The vapor above a mixture of pentane and hexane at room temperature contains 35.5% pentane by mass. What is the mass percent composition of the solution? Pure pentane and hexane have vapor pressures of 425 torr and 151 torr, respectively, at room temperature.

The mass percent of Pentane in solution is 16.49% The mass percent of Hexane in solution is 83.51%

Explanation:

Take 1 kg basis for the vapor: 35.5 mass% pentane = 355 g pentane with 645 g hexane. Convert these values to mol% using their molecular weights:

Pentane: Mp = 72.15 g/mol -> 355g/72.15 g/mol = 4.92mol

Hexane: Mh = 86.18 g/mol -> 645g/86.18 g/mol = 7.48mol

Pentane mol%: yp = 4.92/(4.92+7.48) = 39.68%

Hexane mol%: yh = 100 - 39.68 = 60.32%

Pp-vap = 425 torr = 0.555atm

Ph-vap = 151 torr = 0.199atm

From Raoult's law we know:  

Pp = xp Pp - vap = yp Pt                                       (1)

Ph = xh Ph - vap = yh Pt                                       (2)

Since it is a binary mixture we can write xh = (1 - xp) and yh = (1 - yp), therefore (2) becomes:

(1 - xp) Ph - vap = (1 - yp) Pt                                   (3)

Substituting (1) into (3) we get:

(1-xp) Ph - vap = (1 - yp) xp Pp - vap / yp            (4)

Rearrange for xp:

xp = Ph - vap / (Pp - vap/yp - Pp - vap + Ph - vap)      (5)

Subbing in the values we find:

Pentane mol% in solution: xp = 19.08%  

Hexane mol% in solution: xh = 80.92%

Now for converting these mol% to mass%, take 1 mol basis for the solution and multiplying it by molar mass:

mp = 0.1908 mol 72.15 g/mol

     = 13.766 g

mh = 0.8092 mol 86.18 g/mol

     = 69.737 g

Mass% of Pentane solution = 13.766/(13.766+69.737)

                                                       = 16.49%

Mass% of Hexane solution  = 83.51%

Do you have any options?

Use the universal gas law formula: pv = nrt now, the key word in this problem is stp, so at stp, temperature will always be 0 degrees celsius and pressure will always be 1.0 atm or 760 torr. given something is at stp, we already know the two variables pressure and temperature. the other thing we can find with the given information is moles. to find moles, just divide grams by molar mass of the element. 16.0g / 2(16.00)g/mol = 0.5 moles plug the values in to the equation pv = nrt (1.0 atm)( x ) = (0.5 )(0+273=273k) the r value is just a constant for when we use atm, liters, moles and kelvin. i'm assuming you want your answer in liters, but if you dont just move the decimal 3 to the right in your final answer. so when plugging these numbers in to your calculator and trying to find x, you get 11.20665 liters using significant figures the answer is 11.2 liters