A 1.73 g sample of a molecular compound
is dissolved in 105 g of tetrachloromethane
(carbon tetrachloride). The normal boiling
point of the solution is 61.51�C, the normal
boiling point of CCl4 is 61.2�C. The boiling
point constant for CCl4 is 4.95 K · kg/mol.
What is the molar mass of the compound?
Answer in units of g/mol
delta T = Kb*m
Solve for m
m = mols/kg solvent
Solve for mols
mols = grams/molar mass
Solve for molar mass.
252
To find the molar mass of the compound, we can use the formula:
𝜆 = K*m/M
Where:
𝜆 = boiling point constant for the solvent
K = boiling point elevation, which is the difference between the boiling point of the solution and the boiling point of the pure solvent
m = molality of the solution
M = molar mass of the compound
First, let's calculate the boiling point elevation:
𝜆 = 61.51 - 61.2
𝜆 = 0.31 ºC
Next, we need to convert the mass of the compound and solvent into moles:
Moles of compound = mass of compound / molar mass of compound
Moles of CCl4 = mass of CCl4 / molar mass of CCl4
Given:
Mass of compound = 1.73 g
Mass of CCl4 = 105 g
Molar mass of CCl4 = 153.82 g/mol (source: periodic table)
Moles of compound = 1.73 g / Molar mass of compound
Moles of CCl4 = 105 g / Molar mass of CCl4
Now, let's substitute the values into the equation:
𝜆 = 4.95 K · kg/mol * (1.73 g / Molar mass of compound) / (105 g / Molar mass of CCl4)
Simplifying:
0.31 = 4.95 * (1.73 / Molar mass of compound) * (Molar mass of CCl4 / 105)
Now, let's solve for Molar mass of compound:
Molar mass of compound = (4.95 * 1.73 * Molar mass of CCl4) / (105 * 0.31)
Substituting the values:
Molar mass of compound = (4.95 * 1.73 * 153.82) / (105 * 0.31)
Molar mass of compound ≈ 516 g/mol (rounded to the nearest whole number)
Therefore, the molar mass of the compound is approximately 516 g/mol.
To find the molar mass of the compound, we first need to determine the change in boiling point caused by the presence of the solute.
The change in boiling point (∆Tb) is calculated using the equation:
∆Tb = Kb × m
Where:
∆Tb = change in boiling point
Kb = boiling point constant
m = molality of the solution
We can calculate the molality of the solution using the equation:
molality (m) = moles of solute / mass of solvent (in kg)
Given information:
mass of the compound = 1.73 g
mass of the solvent CCl4 = 105 g
boiling point constant (Kb) for CCl4 = 4.95 K · kg/mol
normal boiling point of solution (Tb-solution) = 61.51°C
normal boiling point of CCl4 (Tb-solvent) = 61.2°C
First, convert the temperatures from Celsius to Kelvin by adding 273.15:
Tb-solution = 61.51 + 273.15 = 334.66 K
Tb-solvent = 61.2 + 273.15 = 334.35 K
Next, calculate the change in boiling point (∆Tb):
∆Tb = Tb-solution - Tb-solvent
∆Tb = 334.66 K - 334.35 K = 0.31 K
Now, calculate the molality (m):
molality (m) = moles of solute / mass of solvent (in kg)
First, convert the mass of the solute from grams to moles:
moles of solute = mass of solute / molar mass of solute
Since we need to find the molar mass of the compound, let's assume it is "M" g/mol. Therefore,
moles of solute = 1.73 g / M g/mol
Finally, we can substitute the values into the molality formula:
m = (1.73 g / M g/mol) / (105 g / 1000 g/kg)
Simplifying,
m = (1.73 / M) / 0.105
Now we can substitute the calculated values into the equation for ∆Tb and solve for the molar mass (M):
0.31 = 4.95 × (1.73 / M) / 0.105
Simplifying,
0.31 × 0.105 = 4.95 × 1.73 / M
0.03255 = 8.5735 / M
M = 8.5735 / 0.03255
M ≈ 263.57 g/mol
Therefore, the molar mass of the compound is approximately 263.57 g/mol.