A solution was prepared by dissolving 72.0 g of glucose in 300.0 g of water. The ressulting solution was found to have a boiling point of 100.68C at 1 atm. Calculate the molar mass of glucose. For water Kb= 0.51 Ckg/mol.
I know the molar mass of glucose if 180 g/mol because I just used the periodic table, but i am not sure how to calculate this using the equation deltaT=imKb.
delta T = i*Kb*molality
You know delta T is 100.68 - 100.00 = ?
i = 1
You know Kb. Solve for m = molality
Then m = mols/kg solvent. You know kg solvent = 0.3000
Knowing m and kg solvent you solve for mols.
Then mols = g/molar mass
You know mols and grams, solve for molar mass.
To calculate the molar mass of glucose using the equation deltaT=imKb, you first need to determine the change in boiling point (deltaT), the molality of the solution (m), and the boiling point constant (Kb) for water.
Given:
Mass of glucose (m1) = 72.0 g
Mass of water (m2) = 300.0 g
Boiling point elevation (deltaT) = 100.68°C
Boiling point constant (Kb) for water = 0.51°C kg/mol
Step 1: Convert the masses to moles
To find the molality (m), it is necessary to convert the masses of glucose and water to moles. The molar mass of glucose is given as 180 g/mol.
Moles of glucose (n1) = mass (m1) / molar mass of glucose
= 72.0 g / 180 g/mol
= 0.4 mol
Moles of water (n2) = mass (m2) / molar mass of water
= 300.0 g / 18.0 g/mol (molar mass of water)
= 16.7 mol
Step 2: Calculate the molality (m)
Molality (m) is defined as the moles of solute (glucose) divided by the mass of the solvent (water) in kilograms.
Molality (m) = moles of solute (n1) / mass of solvent (m2) in kg
= 0.4 mol / 0.3 kg (since 300 g = 0.3 kg)
= 1.33 mol/kg
Step 3: Calculate the molar mass of glucose (M)
Rearranging the formula deltaT = i * m * Kb, we can solve for the molar mass of glucose (M).
deltaT = i * m * Kb
Substitute the given values:
100.68°C = (1) * (1.33 mol/kg) * (0.51°C kg/mol)
Simplify:
100.68°C = 0.6783 mol/kg°C
To isolate the molar mass of glucose, rearrange the equation:
M = (mass of solute (m1) / moles of solute (n1) ) * deltaT / m
= (72.0 g / 0.4 mol ) * 100.68°C / 0.6783 mol/kg°C
≈ 329.3 g/mol
Therefore, the molar mass of glucose is approximately 329.3 g/mol.