The vapour pressure of pure benzene at 88 degree celsius is 960mm and that of toluene at the same temperature is 380 mm . At what mole fraction of benzene the mixture boils at 88 degree celsius?

To determine the mole fraction of benzene in a mixture that boils at 88 degrees Celsius, we can use Raoult's Law. This law states that the vapor pressure of a component in a solution is proportional to its mole fraction in the mixture. Given the vapor pressures of benzene and toluene at the boiling point, we can set up an equation to solve for the desired mole fraction.

Understanding the Concept

When a solution boils, the total vapor pressure equals the atmospheric pressure. In this case, since we are boiling the mixture at 88 degrees Celsius, we can assume that the atmospheric pressure is 760 mmHg (which is standard atmospheric pressure). We know:

• Vapor pressure of pure benzene (P_B) = 960 mmHg
• Vapor pressure of pure toluene (P_T) = 380 mmHg

Applying Raoult's Law

According to Raoult's Law, the total vapor pressure (P_total) of the mixture can be expressed as:

P_total = X_B * P_B + X_T * P_T

Here, X_B is the mole fraction of benzene, and X_T is the mole fraction of toluene. Since we are dealing with a mixture, we know that:

X_B + X_T = 1

We can replace X_T with (1 - X_B):

P_total = X_B * P_B + (1 - X_B) * P_T

Setting Up the Equation

We want the total vapor pressure to equal the atmospheric pressure (760 mmHg). So we can set up the equation:

760 = X_B * 960 + (1 - X_B) * 380

Now let's simplify this equation:

760 = X_B * 960 + 380 - X_B * 380

760 = X_B * (960 - 380) + 380

760 = X_B * 580 + 380

Now, subtract 380 from both sides:

380 = X_B * 580

Next, divide both sides by 580 to isolate X_B:

X_B = 380 / 580

Calculating the Mole Fraction

Now we can compute the value:

X_B = 0.6552 (approximately)

Final Thoughts

This means that the mole fraction of benzene in the mixture when it boils at 88 degrees Celsius is approximately 0.655, or 65.5%. This indicates that in the solution, benzene constitutes a significant portion of the mixture, allowing it to achieve the necessary vapor pressure for boiling at the specified temperature.