If 395.3 g of a substance is dissolved in 872.6 g of cyclohexane solvent, the boiling point of the solution is 87.38 oC. Calculate the apparent molar mass (g/mol) of substance.
Find delta T. That is the difference between the normal boiling point of cyclohexane and 87.38.
delta T = i*Kb*molality
You have delta T, look up Kb (the constant for cyclohexane), and calculate molality.
Then molality = moles/kg
You know molality and kg. Calculate moles.
Finally, moles = grams/molar mass. You know moles and grams, calculate molar mass. This will be the apparent molar mass since you don't know anything about i
To calculate the apparent molar mass of a substance, we need to use the boiling point elevation equation, which is:
ΔTB = Kbm
Where:
ΔTB is the boiling point elevation (the difference between the boiling point of the solution and the boiling point of the pure solvent).
Kb is the molal boiling point constant of the solvent.
m is the molality of the solution (moles of solute per kilogram of solvent).
First, let's calculate the molality (m) of the solution:
Molality (m) = moles of solute / mass of solvent (in kg)
To calculate the moles of solute, we'll divide the mass of the solute by its molar mass.
Let's assume the molar mass of the substance is M (in g/mol).
moles of substance = mass of substance / molar mass
moles of substance = 395.3 g / M
Now, let's calculate the molality:
m = moles of solute / mass of solvent (in kg)
m = (395.3 g / M) / 872.6 g
m = (395.3 / M) / 0.8726
m = 453.1043 / M
Next, we need to find the molal boiling point constant (Kb) for cyclohexane. The Kb value for cyclohexane is approximately 2.53 oC/m.
Now, we can substitute the variables in the boiling point elevation equation:
ΔTB = Kbm
ΔTB = (2.53 oC/m) * (453.1043 / M)
Given that the boiling point of the solution is 87.38 oC, we can substitute the values:
87.38 = (2.53) * (453.1043 / M)
Now, let's solve this equation for M to find the apparent molar mass of the substance.