Vapor pressure in equilibrium

In summary, the student is struggling with a problem given by their teacher, which involves finding the mole fraction of a solution at a certain temperature. The student has attempted to use Raoult's law but has not been successful. They are hoping for someone to provide an answer to their question.
  • #1
filou
1
0
Hi
I have difficulties with a problem that my teacher gave in assignement. Teh teacher said it was a bit higher than our level but I think it far above what I am able to do! so here it is :

The vapor pressure in equilibrium with pentane-hexane solution at 25°C has a mole fraction of pentane equal to 0.15 at that temperature. What is the mole fraction in the solution?

Up to now I found that the vapor pressure of pentane is 511 torr and the one of hexane is 150 torr. I think that I should use Raoult's law but my attempts were not concluant... I hope someone will be able to answer my question.
 
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  • #2
[tex]P^o (P) = 511~,~~P^o (H) = 150 [/tex]

[tex]P(P) = \chi (P.solution) * P^o (P)= 0.15P(tot) [/tex]

[tex]=>~0.15P(tot) = \chi (P)* 511 [/tex]

[tex]And~0.85P(tot) = (1 - \chi(P))*150 [/tex]
 
Last edited:
  • #3


Hi there,

I can understand your difficulties with this problem. It does involve some advanced concepts in chemistry, but with some practice and understanding, I am sure you will be able to solve it.

First, let's review what vapor pressure and equilibrium mean. Vapor pressure is the pressure exerted by the vapor of a liquid in a closed container at a given temperature. In equilibrium, the rate of evaporation of the liquid is equal to the rate of condensation of the vapor, resulting in a constant vapor pressure.

In this problem, we are dealing with a solution of pentane and hexane, which are both volatile liquids. In order to solve this problem, we need to use Raoult's law, which states that the vapor pressure of a solution is equal to the mole fraction of the solvent (in this case, pentane) multiplied by the vapor pressure of the pure solvent. This can be written as P = Xsolvent * P°solvent, where P is the vapor pressure of the solution, Xsolvent is the mole fraction of the solvent, and P°solvent is the vapor pressure of the pure solvent.

So, using the values given in the problem, we can set up the equation as follows:

P = (0.15)(511 torr) + (x)(150 torr)

Where x is the unknown mole fraction of hexane in the solution.

To solve for x, we can rearrange the equation to get:

x = (P - 0.15 * 511 torr) / 150 torr

Now, we know that at equilibrium, the vapor pressure of the solution is equal to the vapor pressure of the pure solvent (P = P°solvent). Therefore, we can substitute P with 511 torr in the equation above, and solve for x.

x = (511 torr - 0.15 * 511 torr) / 150 torr

x = 0.85

So, the mole fraction of hexane in the solution is 0.85.

I hope this helps you understand the problem and how to solve it. With practice, you will become more comfortable with these types of problems. Good luck!
 

1. What is vapor pressure in equilibrium?

Vapor pressure in equilibrium is the pressure exerted by the vapor of a substance in a closed system when the rate of condensation and evaporation are equal.

2. How is vapor pressure in equilibrium determined?

Vapor pressure in equilibrium can be determined by measuring the pressure of the vapor in a closed system at a constant temperature.

3. What factors affect vapor pressure in equilibrium?

The factors that affect vapor pressure in equilibrium include temperature, intermolecular forces, and the nature of the substance.

4. How does temperature affect vapor pressure in equilibrium?

As temperature increases, the vapor pressure in equilibrium also increases. This is because higher temperatures increase the kinetic energy of the molecules, leading to a higher rate of evaporation and therefore a higher vapor pressure.

5. What is the significance of vapor pressure in equilibrium?

Vapor pressure in equilibrium is important in understanding the behavior of substances in a closed system. It is also used in various industrial processes, such as distillation, to separate mixtures based on their different vapor pressures.

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