0.959 g of a hydrocarbon is dissolved in 10.00g of benzene. The freezing point of the solution is 1.16C. Find the molecular mass of the hydrocarbon. Benzene has a Kf of 5.12 and a freezing points of 5.53 degrees C.

Not sure how to go about solving this problem? Thanks!

Use the freezing point depression formula.

dT = Kf*m
Substitute and solve for m = molality.

m = mols/kg solvent.
Substitute and solve for mols.

mols = grams/molar mass
You know mols and grams, solve for mola rmass.

To solve this problem, we can use the concept of Freezing Point Depression, which states that the freezing point of a solution is lower than the freezing point of the pure solvent.

First, we need to calculate the change in freezing point (∆Tf) using the formula:

∆Tf = Kf * i * m

where Kf is the freezing point depression constant (given as 5.12), i is the van't Hoff factor (which represents the number of particles the solute dissociates into), and m is the molality of the solution (given by moles of solute per kg of solvent).

Here, we are given the mass of the hydrocarbon as 0.959 g and the mass of the benzene as 10.00 g.

1. First, calculate the molality of the solution (m):

molality (m) = moles of solute / mass of solvent

Since the mass of the solution is given by the mass of benzene (10.00 g), the mass of the solvent (benzene) is also 10.00 g.

moles of solute = mass of solute / molar mass of solute

2. Calculate the change in freezing point (∆Tf):

∆Tf = Kf * i * m

3. Finally, calculate the molecular mass of the hydrocarbon:

molecular mass = molar mass of solute / number of moles of solute

Now, let's calculate step by step.

Step 1: Calculate the moles of solute

moles of solute = mass of solute / molar mass of solute
Given mass of solute = 0.959 g

To calculate the molar mass of the solute, we need to know the formula of the hydrocarbon.

To solve this problem, we will be using the concept of freezing point depression.

Freezing point depression refers to the phenomenon where the freezing point of a solution is lower than that of the pure solvent. The change in freezing point is directly proportional to the molal concentration of the solute.

The formula we will be using here is:

ΔTf = Kf * m

Where:
ΔTf = change in freezing point
Kf = molal freezing point depression constant (given as 5.12)
m = molality of the solution

First, we need to calculate the molality of the solution. Molality (m) is defined as the moles of solute per kilograms of solvent.

Given:
Mass of the solute = 0.959 g
Mass of the solvent (benzene) = 10.00 g

Step 1: Calculate the number of moles of solute (hydrocarbon)
To obtain the number of moles, we use the formula:

Moles = Mass / Molar Mass

Since the molecular mass of the hydrocarbon is unknown, we will represent it as "M" for now.

Moles of solute = 0.959 g / M

Step 2: Calculate the molality (m)
Molality is the moles of solute divided by the mass of the solvent in kilograms.

Molality (m) = Moles of solute / (Mass of solvent in kg)
= [0.959 g / M] / [10.00 g / 1000]

Step 3: Calculate the change in freezing point (ΔTf)
The change in freezing point can be found using the formula mentioned earlier:

ΔTf = Kf * m
= 5.12 * m

Given that the change in freezing point is 1.16 °C, we can write the equation as:

1.16 = 5.12 * m

Step 4: Solve for molality (m)

Rearranging the equation:
m = 1.16 / 5.12

Step 5: Calculate the molecular mass of the hydrocarbon (M)

Now that we have determined the molality (m), we can substitute it back into the equation for molality:

m = [0.959 g / M] / [10.00 g / 1000]

Rearranging the equation to solve for M:
M = [0.959 g / (m * 10.00 g)] * 1000

Substituting the value of m calculated earlier,
M = [0.959 g / ((1.16 / 5.12) * 10.00 g)] * 1000

Simplifying and calculating the value of M will give you the molecular mass of the hydrocarbon.