Density and Molarity Relationship

The first step in solving this problem is to understand the relationship between molarity and density. The density of a solution is directly related to its molarity. Molarity is defined as the number of moles of solute per liter of solution, while density is the mass of the solution per unit volume. Therefore, we can use the given density to calculate the molarity of the solution.

Calculating Molarity

To calculate the molarity, we need to convert the given density to grams per liter. The density of the solution is given as 1.063 g/cm3. Since 1 cm3 is equal to 1 mL, we can convert the density to grams per liter by multiplying it by 1000.

Density = 1.063 g/cm3 x 1000 cm3/L = 1063 g/L

Next, we need to calculate the molar mass of K2CrO4, which is the solute in the solution. The molar mass of K2CrO4 is calculated as follows:

K2CrO4 = (2 x atomic mass of K) + atomic mass of Cr + (4 x atomic mass of O)

The atomic masses are as follows:

Atomic mass of K = 39.10 g/mol
Atomic mass of Cr = 52.00 g/mol
Atomic mass of O = 16.00 g/mol

Molar mass of K2CrO4 = (2 x 39.10 g/mol) + 52.00 g/mol + (4 x 16.00 g/mol) = 194.20 g/mol

Now, we can calculate the molarity using the formula:

Molarity = (mass of solute in grams) / (molar mass of solute in g/mol) / (volume of solution in liters)

We are given the molarity as 0.438 M, and we have calculated the molar mass as 194.20 g/mol. We can rearrange the formula to solve for the volume of the solution in liters:

Volume of solution = (mass of solute in grams) / (molar mass of solute in g/mol) / (molarity)

Using the given density, we can calculate the mass of the solution as follows:

Mass of solution = density x volume of solution

Since the volume of solution is the same as the volume of water, we can substitute the given density and volume into the equation:

Mass of solution = 1.063 g/cm3 x volume of water

Now, we can substitute the mass of the solution, molar mass of K2CrO4, and molarity into the volume equation:

1.063 g/cm3 x volume of water = (mass of solute in grams) / (molar mass of solute in g/mol) / (molarity)

Calculating Vapour Pressure of Water

To calculate the vapor pressure of water above this solution, we can use Raoult's law. Raoult's law 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.

The mole fraction of the solvent can be calculated using the molarity of the solution. The mole fraction is defined as the moles of solvent divided by the total moles of solute