pressure over ideal binary liquid mixture containing 10 moles each of liquid A and B is decreased isothermally.if pA=200mm of Hg and pB=100mm of Hg. find pressure at which half of liquid is converted into vapour

To find the pressure at which half of the liquid in an ideal binary mixture is converted into vapor, we can use Raoult's Law. This law states that the partial vapor pressure of each component in an ideal solution is proportional to its mole fraction in the liquid phase. Let's break this down step by step.

Understanding the Components

In our scenario, we have two liquids, A and B, each with 10 moles. The given vapor pressures at a certain temperature are:

• pA = 200 mm Hg
• pB = 100 mm Hg

Calculating Initial Conditions

Initially, the total number of moles in the mixture is:

Total moles = 10 moles of A + 10 moles of B = 20 moles

Finding Mole Fractions

When half of the liquid is converted into vapor, we will have 10 moles of vapor. The remaining liquid will consist of 10 moles of A and 10 moles of B, so the mole fractions in the liquid phase will be:

• Mole fraction of A (XA) = moles of A / total moles of liquid = 10 / 20 = 0.5
• Mole fraction of B (XB) = moles of B / total moles of liquid = 10 / 20 = 0.5

Applying Raoult's Law

According to Raoult's Law, the total vapor pressure (P) of the system can be calculated as:

P = pA * XA + pB * XB

Substituting the values we have:

P = (200 mm Hg * 0.5) + (100 mm Hg * 0.5)

P = 100 mm Hg + 50 mm Hg = 150 mm Hg

Final Result

The pressure at which half of the liquid mixture is converted into vapor is 150 mm Hg. This pressure reflects the balance between the vapor pressures of the two components in the mixture when they are equally represented in the liquid phase.

Conclusion

This example illustrates how Raoult's Law can be applied to binary mixtures to determine the vapor pressure at specific conditions. Understanding these principles is crucial for various applications in chemistry and chemical engineering, especially in distillation processes and other separation techniques.