what is the molecular mass of a solute if a solution containing 150 g of that solute

and 1.0 kg of water has a boiling point of
102.0 degree c? (Kb= 0.512 degree C/m)

Technically, the problem doesn't specify if it is an ionic or a molecular compound. Without that information you can't work the problem. When the problem doesn't say, I always assume it is molecular and not ionic.

delta T = Kb*molality
Solve for molality.

molality = moles/kg solvent.
Solve for moles.

moles = grams/molar mass
Solve for grams.

To find the molecular mass of the solute, you will need to use the equation for boiling point elevation:

ΔTb = Kb * m

Where:
ΔTb is the change in boiling point (in degrees Celsius)
Kb is the molal boiling point constant (in degrees Celsius per molal)
m is the molality (in molal)

First, let's calculate the change in boiling point (ΔTb). We are given that the solution's boiling point is 102.0 °C, while the boiling point of pure water is 100.0 °C.

ΔTb = 102.0 °C - 100.0 °C = 2.0 °C

Next, we need to calculate the molality (m). Molality is defined as the number of moles of solute per kilogram of solvent. Given that the solution contains 1.0 kg of water, we can assume the mass of the solute is 150 g.

m = moles of solute / mass of water (in kg)

First, convert the mass of water to kilograms:
mass of water = 1.0 kg

Next, convert the mass of the solute to moles using the molecular mass (M):

moles of solute = mass of solute / M

Since we want to find the molecular mass, rearrange the equation:

M = mass of solute / moles of solute

M = 150 g / (moles of solute)

Now, we need to find the moles of solute using the molality (m):

m = moles of solute / mass of water (kg)

Rearrange the equation to find the moles of solute:

moles of solute = m * mass of water (kg)

Now, substitute this into the equation for molecular mass:

M = 150 g / (m * mass of water (kg))

Finally, substitute the values into the equation and solve for M:

M = 150 g / (m * 1.0 kg)

Note that we are not given the molality (m). To calculate it, we need to use the equation:

m = ΔTb / Kb

Now, substitute the values into the equation for molality and solve for m:

m = 2.0 °C / 0.512 °C/m

Once you find the value of m, substitute it back into the equation for molecular mass (M = 150 g / (m * 1.0 kg)) to get the final answer.