53.94 g of a substance of molecular mass 182 is dissolved in 1000g of water at this temperature.the vapour presser of water is 17.5 mmhg .calculate the vapour presser of this dilute solution

17.4mmHg

To calculate the vapor pressure of the dilute solution, we can use Raoult's law, which states that the vapor pressure of a solution is directly proportional to the mole fraction of the solvent.

To start, we need to calculate the mole fraction of the solvent (water) in the solution. We can use the given mass of the solute and its molecular mass to find the number of moles of the solute.

Given:
Mass of solute (substance) = 53.94 g
Molecular mass of substance = 182 g/mol
Mass of solvent (water) = 1000 g
Vapor pressure of water = 17.5 mmHg

Let's calculate the number of moles of the solute (substance):
Number of moles = Mass / Molecular mass
Number of moles = 53.94 g / 182 g/mol
Number of moles ≈ 0.296 mol

Now, let's calculate the mole fraction of the solvent:
Mole fraction of water (solvent) = Moles of water / Total moles
Mole fraction of water ≈ 1000 g / (18 g/mol * 0.55 mol)
Mole fraction of water ≈ 0.901

Finally, we can use Raoult's law to calculate the vapor pressure of the dilute solution:
Vapor pressure of the dilute solution = Mole fraction of water * Vapor pressure of water
Vapor pressure of the dilute solution ≈ 0.901 * 17.5 mmHg

Therefore, the vapor pressure of the dilute solution is approximately 15.7745 mmHg.