Again, I know I keep posting questions but I'm begging you for help.
At 25°C the vapour pressure of pure pentane is 511 torr and that of hexane is 150. torr.
What is the mole fraction of pentane in a pentane-hexane solution that has a vapour pressure of 339 torr at 25°C?
What is the mole fraction of hexane in the vapour that is in equilibrium with this solution?
(Assume ideal gas behaviour.)
To find the mole fraction of pentane in the solution and the mole fraction of hexane in the vapor, you can use Raoult's Law.
Raoult's Law states that the partial pressure of a component in a solution is directly proportional to its mole fraction in the solution.
Let's denote the mole fraction of pentane as x_pentane and the mole fraction of hexane as x_hexane.
1. Mole fraction of pentane in the solution:
According to Raoult's Law, the vapor pressure of a solution can be calculated as the sum of the vapor pressures of the individual components multiplied by their mole fractions:
P_solution = P_pentane * x_pentane + P_hexane * x_hexane
Given:
P_solution = 339 torr
P_pentane = 511 torr
P_hexane = 150 torr
By rearranging the equation, we can solve for x_pentane:
x_pentane = (P_solution - P_hexane * x_hexane) / P_pentane
2. Mole fraction of hexane in the vapor:
For the vapor in equilibrium with the solution, the total vapor pressure is equal to the partial pressure of pentane plus the partial pressure of hexane:
P_vapor = P_pentane * x_pentane + P_hexane * x_hexane
Again, rearranging the equation, we can solve for x_hexane:
x_hexane = (P_vapor - P_pentane * x_pentane) / P_hexane
Remember to convert the vapor pressure values to the same unit (torr) before performing the calculations.
Hope this helps! Let me know if you have any further questions.
No problem at all! I'm here to help you with your questions. For this problem, we can use Raoult's Law to find the mole fraction of pentane in the solution and the mole fraction of hexane in the vapor.
Raoult's Law states that the partial pressure of each component in an ideal solution is proportional to its mole fraction in the solution. Mathematically, it can be expressed as:
P_A = X_A * P_A^o
where P_A is the partial pressure of component A in the solution, X_A is the mole fraction of component A in the solution, and P_A^o is the vapor pressure of pure component A.
Let's use this equation to find the mole fraction of pentane (Xpentane) in the solution:
Given:
Ppentane^o = 511 torr
Phexane^o = 150 torr
Psolution = 339 torr
Using Raoult's Law for pentane:
Ppentane = Xpentane * Ppentane^o
Since the total pressure in the solution is the sum of the partial pressures of pentane and hexane, we can calculate the mole fraction of pentane as follows:
Ppentane + Phexane = Psolution
Substituting the values:
(Xpentane * Ppentane^o) + (Xhexane * Phexane^o) = Psolution
Since we know the vapor pressure of the two components, we can rewrite it as:
(Xpentane * 511 torr) + (Xhexane * 150 torr) = 339 torr
Now we have an equation with two unknowns (Xpentane and Xhexane), but since the sum of the mole fractions in a solution is equal to 1, we can subtract Xpentane from 1 to express Xhexane in terms of Xpentane:
Xhexane = 1 - Xpentane
Now we can substitute this value back into the equation:
(Xpentane * 511 torr) + ((1 - Xpentane) * 150 torr) = 339 torr
Now we can solve this equation to find the value of Xpentane.