A 2.97 g sample of a molecular compound
is dissolved in 103 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?
delta T = Kb*molality
Solve for molality
m = moles/kg solvent
Solve for moles
moles = grams/molar mass
Solve for molar mass.
pv=nrt
To find the molar mass of the compound, we can use the formula:
ΔTb = Kbm
where:
ΔTb is the boiling point elevation,
Kb is the boiling point constant for the solvent (CCl4 in this case),
m is the molality of the solution.
First, let's calculate the molality (m) of the solution.
Molality (m) is defined as the number of moles of solute per kilogram of solvent. We can calculate it using the formula:
m = moles of solute / mass of solvent (in kg)
Given:
mass of the solute = 2.97 g
mass of the solvent = 103 g
Converting the masses to kg:
mass of the solute = 2.97 g / 1000 = 0.00297 kg
mass of the solvent = 103 g / 1000 = 0.103 kg
Now we can calculate the molality:
m = 0.00297 kg / 0.103 kg = 0.0288 mol/kg
Next, we can use the boiling point elevation formula to find the molar mass of the compound.
ΔTb = Kbm
Given:
ΔTb = 61.51°C - 61.2°C = 0.31°C = 0.31 K
Kb = 4.95 K · kg/mol
m = 0.0288 mol/kg
Rearranging the formula:
m = ΔTb / (Kb * M)
where M is the molar mass of the compound.
So, we can solve the equation for M:
M = ΔTb / (Kb * m)
= 0.31 K / (4.95 K · kg/mol * 0.0288 mol/kg)
= 3.4521 mol/mol
Therefore, the molar mass of the compound is approximately 3.4521 g/mol.
To find the molar mass of the compound, we can use the formula:
ΔTb = Kb * m * i
Where:
- ΔTb is the change in boiling point (in Kelvin)
- Kb is the boiling point constant for the solvent
- m is the molality of the solution (moles of solute per kilogram of solvent)
- i is the van't Hoff factor, which represents the number of particles the solute dissociates into in the solution.
In this case, since the molecular compound is dissolved in tetrachloromethane (CCl4), we can assume that it does not dissociate and i is equal to 1.
First, let's calculate the change in boiling point (ΔTb) using the given values:
ΔTb = normal boiling point of solution - normal boiling point of pure CCl4
= 61.51ºC - 61.2ºC
= 0.31ºC
Since the boiling point constant for CCl4 is given as 4.95 K·kg/mol and we have the mass of the solvent, we can calculate the molality (m) of the solution using the formula:
m = (moles of solute) / (kg of solvent)
To find the moles of solute, we need to convert the given mass of the compound (2.97 g) to moles. We can do this by dividing the mass by the molar mass of the compound.
Finally, we can rearrange the above formula to find the molar mass of the compound:
Molar mass = (moles of solute) / (molality)
Let's calculate the values:
1. Convert the mass of the compound (2.97 g) to moles:
Moles = Mass / Molar mass
Moles = 2.97 g / X
2. Calculate the molality (m) of the solution:
Molality = Moles / kg of solvent
Molality = Moles / 0.103 kg
3. Calculate the molar mass of the compound:
Molar mass = Moles / Molality
Molar mass = (2.97 g / X) / (2.97 g / 0.103 kg)
Now, we can calculate the molar mass by substituting the known values:
Molar mass = (2.97 g / X) / (2.97 g / 0.103 kg)
Simplifying this expression, we find:
Molar mass = X / 0.103 kg
Therefore, the molar mass of the compound is X g/mol.