A solution of pentane and ethanol (CH3CH2OH)that is 50.% pentane by mass is boiling at 57.2°C. The vapor is collected and cooled until it condenses to form a new solution. Calculate the percent by mass of pentane in the new solution. Here's some data you may need:

normal boiling point density vapor pressure at
57.2°C
pentane 36.°C 0.63gmL 1439.torr
ethanol 78.°C 0.79gmL 326.torr
Be sure your answer has 2 significant digits.
dont round during math only for answer!
Note for advanced students: you may assume the solution and vapor above it are ideal.

The correct answer is 81.52 percent.

Explanation:

Based on the given information, the boiling point of pentane is 36 degree C and the boiling point of ethanol is 78 degree C. The density of pentane and ethanol is 0.63 g/ml and 0.79 g/ml. The vapor pressure of pentane at 57.2 degree C is 1439 torr and the vapor pressure of ethanol at 57.2 degree C is 326 torr.  

In the given case, 50 percent pentane by mass signifies that mass of pentane is 50 grams. Thus, the mass of ethanol will be 100-50 = 50 grams.  

The moles or n can be calculated by using the formula,  

n = weight/molecular mass

The molecular mass of pentane is 72.15 g per mol and the molar mass of ethanol is 46.07 g/mol.  

The moles of pentane is,  

= 50 g/72.15 g/mol = 0.6930 mol

The moles of ethanol is,  

= 50 g/46.07 g/mol = 1.0853 mol

The mole fraction of pentane is,  

= 0.6930 mol / (0.6930 + 1.0853) mol = 0.3897  

The mole fraction of ethanol is,  

= 1.0853 mol / (0.6930 + 1.0853) mol = 0.6103

Now the vapor pressure of solution will be,  

= pressure of pentane * mole fraction of pentane + pressure of ethanol * mole fraction of ethanol

= (1439 * 0.3897) + (326 * 0.6103)

= 759.736 torr

The vapor pressure of pentane within the solution,  

= vapor pressure of pentane * mole fraction of pentane

= 1439 torr * 0.3897

= 560.778 torr

The fraction of pentane is,  

= 560.778 / 759.736 = 0.738

Let us assume that the total mole is 1, the mole fraction of pentane is 0.738, so the mole fraction of ethanol will become, 1-0.738 = 0.262

The mass of pentane = 0.738 * 72.15 = 53.2467

The mass of ethanol = 0.262 * 46.07 = 12.07034

The percent by mass of pentane in new solution will be,  

Mass% = mass of pentane/Total mass * 100%

= 53.2467/(53.2467 + 12.07034) * 100%

= 53.2467/65.31704 * 100 %

= 81.52 %