200. g of a nonelectrolyte is dissolved in 1.00 kg of water. the boiling point of the solution is then measured to be 101.5 degrees C. What is the molar mass of the compound? The Kb for water is 0.51 degrees Celsius/m
To find the molar mass of the compound, we need to use the formula for the boiling point elevation.
The boiling point elevation (∆Tb) is given by the equation:
∆Tb = Kb * m * i
Where:
∆Tb: boiling point elevation
Kb: boiling point elevation constant for the solvent (given as 0.51 °C/m for water)
m: molality of the solution (moles of solute per kg of solvent)
i: van't Hoff factor (number of particles the solute dissociates into)
In this case, since the compound is a nonelectrolyte, it does not dissociate into ions, so the van't Hoff factor (i) is equal to 1.
We know the boiling point elevation (∆Tb) is 101.5 °C, and the molality (m) is calculated by dividing the moles of solute (nonelectrolyte) by the mass of the solvent (water).
The moles of the solute can be calculated using the formula:
moles = mass / molar mass
Given that the mass of the nonelectrolyte is 200 g and the mass of the water is 1.00 kg (which is equal to 1000 g), we can solve for the moles of solute:
moles = 200 g / molar mass
Now, we can calculate the molality (m):
m = moles of solute / mass of water
m = (200 g / molar mass) / 1000 g
Before proceeding, let's rearrange the equation for molality (m) to solve for the moles of solute:
moles of solute = m * mass of water
moles of solute = m * 1000 g
Substituting this back into the equation for moles (moles = 200 g / molar mass), we have:
200 g / molar mass = m * 1000 g
Rearranging the equation to solve for molar mass:
molar mass = 200 g / (m * 1000 g)
Now, substitute the given values into the equation:
molar mass = 200 g / (101.5 °C / (0.51 °C/m) * 1000 g)
Simplifying, we have:
molar mass = 200 g / (101.5 / (0.51) * 1000)
molar mass = 200 g / (101.5 / 0.51 * 1000)
molar mass = 200 g / (199019.6078)
molar mass ≈ 1.0069 g/mol
Therefore, the molar mass of the compound is approximately 1.0069 g/mol.
delta T = Kb*m
Calculate m
moles = grams/molar mass
calculate molar mass.