Answer: The boiling point elevation constant (Kb) of ethanol in the given solution is approximately 0.932 Celsius/mol.
Step-by-step explanation:
To find the boiling point elevation constant (Kb) of ethanol, we can use the formula:
ΔTb = Kb * m
where ΔTb is the change in boiling point, Kb is the boiling point elevation constant, and m is the molality of the solution.
In this case, we are given the following information:
- Mass of glycerin = 52 grams
- Mass of ethanol = 250 grams
- Change in boiling point = 2.78 Celsius
To find the molality (m) of the solution, we need to calculate the moles of glycerin and the mass of the solvent (ethanol).
First, we convert the mass of glycerin to moles using its molar mass. The molar mass of glycerin is approximately 92.09 g/mol.
Moles of glycerin = mass of glycerin / molar mass of glycerin
Moles of glycerin = 52 g / 92.09 g/mol
Next, we calculate the mass of the solvent (ethanol) by subtracting the mass of glycerin from the total mass of the solution.
Mass of solvent (ethanol) = mass of solution - mass of solute
Mass of solvent (ethanol) = 250 g - 52 g
Now, we can calculate the molality (m) using the moles of glycerin and the mass of the solvent.
Molality (m) = moles of glycerin / mass of solvent (ethanol)
Molality (m) = (52 g / 92.09 g/mol) / (198 g)
Finally, we can substitute the values of ΔTb (2.78 Celsius) and m into the formula to solve for Kb (the boiling point elevation constant).
ΔTb = Kb * m
2.78 Celsius = Kb * [(52 g / 92.09 g/mol) / (198 g)]
Simplifying the equation and solving for Kb:
Kb = (2.78 Celsius * (198 g)) / [(52 g / 92.09 g/mol)]
Calculating the value, we find that the boiling point elevation constant (Kb) of ethanol in the given solution is approximately 0.932 Celsius/mol.
I hope this helps :)