The boiling point elevation of a solution consisting of 2.92 g of a nonvolatile solute in 82.4 g of benzene is 1.077 oC. What is the molecular weight of the unknown solute?
delta T = Kb*molality.
Step 1. Calculate molality from the above.
Step 2. Remember that molality = # mols/kg solvent. Calculate # mols from that.
Step 3. Use # mols = g/molar mass to calculate molar mass.
Post your work if you get stuck.
To find the molecular weight (molar mass) of the unknown solute, we need to use the equation for the boiling point elevation.
The formula for boiling point elevation is given by:
ΔTb = Kb * m
Where:
- ΔTb is the boiling point elevation
- Kb is the molal boiling point elevation constant for the solvent (benzene in this case)
- m is the molality of the solution (moles of solute per kilogram of solvent)
First, we need to calculate the molality (m) of the solution. Molality is defined as the moles of solute divided by the mass of the solvent in kilograms.
m = (moles of solute) / (mass of benzene in kg)
To calculate the moles of solute, we can use the formula:
moles of solute = (mass of solute) / (molar mass of solute)
Using the given values, the boiling point elevation (ΔTb) is 1.077 oC, and the mass of benzene (solvent) is 82.4 g.
First, let's convert the given values to the appropriate units:
- Mass of benzene (solvent) = 82.4 g = 0.0824 kg
Now, we need to calculate the molality (m):
m = (moles of solute) / 0.0824 kg
Next, let's calculate the moles of solute:
moles of solute = 2.92 g / molar mass of solute
Since we don't know the molar mass of the solute, let's represent it as "X".
Now we can substitute these values into the equation for boiling point elevation:
1.077 oC = Kb * (2.92 g / (X * 0.0824 kg))
Simplifying this equation, we get:
1.077 oC = Kb * (2.92 g / (X * 0.0824))
Finally, we can rearrange the equation to solve for X (the molar mass of the unknown solute):
X = (2.92 g / (1.077 oC * 0.0824)) / Kb
To find the value of Kb, you need to consult a reference source or look it up in a chemistry textbook. The molal boiling point elevation constant (Kb) is specific to the solvent (benzene) and is usually given in units of oC/m or K/m.
Once you have the value of Kb, substitute it into the equation and solve for X to find the molecular weight of the unknown solute.