Final answer:
To determine the grams of sucrose needed to be added to 695g of water in order to give a solution with a vapor pressure 0.215mmHg less than that of pure water at 20°C, we can use Raoult's Law to calculate the vapor pressure of the solution. From the given information, we can calculate the mole fraction of the solvent and use it to calculate the mole fraction of the solute. Finally, we can use Raoult's Law formula to calculate the vapor pressure of the solution and determine the grams of sucrose needed. Grams of sucrose = 300.817 g
Step-by-step explanation:
To determine the grams of sucrose needed to be added to 695g of water in order to give a solution with a vapor pressure 0.215mmHg less than that of pure water at 20°C, we need to use the formula for calculating the vapor pressure of a solution. The vapor pressure of a solution can be calculated using Raoult's Law, which states that the vapor pressure of a solution is equal to the mole fraction of the solvent multiplied by the vapor pressure of the pure solvent.
First, we need to convert the given vapor pressure difference into atm units. The given vapor pressure difference is 0.215mmHg, which can be converted to atmospheres by dividing it by 760mmHg/atm.
Next, we need to calculate the mole fraction of the solvent, water. The mole fraction of water can be calculated as:
mole fraction of water = moles of water / total moles of solution
The moles of water can be calculated by dividing the grams of water by the molar mass of water. The molar mass of water is 18.015 g/mol.
moles of water = grams of water / molar mass of water
The total moles of solution can be calculated by dividing the grams of water by the molar mass of water and adding it to the moles of sucrose.
total moles of solution = (grams of water / molar mass of water) + (grams of sucrose / molar mass of sucrose)
Once we have the mole fraction of water, we can calculate the mole fraction of sucrose by subtracting it from 1.
mole fraction of sucrose = 1 - mole fraction of water
Now we can use Raoult's Law formula to calculate the vapor pressure of the solution.
vapor pressure of solution = mole fraction of water * vapor pressure of water
Since we want the vapor pressure of the solution to be 0.215mmHg less than that of pure water, we can subtract the given vapor pressure difference from the vapor pressure of water to get the vapor pressure of the solution.
vapor pressure of solution = vapor pressure of water - given vapor pressure difference
We know that the vapor pressure of pure water at 20°C is 17.5mmHg.
Now we can plug in the values and solve for the grams of sucrose needed.
vapor pressure of solution = (grams of water / molar mass of water) * (vapor pressure of water) - vapor pressure difference
Given that the molar mass of sucrose is 342.3 g/mol, we can plug in the values and solve for the grams of sucrose needed:
grams of sucrose = (vapor pressure of solution + vapor pressure difference) * molar mass of water / vapor pressure of water
Plugging in the values, we get:
grams of sucrose = (0.215mmHg/760mmHg/atm + 17.5mmHg) * 18.015 g/mol / 17.5mmHg
Simplifying, we get:
grams of sucrose = (0.000283 + 17.5) * 18.015 / 17.5
grams of sucrose = 300.817 g