Question

A solution is composed of 1.90 mol cyclohexane (P°=97.6 torr) and 2.60 mol acetone (P°=229.5 torr). What is the mole fraction of cyclohexane in the vapor?

Answer 1

Answer:

$\chi_{c(g)} = 0.235$

Explanation:

The mole fraction of cyclohexane in the vapor $\chi_{c(g)}$ is:

$\chi_{c(g)} = \frac{P_{c}}{P_{T}}$                                                        (1)

where $P_{c}$: is the partial pressure of cyclohexane and $P_{T}$: is the total pressure.

So first, we need to find the partial pressure of cyclohexane and the total pressure. To do that, we can use Raoult's Law:

$P_{T} = P_{c} + P_{a} = \chi_{c}*P_{c}^{\circ} + \chi_{a}*P_{a}^{\circ}$ (2)

where Pc and Pa: are the partial pressures of cyclohexane and acetone, respectively, χc and χa: are the mole fractions of cyclohexane and acetone, respectively, and Pc⁰ = 97.6 torr and Pa⁰ = 229.5 torr.

To find the partial pressure of cyclohexane and acetone, we need to calculate its mole fractions:

$\chi_{c} = \frac{n_{c}}{n_{c} + n_{a}}$

where nc: are the moles of cyclohexane and na: are the moles of acetone.

$\chi_{c} = \frac{1.90 mol}{1.90 mol + 2.60 mol} = 0.42$    

$\chi_{a} = \frac{n_{a}}{n_{c} + n_{a}} = \frac{2.60 mol}{1.90 mol + 2.60 mol} = 0.58$  

Now, the total pressure can be calculated using equation (2):

$P_{T} = \chi_{c}*P_{c}^{\circ} + \chi_{a}*P_{a}^{\circ} = 0.42*97.6 torr + 0.58*229.5 torr = 40.99 torr + 133.11 torr= 174.10 torr$

Finally, the mole fraction of cyclohexane in the vapor (equation 1) is:

$\chi_{c(g)} = \frac{P_{c}}{P_{T}} = \frac{40.99 torr}{174.10 torr} = 0.235$

I hope it helps you!

Answer 2

Answer:

0.2990

Explanation:

All liquids intend to vaporize independent of the temperature if the pressure is higher enough. This pressure is called the vapor pressure. When it occurs, the liquid and the vapor phases will be in equilibrium, and so the fractions of the components of the liquids and the vapor can be calculated.

The molar fraction of the liquid (x) can be calculated by the composition, so, calling xc for cyclohexane, and ca for acetone:

xc = 1.90/(1.90 + 2.60) = 0.4222

xa = 1 - 0.4222 = 0.5778

The total pressure of the system (P) can be calculated by Dalton's Law:

P = Pc + Pa

Where Pc and Pa are the partial pressures of the components. The partial pressures can be calculated by the Raoult's Law:

Pc = xc*P°c

Pa = xa*P°a

Where P° is the vapor pressure, so:

P = xc*P°c + xa*P°a

P = 0.4222*97.6 + 0.5778*229.5

P = 137.8 torr

The molar fraction at the vapor phase (y) is the partial pressure divided by the total pressure:

yc = Pc/P

yc = (xc*P°c)/P

yc = (0.4222*97.6)/137.8

yc = 0.2990