Help with vapor pressure of solutions! I don\'t know what I\'m doing wrong here.

Question

Help with vapor pressure of solutions! I don't know what I'm doing wrong here.

The vapor pressure of ethanol (CH3OH) at 20 degree C is 44 mmHg, and the vapor pressure of methanol (CH3OH) at the same temperature is 94 mmHg. A mixture of 27.1 g of methanol and 48.1 g of ethanol is prepared and can be assumed to behave as an ideal solution. Calculate the vapor pressure of methanol and ethanol above this solution at 20 degree C. Methanol Ethanol Calculate the mole fraction of methanol and ethanol in the vapor above this solution at 20 degree C. Methanol Ethanol

Explanation / Answer

Logic:

Let

pT = total vapor pressure of the solution,

then

According to Raoult's law:

pT = pe + pm = peoXe + pmoXm

Where:

pe & pm are partial vapor pressures of ethanol and methanol, respectively.

peo & pmo are pure vapor pressures of ethanol and methanol, respectively.

Xe & Xm are the mole fractions of ethanol and methanol in the liquid phase, respectively.

However, according to Dalton's law:

pT = pe + pm = pTYe + pTYm

Where:

Ye & Ym are the mole fractions of ethanol and methanol in the vapour phase, respectively.

Solution:

Calculation of vapor pressure of solution:

First calculate the number of moles of ethanol and methanol.

no. of moles of ethanol = ne = mass of ethanol / molar mass of ethanol = 48.1 g / 46 g mol-1 = 1.04 mol

no. of moles of methanol = nm = mass of methanol / molar mass of methanol = 27.1g / 32 g mol-1 =0.84 mol

Total number of moles of mixture = 1.88

Now calculate the mole fractions.

mole fraction of ethanol = Xe = ne / ne + nm = 1.04 / 1.88 = 0.55

mole fraction of methanol = Xm = 1- Xe = 1 - 0.55 = 0.45

Now calculate the partial vapor pressures of ethanol and methanol.

pe = peoXe = 44 x 0.55 = 24.2 mm Hg

pm = pmoXm = 94 x 0.45= 42.3 mm Hg

Therefore:

pT = pe + pm = 24.2 + 42.3 = 66.5 mm Hg

Calculation of mole fraction of methanol in vapor phase:

According to Dalton's law:

pm = pTYm

or

Ym = pm / pT = 42.3 / 66.5 = 0.64

Note:

pe = peoXe = pTYe

pm = pmoXm = pTYm

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.