Im not sure how to answer any of these questions, can someone explain each stage?

Question

Acetic acid and acetone are used for the purification of PLA production. A liquid mixture of acetic acid and acetone is in vapour liquid equilibria (VLE) at 100 °C. The mole fraction of acetic acid in the liquid phase is 0.4. Assuming ideal gas and ideal solution conditions, and using Antoine Equation to estimate the saturated vapor pressure, determine:

The fugacity of the acetic acid

The pressure of the system

The vapour phase mole fraction of acetic acid

The percentage, %, of the fluid that is in the vapour phase when the total mole fraction of acetic acid in the entire system is 0.3

The K-value for acetic acid

Answer 1

This problem involves the use of thermodynamic principles and equations to calculate various properties of a VLE mixture of acetic acid and acetone at 100°C. Here are the steps to solve each part of the problem:

1. The fugacity of the acetic acid: The fugacity of a component in a mixture is a measure of its effective pressure, which takes into account its deviation from ideal behavior. For an ideal gas, the fugacity is equal to the pressure. However, in a mixture, the fugacity depends on the composition and interactions between the components. In this case, we are given that the mixture is at VLE, so the fugacity of the acetic acid in the liquid phase is equal to the fugacity of the acetic acid in the vapor phase. Using the Antoine equation, we can estimate the saturation pressure of acetic acid at 100°C. Then, we can use the vapor-phase mole fraction of acetic acid (which we'll determine in part 3) to calculate the partial pressure of acetic acid in the vapor phase. Finally, we can use the definition of fugacity to calculate the fugacity of acetic acid in the vapor phase.
2. The pressure of the system: We can use the ideal gas law to relate the pressure, volume, and number of moles of the mixture. Since the problem statement doesn't give us any information about the volume or number of moles, we can assume that the volume is fixed and that the mole fraction of acetone is (1 - 0.4) = 0.6. Then, we can use the ideal gas law to solve for the pressure.
3. The vapor phase mole fraction of acetic acid: The vapor phase mole fraction of acetic acid is related to the liquid phase mole fraction by the equilibrium constant, which is also known as the K-value. We can assume that the mixture is ideal and use Raoult's law to express the K-value in terms of the vapor pressures of acetic acid and acetone. Then, we can use the mole fraction of acetic acid in the liquid phase and the K-value to solve for the mole fraction of acetic acid in the vapor phase.
4. The percentage of the fluid in the vapor phase: The total mole fraction of acetic acid in the mixture is given as 0.3. We can use the mole fraction of acetic acid in the vapor phase (which we calculated in part 3) to solve for the mole fraction of acetic acid in the liquid phase. Then, we can use the definition of mole fraction to calculate the total number of moles of the mixture. Finally, we can use the mole fraction of acetic acid in the vapor phase and the total number of moles to calculate the number of moles of the mixture in the vapor phase, and express it as a percentage of the total number of moles.
5. The K-value for acetic acid: As mentioned earlier, the K-value is related to the vapor pressures of the components in the mixture. For an ideal mixture, the K-value is equal to the ratio of the vapor pressure of the component to the saturation pressure of the pure component. In this case, we are given the mole fraction of acetic acid in the liquid phase, so we can use Raoult's law to calculate the vapor pressure of acetic acid in the mixture. Then, we can use the Antoine equation to estimate the saturation pressure of pure acetic acid at 100°C and calculate the K-value using the equation mentioned earlier.