A 15.0 g sample of an unknown compound is dissolved in 100.0 g of benzene. The boiling point is raised 2.67 oC above the boiling point of pure benzene. What is the molar mass of the sample? Kb for benzene is 2.67oC/m.
delta T = Kb*molality
Solve for molality = m
m = moles solute/kg solvent
Solve for moles solute
moles solute = grams solute/molar mass solute.
Solve for molar mass.
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To find the molar mass of the unknown compound, we can use the equation:
ΔT = Kb * m * i
where,
ΔT = boiling point elevation
Kb = molal boiling point elevation constant for benzene (2.67 °C/m)
m = molality of the solution
i = van't Hoff factor (number of particles in solution)
First, we need to find the molality of the solution using the mass of the solute (unknown compound) and the mass of the solvent (benzene).
Molality (m) is calculated as:
m = moles of solute / mass of solvent (in kg)
First, let's calculate the number of moles of the unknown compound using its mass and molar mass.
Given:
Mass of the unknown compound (solute) = 15.0 g
To calculate the moles of the unknown compound, we need its molar mass. However, since the molar mass is unknown, we'll use "M" to represent it.
Moles of solute = Mass of solute / Molar mass
Now, we need to convert the mass of the solvent (benzene) from grams to kilograms.
Mass of benzene (solvent) = 100.0 g = 100.0 g / 1000 = 0.1000 kg
Now, we can calculate the molality (m):
m = Moles of solute (unknown compound) / Mass of solvent (benzene)
Next, we can use the boiling point elevation equation ΔT = Kb * m * i.
Given:
ΔT = 2.67 °C (boiling point elevation)
Kb = 2.67 °C/m (molal boiling point elevation constant for benzene)
Rearranging the equation, we get:
m = ΔT / (Kb * i)
The van't Hoff factor (i) for the unknown compound depends on its dissociation in solution, but since it is not provided in the given information, we assume it to be 1.
Therefore, the equation becomes:
m = ΔT / Kb
Now, we can substitute the given values into the equation to find molality (m):
m = 2.67 °C / (2.67 °C/m)
m = 1 mol/kg
Now, we have the molality (m) of the solution. We can use this to find the moles of the unknown compound dissolved in benzene.
moles of solute = molality (m) * mass of solvent (in kg)
moles of solute = 1 mol/kg * 0.1000 kg
moles of solute = 0.1000 mol
Now, we can calculate the molar mass (M) of the unknown compound using the moles of the solute and its mass.
Molar mass (M) = Mass of solute / Moles of solute
Molar mass (M) = 15.0 g / 0.1000 mol
Molar mass (M) = 150 g/mol
Therefore, the molar mass of the unknown compound is 150 g/mol.
To find the molar mass of the unknown compound, we need to use the concept of boiling point elevation.
Boiling point elevation occurs when a non-volatile solute is dissolved in a solvent, causing an increase in the boiling point of the solvent.
The relationship between the change in boiling point (∆Tb), the molality of the solute (m), and the molal constant (Kb) can be expressed by the equation:
∆Tb = Kb * m
In this case, the change in boiling point (∆Tb) is given as 2.67 oC, and the molal constant (Kb) for benzene is also given as 2.67 oC/m.
To find the molality (m), we need to calculate the moles of solute dissolved in the solvent (benzene) using the formula:
moles of solute = mass of solute / molar mass of solute
The mass of the solute is given as 15.0 g.
Now, let's calculate the moles of solute:
moles of solute = 15.0 g / molar mass of solute
Substituting the given values, we have:
2.67 oC = (2.67 oC/m) * (moles of solute / 0.1 kg)
Simplifying this equation, we get:
2.67 = 26.7 * (moles of solute / 0.1)
To isolate the moles of solute, we rearrange the equation:
moles of solute = 2.67 * 0.1 / 26.7
Solving this equation gives the moles of solute dissolved in the solvent.
Now, to find the molar mass of the solute, we rearrange the formula for moles of solute:
molar mass of solute = mass of solute / moles of solute
Substituting the given values, we have:
molar mass of solute = 15.0 g / moles of solute
Now, calculate the molar mass of the solute to find the answer.