Solution of methanol and ethanol are substantially ideal.
(a) Compute the vapour-liquid equilibria for this system at 1 and at 5 atm abs pressure, and plot xy and txy diagrams at each pressure
(b) For each pressure compute relative volatilities , and determine an average value.
( c ) Using Eq.with the average volatilities ,compare the values of y* at each value of x so obtained with those computed directly from the vapour pressures.
Oh, chemistry, my favorite subject! Let's dive into it with a touch of humor:
(a) Vapour-liquid equilibria, huh? More like a balancing act between the ethereal vapors and the liquid goodness. At 1 atm, the xy plot might resemble a swirly maze, with methanol and ethanol taking turns to escape into the vapor phase. At 5 atm, it might look like a chaotic dance party, with both molecules jostling to join the vapor crowd.
Now, the txy diagram is all about temperatures and compositions playing games. It's like trying to find the perfect balance between a cool breeze and a refreshing drink. At 1 atm, you may see methanol and ethanol doing a tango, gracefully transitioning from liquid to vapor. At 5 atm, it's a wild salsa, with molecules quickstepping between the two phases.
(b) Ah, the relative volatilities. Imagine methanol and ethanol having a competition on who can turn into vapor faster. It's like a race between a Flash and a speedster squirrel. Calculate their relative volatilities for each pressure, and then take an average. Maybe they'll surprise you with a tie, or maybe one will outshine the other like a superstar on a red carpet.
(c) Ah, the magic of equations! Use the average volatilities in an equation to compare the calculated values of y* (the composition of the vapor phase) with the values obtained directly from vapor pressures. Is it a perfect match, or will there be some surprises? It's like comparing a fortune teller's predictions with what actually happens. Will the equation have all the answers, or will it leave you scratching your head?
Remember, in the world of chemistry, nothing is ever as straightforward as it seems. But don't fret, my friend, that's what makes it all the more interesting!
To compute the vapor-liquid equilibria for the methanol and ethanol system at different pressures and create xy and txy diagrams, you need to follow these steps:
(a) Vapour-liquid Equilibria Calculation and Diagrams:
1. Collect the necessary data: You will need the Antoine equation parameters for methanol and ethanol to calculate their vapor pressures at different temperatures. The Antoine equation is commonly used to estimate vapor pressures.
2. Use the Antoine equation to calculate the vapor pressures of methanol and ethanol at different temperatures: The Antoine equation has the form: log(P) = A - (B / (T + C)), where P is the vapor pressure, T is the temperature in Celsius, and A, B, and C are Antoine equation parameters specific to each substance.
3. Convert the temperatures to Kelvin and calculate the vapor pressures of methanol and ethanol at each temperature using the Antoine equation.
4. Determine the mole fractions of methanol and ethanol in the liquid phase: Assume initially a feed mixture composition, for example, 50% methanol and 50% ethanol.
5. Apply the Rachford-Rice equation to calculate the vapor and liquid phase compositions at equilibrium: The Rachford-Rice equation relates the vapor and liquid phase compositions to the volatile components' physical quantities and the system's overall composition. This equation helps solve the phase equilibrium problem.
6. Plot xy and txy diagrams: Once you have obtained the vapor and liquid phase compositions at equilibrium, plot the xy diagram(s) by plotting the liquid phase mole fraction (x) of either methanol or ethanol on the x-axis and the vapor phase mole fraction (y) of the respective component on the y-axis. To plot txy diagram(s), instead of mole fractions, use temperatures on the x-axis and vapor phase mole fractions (y) on the y-axis.
(b) Relative Volatilities Calculation:
1. For each pressure, calculate the relative volatilities (α) using the average of the vapor pressures obtained for each component. Relative volatility measures the difference in vapor pressure between two components and is defined as α = (Pethanol / Pmethanol).
2. Compute the average value of the relative volatilities obtained at different pressures by taking the average of the relative volatilities calculated in step 1.
(c) Comparing y* values:
1. Use the average relative volatilities obtained in step 2 to calculate the values of y* for each value of x. The equation to use is y* = α * x / (1 + (α - 1) * x).
2. Compare the values of y* obtained in step 1 with those computed directly from the vapor pressures (Pethanol / P), where P is the total pressure.
By following these steps, you will be able to compute the vapor-liquid equilibria, plot xy and txy diagrams, calculate relative volatilities, and compare y* values for the methanol and ethanol system at different pressures.