPa / 101.3 kPa ≈ 0.964

For nitrobenzene:

X_nb = P_nb / P_total = 3.6 kPa / 101.3 kPa ≈ 0.036

Calculating Weight Percentages

Now, to find the weight percentage of nitrobenzene in the vapor, we need to convert the mole fractions to weight fractions. This requires the molar masses of the substances:

• Molar mass of water (H₂O) = 18 g/mol
• Molar mass of nitrobenzene (C₆H₅NO₂) = 123 g/mol

Next, we can calculate the weight of each component in the vapor:

Weight of water = X_w × Molar mass of water = 0.964 × 18 g/mol ≈ 17.352 g

Weight of nitrobenzene = X_nb × Molar mass of nitrobenzene = 0.036 × 123 g/mol ≈ 4.428 g

Final Calculation of Weight Percentage

The total weight of the vapor is the sum of the weights of both components:

Total weight = Weight of water + Weight of nitrobenzene = 17.352 g + 4.428 g ≈ 21.780 g

Now, we can find the weight percentage of nitrobenzene in the vapor:

Weight % of nitrobenzene = (Weight of nitrobenzene / Total weight) × 100

Weight % of nitrobenzene = (4.428 g / 21.780 g) × 100 ≈ 20.3%

Summary

Thus, the weight percentage of nitrobenzene in the vapor above the mixture at 372 K is approximately 20.3%. This calculation illustrates how vapor pressures and mole fractions can be utilized to derive weight percentages in a mixture of immiscible liquids.