Cyclohexane (C_6H_12) was mixed with an unknown volatile organic compound to pro

Question

Cyclohexane (C_6H_12) was mixed with an unknown volatile organic compound to produce a new solution. At 25 degreeC the vapor pressure of pure cyclohcxane is 312 torr and the vapor pressure of the pure unknown is 39 torr. It was found that when 51.50 g of cyclohcxane was added to 41.69 g of the unknown, the resulting total vapor pressure of the solution was found to be 193 torr. What is the molecular weight of the unknown? If you couldn't find the number ot moles, determine the molecular weight using 0.316 moles.

Explanation / Answer

cyclohexane is mixed with unknown volatile organic compound to produce new solution . At 25oC the vapour pressure of pure cyclohexane is 312 torr and vapour pressure of pure unknown compound is 39 torr. It was found that when 51.5 g of cyclohexane was added to the 41.69 g of unknown the vapour pressure of resulting solution was found to be 193 torr, what is the molecular weight of unknown?

If you couldn’t find number of moles determine molecular weight using 0.316moles.

Answer:

Vapour pressure of Pure cyclohexane: 312 torr

Vapour pressure of Pure unknown compound : 39 torr

No. of moles of cyclohexane in mixture : 51.5/84.16 = 0.6119

Vapour pressure of resulting mixture is : 193 torr

Ptotal = P°cyclohex cyclohex + P°unk unk

Where, P°cyclohex = vapour pressure of pure cyclohexane

              P°unk = vapour pressure of pure Unknown compound

              cyclohex = mole fraction of cyclohexane (moles of cyclohexane/moles of          cyclohexane +Moles of unknown)

           unk = mole fraction of unknown (moles of Unknowns/moles of          cyclohexane +Moles of unknown)

by substituting the values in abouve equation

193 = 312 * (0.6119/0.6119+Xunk)+ 39 * (Xunk/0.6119+Xunk)

193 = (97.3128/0.6119+Xunk) + (39 * Xunk/0.6119+Xunk)

193 = (97.3128 + 39* Xunk)/(0.6119+Xunk)

193 *(0.6119+Xunk) = (97.3128 + 39* Xunk)

118.09 + 193 Xunk = 97.3128 + 39Xunk

20.7839 = 157 Xunk

Xunk = 0.132

Molecular weight of unknown is = weight of unknown / total number of moles of unknown,

Molecular weight of unknown is = 41.61/0.132

Molecular weight of unknown is = 315.22 g/mol

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