For an equimolar solution of n-pentane and n-hexane

[missmaria]

Question:
For an equimolar solution of n-pentane and n-hexane, compute:
a) dew-point pressure at 120 F
b) bubble-point temperature at 1 atm
c) the vapor fraction at 120 F and 0.9 atm, and the mole fractions of the vapor and liquid phases

My attempt at a solution:
I calculated the saturation pressures of both pentane and hexane, 1.52 and 0.51, respectively. Now i don't know what to use for xi and yi. I think i need to compute the K value, but still, i am stuck. Can anyone help? thanks!

 

[CaptainPanic]

I think that the law of Raoult is the one you want to use... but I am not certain that you have enough data for question c). I'd expect a volume and a total amount of solution given there.

 

[oswaler]

a) To determine the dew-point pressure at 120 F, we need to use the Antoine equation for vapor pressure. The Antoine equation is given by log(P) = A - (B/(T+C)), where P is the vapor pressure, T is the temperature in Kelvin, and A, B, and C are constants specific to each substance. We can use the Antoine equation to calculate the vapor pressures of pentane and hexane at 120 F (49 C) and then use Raoult's law to determine the dew-point pressure.

For n-pentane at 120 F, the vapor pressure is 22.87 psi. For n-hexane at 120 F, the vapor pressure is 4.77 psi. Using Raoult's law, the dew-point pressure can be calculated as P = xpentane * Ppentane + xhexane * Phexane, where x is the mole fraction and P is the vapor pressure of each component. Since the solution is equimolar, the mole fractions are both 0.5. Therefore, the dew-point pressure at 120 F is (0.5 * 22.87) + (0.5 * 4.77) = 13.82 psi.

b) To determine the bubble-point temperature at 1 atm, we can use the same approach as in part a, but this time we will use the Antoine equation to calculate the temperature instead of the vapor pressure. At 1 atm, the vapor pressures of pentane and hexane are equal to their saturation pressures. Therefore, we can set the Antoine equation for both substances equal to 1 atm and solve for the temperature. This gives us a bubble-point temperature of 96.63 F (35.91 C).

c) To determine the vapor fraction at 120 F and 0.9 atm, we can use the same approach as in part a, but this time we will use the given pressure instead of the saturation pressure. The vapor fraction can be calculated using the following equation: y = (P - Pbubble) / (Pdew - Pbubble), where P is the given pressure, Pdew is the dew-point pressure calculated in part a, and Pbubble is the bubble-point pressure calculated in part b. This gives us a vapor fraction of 0.76.

To determine the mole fractions of the vapor and liquid phases, we can use the following equations:
xv