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A chemist wants to determine the molar mass of a naturally occurring substance isolated from spearmint. She adds 4.231 g of this substance to 25.00 g of acetone (C3H6O; molar mass 58.08 g/mol). The vapor pressure of the solution is determined to be 0.2474 atm at 25°C. If the vapor pressure of pure acetone at this temperature is 0.2630 atm, what is the mole fraction of the solvent in this solution? Give your answer to four significant digits.

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The molar mass is 151 g/mol.

What is Raout's law?

The Raout's law is used to describe the relationship between the partial pressures of the solution and that of the solute. Given that we have the partial pressure of the pure solvent is 0.2630 atm and the partial pressure of the solution is 0.2474 atm

Using Raout's law;

Psolution = Psolvent * mole fraction

Number of acetone = 25.00 g/58.08 g/mol = 0.43 moles

Number of substance =  4.231 g/ MM

Where MM = molar mass

0.2474 atm = 0.2630 atm * Moles of acetone/Total number of moles

Let the Moles of substance be x

0.2474 atm = 0.2630 atm *  0.43/0.43 + x

0.2474  = 0.113/0.43 + x

0.2474(0.43 + x) = 0.113

0.106 + 0.2474x =  0.113

0.2474x = 0.113 - 0.106

x = 0.113 - 0.106/0.2474

x = 0.028

Then;

x = 4.231 / MM

0.028 =  4.231 / MM

MM = 4.231 / 0.028

MM = 151 g/mol

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