A 1.45 g sample of an unknown compound is dissolved in 25.00 mL benzene (d=0.879 g/mL). The solution freezes at 4.25 C. What is the molar mass of the unknown?
I want to say that you aren't helping very much. What is the freezing point constant? What is the freezing point for benzene. You need to look up those values. You may use your text, the web, or your notes.
mass = volume x density so mass benzene is
mass = 25.00 mL x 0.879 g/mL = 21.98 g = 0.02198 kg.
delta T = Kf*m. Substituting into the equation we have
freezing point benzene - 4.25 = delta T.
Substitute into delta T = Kf*m and solve for m = molality.
Then molality = moles/kg solvent and I've solved for kg solvent above and solve for moles, then mols = grams/molar mass. You have mols and grams, solve for molar mass. Post your work if you get stuck.
To determine the molar mass of the unknown compound, we can use the formula:
ΔT = Kf * m
Where:
ΔT = freezing point depression
Kf = cryoscopic constant of the solvent
m = molality of the solution
We need to find the molality of the solution first. The molality (m) is defined as the number of moles of solute per kilogram of solvent.
Step 1: Determine the number of moles of benzene (the solvent):
The mass of benzene (solvent) can be calculated using its density:
Mass of benzene = Volume of benzene * Density
= 25.00 mL * 0.879 g/mL
= 21.975 g
To convert grams to kilograms:
Mass of benzene = 21.975 g / 1000
= 0.021975 kg
Step 2: Determine the number of moles of the unknown compound:
The mass of the unknown compound is given as 1.45 g.
Step 3: Calculate the molality of the solution:
Molality (m) = moles of solute / mass of solvent (in kg)
Since the mass of the solvent is already in kilograms, the equation becomes:
Molality (m) = moles of solute / 0.021975 kg
To find the moles of solute:
Moles of solute = mass of solute / molar mass of unknown compound
We can rearrange the equation to solve for the molar mass:
Molar mass of unknown compound = mass of solute / (moles of solute / 0.021975 kg)
Step 4: Calculate the moles of solute:
Moles of solute = mass of solute / molar mass of unknown compound
= 1.45 g / molar mass of unknown compound
Substitute this into the equation for the molality:
Molality (m) = (1.45 g / molar mass of unknown compound) / 0.021975 kg
Now we have all the necessary information to calculate the molar mass of the unknown compound.
To find the molar mass of the unknown compound, we need to use the freezing point depression equation. The freezing point depression is given by:
ΔT = K_f * m
Where:
ΔT is the change in freezing point (in degrees Celsius),
K_f is the cryoscopic constant (which depends on the solvent),
m is the molality of the solution (moles of solute per kilogram of solvent).
In this case, we have the mass of the solvent (benzene, 25.00 mL) and its density (0.879 g/mL). With these values, we can calculate the mass of the benzene:
mass_benzene = density_benzene * volume_benzene
mass_benzene = 0.879 g/mL * 25.00 mL
mass_benzene = 21.975 g
Next, we calculate the molality of the solution:
molality = moles_solvent / kilograms_solvent
Since we know the mass of the solute (1.45 g), we can convert it to moles using the molar mass of the unknown compound (M):
moles_solvent = mass_solvent / molar_mass
moles_solvent = 1.45 g / M
Since the mass of benzene (solvent) is much greater than the mass of the solute, we can approximate the moles_solvent ≈ moles_solute. Therefore, the equation becomes:
molality ≈ moles_solute / kilograms_benzene
m ≈ 1.45 g / (M * 0.021975 kg)
Finally, we can plug this molality value into the freezing point depression equation to find the change in freezing point (ΔT):
ΔT = K_f * m
4.25 C = K_f * (1.45 g) / (M * 0.021975 kg)
Now we solve this equation for the molar mass (M) of the unknown compound.