A solution is prepared by adding 30.00 g of lactose (milk sugar) to 110.0 g of water at 55 °C. The vapor pressure of pure water at 55 °C is 118.0 torr. The MW of lactose is 342.3 g/mol. What is the partial pressure of water above the

solution?

The answer is 116.3 if you don't feel like plugging the numbers in.

moles lactose = grams/molar mass

moles H2O = moles/molar mass
mole fraction H2O = moles H2O/total moles.
Psoln = XH2O*PoH2O

Well, let me break this down for you. You have lactose, the milk sugar, hanging out with water, having a little party at 55 °C. But we're not here to party, we're here to answer your question.

To find the partial pressure of water above the solution, we need to use something called Raoult's law. Don't worry, it's not that complicated.

Raoult's law states that the partial 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.

First, let's find the mole fraction of water in the solution. To do that, we need to know the moles of water and lactose.

The moles of water can be calculated using its molecular weight (MW) and mass. So, the moles of water = mass of water / MW of water.

Given that the MW of water is 18.0 g/mol and the mass of water is 110.0 g, we can calculate the moles of water.

moles of water = 110.0 g / 18.0 g/mol = 6.11 mol

Now, let's find the moles of lactose. Using the MW of lactose (342.3 g/mol) and the mass of lactose (30.00 g), we can calculate the moles of lactose.

moles of lactose = 30.00 g / 342.3 g/mol = 0.0875 mol

Now that we have the moles of water and lactose, we can find the mole fraction of water.

mole fraction of water = moles of water / (moles of water + moles of lactose)
= 6.11 mol / (6.11 mol + 0.0875 mol)
= 0.985

Remember Raoult's law? We can use the mole fraction of water to calculate the partial pressure of water above the solution.

partial pressure of water = mole fraction of water * vapor pressure of pure water at 55 °C

Given that the vapor pressure of pure water at 55 °C is 118.0 torr, we can calculate the partial pressure of water.

partial pressure of water = 0.985 * 118.0 torr
≈ 116.23 torr

So, the partial pressure of water above the solution is approximately 116.23 torr.

To find the partial pressure of water above the solution, you will need to use Raoult's Law, which states that the partial pressure of a component in a mixture is proportional to the mole fraction of that component in the mixture.

The mole fraction of water (Xwater) can be calculated by dividing the moles of water by the total moles of all components present in the solution.

First, we need to calculate the moles of lactose (nLactose) and water (nWater) in the solution.

Moles of lactose (nLactose) = mass of lactose / molecular weight of lactose
nLactose = 30.00 g / 342.3 g/mol
nLactose = 0.0876 mol

Moles of water (nWater) = mass of water / molecular weight of water
nWater = 110.0 g / 18.015 g/mol
nWater = 6.107 mol

Next, we calculate the total moles of all components (nTotal) in the solution.
nTotal = nLactose + nWater
nTotal = 0.0876 mol + 6.107 mol
nTotal = 6.1946 mol

Now, we can calculate the mole fraction of water (Xwater).
Xwater = nWater / nTotal
Xwater = 6.107 mol / 6.1946 mol
Xwater ≈ 0.9869

According to Raoult's Law, the partial pressure of water (Pwater) is equal to the mole fraction of water (Xwater) multiplied by the vapor pressure of pure water (Pwater pure).
Pwater = Xwater * Pwater pure
Pwater = 0.9869 * 118.0 torr
Pwater ≈ 116.48 torr

Therefore, the partial pressure of water above the solution is approximately 116.48 torr.

2.216

92.7