NEED THE COMPLETE AND CLEAR SOLUTION PLEASE thanks the vapor pressure of water a

Question

NEED THE COMPLETE AND CLEAR SOLUTION PLEASE thanks

the vapor pressure of water at 35°C is 42.175 mmHg. the vapor pressure of ethanol at 35° is 100.5 mmHg. What is the vapor pressure of a solution prepared by dissolving 250g of ethanol in 375g of water

A student needs to prepare an aqueous solution of sucrose at a temperature of 20o C with a vapor pressure of 15.0 mm Hg. How many grams of sucrose (mm = 342 g/mol) does she need if she uses 375 g H2O? (The vapor pressure of water at 20o C is 17.5 mm Hg.)

Explanation / Answer

Part A: We would use Raoult's law to solve this problem

Total partial pressure is sum total of all the components in solution

that is,

Ptotal = P(ethanol) + P(water)

We know,

partial pressure of each component = mole fraction x vapor pressure of pure component

Ptotal = (P*x) ethanol + (P*x) water

where,

P* = vapor pressure of pure components

x = mole fractions

mole fraction ethanol = moles of ethanol / total moles

mole fraction water = moles of water / total moles

Feeding the values given above,

mole fraction of ethanol = (250 g / 46.07 g/mol) / (250 g / 46.07 g/mol + 375 g / 18.02 g/mol) = 0.207

mole fraction of water = 1 - mole fraction of ethanol = 0.793

Ptotal = 42.175 x 0.793 + 100.5 x 0.207 = 54.25 mm Hg

Thus, the solution vapor pressure would be 54.25 mm Hg

Part B: Given P(solution) = 15.0 mm Hg

P(solution) = P(water) x mole fraction of water

moles of sucrose (x) = g sucrose / 342 g/mol

moles of water = 375 g / 18.02 g/mol = 20.81 mols

mole fraction of water = 20.81 / (x + 20.81)

thus,

P(solution) = 15.0 = 17.5 x 20.81/(x + 20.81)  

15x + 312.15 = 364.175

x = 3.47 = g/342 g/mol

g of sucrose = 1186.17g

Thus, 1186.17 g of sucrose would be needed to prepare this solution.

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