Calculate the molar mass of a compound that raises the boiling point of water to 100.15oC when 40.5 g of the compound is dissovled in 500 g of water.
and
A mass of 41 g of an unknown nonelectrolyte is dissolved in 429 g naphthalene. The nonelectrolyte lowers naphthalene's freezing point by 7.2 oC. What is the molecular mass of the unknown substance? (Kf = 6.8 oC/mola
#1.
a. delta T = Kb*molality
You know delta T and Kb, solve for molality.
b. Then molality = mols/kg solvent.
You know molality and kg solvent, solve for mols.
c. mols = grams/molar mass. You know mols and grams, solve for molar mass.
#2.
Same kind as #1. Post your work if you get stuck.
To calculate the molar mass of the compound in the first question, we need to use the formula:
ΔT = Kbm
Where ΔT is the change in boiling point, Kb is the molal boiling point elevation constant, and m is the molality of the solution.
Given:
ΔT = 100.15oC
Kb (for water) = 0.52oC/molal
m = (40.5 g / compound molar mass) / (500 g water / 1000 g/mol)
First, let's calculate the molality (m):
m = (40.5 g / compound molar mass) / (500 g water / 1000 g/mol)
m = (40.5 / compound molar mass) / 0.5
m = 81 / (compound molar mass)
Now, we can use the formula to calculate the molar mass:
100.15 = (0.52) * (81 / (compound molar mass))
100.15 = 0.52 * 81 / (compound molar mass)
(compound molar mass) = 0.52 * 81 / 100.15
Now we can calculate the value of (compound molar mass):
(compound molar mass) ≈ 0.4192 g/mol
Therefore, the molar mass of the compound is approximately 0.4192 g/mol.
Moving on to the second question,
To calculate the molecular mass of the unknown substance, we need to use the formula:
ΔT = Kfm
Where ΔT is the change in freezing point, Kf is the molal freezing point depression constant, and m is the molality of the solution.
Given:
ΔT = -7.2oC (negative because it's a freezing point depression)
Kf (for naphthalene) = 6.8 oC/molal
m = (41 g / unknown substance molar mass) / (429 g naphthalene / 128.2 g/mol)
First, let's calculate the molality (m):
m = (41 g / unknown substance molar mass) / (429 g naphthalene / 128.2 g/mol)
m = (41 / unknown substance molar mass) / (429 / 128.2)
m = (41 * 128.2) / (unknown substance molar mass * 429)
Now, we can use the formula to calculate the molecular mass:
-7.2 = (6.8) * [(41 * 128.2) / (unknown substance molar mass * 429)]
-7.2 = 6.8 * (41 * 128.2) / (unknown substance molar mass * 429)
(unknown substance molar mass * 429) = 6.8 * (41 * 128.2) / (-7.2)
unknown substance molar mass = (6.8 * (41 * 128.2)) / (-7.2 * 429)
Now we can calculate the value of the unknown substance molar mass:
unknown substance molar mass ≈ 178.85 g/mol
Therefore, the molecular mass of the unknown substance is approximately 178.85 g/mol.
To calculate the molar mass of a compound that raises the boiling point of a solvent or lowers the freezing point of a solvent, we can use the formula:
ΔT = K * m * i
where:
ΔT is the change in boiling or freezing point
K is the molal freezing point depression or boiling point elevation constant for the solvent
m is the molality of the solute (moles of solute per kilogram of solvent)
i is the Van't Hoff factor (number of particles the solute dissociates into when it dissolves)
Let's calculate the molar mass for both compounds:
1. Calculation for the compound that raises the boiling point of water:
Given:
Mass of the compound (m1) = 40.5 g
Mass of water (m2) = 500 g
Boiling point elevation (ΔT) = 100.15 oC
First, we need to calculate the molality (m) of the compound:
Moles of water = m2/Molar mass of water
Moles of compound = m1/Molar mass of the compound
Molality (m) = Moles of compound / Mass of water (in kg)
= (m1 / Molar mass of the compound) / (m2 / Molar mass of water)
Rearranging the formula:
Molar mass of the compound = (m1 * Molar mass of water * ΔT) / (m2 * K)
You need to know the value of the boiling point elevation constant for water (K) to complete the calculation.
2. Calculation for the unknown nonelectrolyte:
Given:
Mass of the unknown nonelectrolyte (m1) = 41 g
Mass of naphthalene (m2) = 429 g
Freezing point depression (ΔT) = 7.2 oC
Freezing point depression constant for naphthalene (Kf) = 6.8 oC/m
First, we calculate the molality (m) of the unknown nonelectrolyte:
Moles of naphthalene = m2/Molar mass of naphthalene
Moles of the unknown nonelectrolyte = m1/Molar mass of the unknown substance
Molality (m) = Moles of the unknown nonelectrolyte / Mass of naphthalene (in kg)
= (m1 / Molar mass of the unknown substance) / (m2 / Molar mass of naphthalene)
Rearranging the formula:
Molar mass of the unknown substance = (m1 * Molar mass of naphthalene * ΔT) / (m2 * Kf)
You need to know the value of the freezing point depression constant for naphthalene (Kf) to complete the calculation.