Question

How many grams of glucose (a nonelectrolyte, 180.2 g/mol) are dissolved in 575 g of water (18.02 g/mol) to produce a solution with a vapor pressure of 40.6 mmHg at 35°C? At 35°C, the vapor pressure of pure water is 42.2 mmHg.

Answer 1

There are 214 grams of glucose dissolved in 575 grams of water. To calculate the grams of glucose dissolved in water, use Raoult's law to find the mole fraction of water in the solution. Then, subtract the mole fraction of water from 1 to find the mole fraction of glucose. Convert the moles of glucose to grams by multiplying by the molar mass of glucose.

Step-by-step explanation:

To determine the number of grams of glucose dissolved in water, we need to use Raoult's law which states that the vapor pressure of a solvent above a solution is equal to the vapor pressure of the pure solvent multiplied by the mole fraction of the solvent in the solution.

Given that the vapor pressure of pure water is 42.2 mmHg and the vapor pressure of the solution is 40.6 mmHg, we can calculate the mole fraction of water in the solution:

Mole fraction of water = (Vapor pressure of water in solution)/(Vapor pressure of pure water)

= 40.6 mmHg/42.2 mmHg

= 0.9630

Since glucose is a nonelectrolyte, its mole fraction in the solution is equal to its mole fraction in the solvent:

Mole fraction of glucose = 1 - Mole fraction of water

= 1 - 0.9630

= 0.0370

Now, we can calculate the moles of glucose dissolved in the solution:

Moles of glucose = Mole fraction of glucose x Moles of solvent

= 0.0370 x (575 g / 18.02 g/mol)

= 1.189 mol

Finally, we can convert moles of glucose to grams:

Grams of glucose = Moles of glucose x Molecular mass of glucose

= 1.189 mol x 180.2 g/mol

= 214 g

Therefore, there are 214 grams of glucose dissolved in 575 grams of water.