To calculate the molar mass of the unknown compound, we need to use the freezing point depression equation:
ΔT = K_f * m
where:
ΔT = freezing point depression (-1.2 ∘C)
K_f = freezing point depression constant for water (∼1.86 ∘C/m)
m = molality of the solution (moles of solute per kg of solvent)
First, let's calculate the molality (m) of the solution:
m = moles of solute / kg of solvent
To determine moles of solute, we need to convert the given mass of the unknown compound into moles. We can use the molecular weight (molar mass) for this calculation. Let's call the number of moles of the unknown compound "n":
n = mass of compound / molar mass of compound
Now, let's calculate the molality:
m = n / mass of water (in kg)
To convert the mass of water from grams to kilograms, divide by 1000:
mass of water (in kg) = mass of water (in g) / 1000
Finally, we can substitute the values into the freezing point depression equation and solve for the molar mass of the unknown compound:
ΔT = K_f * (n / mass of water (in kg))
Rearranging the equation:
molar mass of compound = (n / (ΔT / K_f)) * mass of water (in kg)
Now we can substitute the given values:
ΔT = -1.2 ∘C
K_f = 1.86 ∘C/m
mass of compound = 32.9 g
mass of water = 130.0 g
Calculations:
1. Convert the mass of water to kilograms:
mass of water (in kg) = 130.0 g / 1000 = 0.130 kg
2. Calculate the moles of the unknown compound:
n = 32.9 g / molar mass of compound
3. Calculate the molality:
m = n / mass of water (in kg)
4. Substitute the values into the rearranged equation:
molar mass of compound = (n / (ΔT / K_f)) * mass of water (in kg)
By solving this equation, we can determine the molar mass of the unknown compound.