An unknown solute (a nonelectrolyte) was obtained and 5.37 g was weighed out. After dissolving the solute in water, the mass of the solution was 26.58 g. From the experimental results, the freezing point depression was found to be 3.6oC. If the freezing point depression constant, Kf, for water is 1.86oC.kg/mol, what is the molar mass of the unknown solute?

delta T = i*Kf*molality

First, I don't know about the value you show for Kf for water. It is 1.86 degrees C/molal and not kg/mol.
You know delta T, i = 1, Kf = 1.86, calculate molality.
Then molality = moles/kg solvent. You now know molality and kg solvent (26.58 g - 5.37 g = ?? changed to kg). Calculate moles.
Then moles = grams/molar mass. You know moles and grams, calculate molar mass.

To find the molar mass of the unknown solute, we can use the formula:

\(\Delta T_f = K_f \cdot m \)

where:
\(\Delta T_f\) = freezing point depression
\(K_f\) = freezing point depression constant
\(m\) = molality of the solute

First, let's calculate the molality of the solute using the formula:

\(m = \frac{{\text{{moles of solute}}}}{{\text{{mass of solvent (in kg)}}}}\)

Given that the mass of the unknown solute is 5.37 g and the mass of the solution is 26.58 g, we can calculate the mass of the solvent:

\( \text{{mass of solvent}} = \text{{mass of solution}} - \text{{mass of solute}} \)
\( \text{{mass of solvent}} = 26.58 \, \text{g} - 5.37 \, \text{g} \)
\( \text{{mass of solvent}} = 21.21 \, \text{g} \)

Converting the mass of the solvent to kg:

\( \text{{mass of solvent (in kg)}} = \frac{{21.21 \, \text{g}}}{{1000 \, \text{g/kg}}} = 0.02121 \, \text{kg} \)

Next, calculate the molality of the solute:

\( m = \frac{{\text{{moles of solute}}}}{{\text{{mass of solvent (in kg)}}}} \)

To find the moles of solute, we can use the formula:

\( \text{{moles of solute}} = \frac{{\text{{mass of solute}}}}{{\text{{molar mass of solute}}}} \)

Rearranging the above equation, we get:

\( \text{{molar mass of solute}} = \frac{{\text{{mass of solute}}}}{{\text{{moles of solute}}}} \)

Now, substitute the given values:

\( \text{{molar mass of solute}} = \frac{{5.37 \, \text{g}}}{{\text{{moles of solute}}}} \)

To find the moles of solute, we can use the formula:

\( \text{{moles of solute}} = \frac{{\text{{freezing point depression}}}}{{\text{{freezing point depression constant}}}} \)

Substituting the given values:

\( \text{{moles of solute}} = \frac{{3.6 \, \text{°C}}}{{1.86 \, \text{°C.kg/mol}}} \)

Now, substitute the moles of solute in the equation for the molar mass of solute:

\( \text{{molar mass of solute}} = \frac{{5.37 \, \text{g}}}{{\frac{{3.6 \, \text{°C}}}{{1.86 \, \text{°C.kg/mol}}}}} \)

\( \text{{molar mass of solute}} = \frac{{5.37 \, \text{g}}}{{3.6 \, \text{°C} \cdot \frac{{1.86 \, \text{°C.kg/mol}}}}{{1 \, \text{mol}}}}} \)

Simplifying:

\( \text{{molar mass of solute}} = \frac{{5.37 \times 1 \times 1.86}}{{3.6}} \, \text{g/mol} \)

\( \text{{molar mass of solute}} = 2.77 \, \text{g/mol} \)

Therefore, the molar mass of the unknown solute is 2.77 g/mol.

To find the molar mass of the unknown solute, we can use the formula:

ΔTf = Kf * m

Where:
ΔTf is the freezing point depression
Kf is the freezing point depression constant for water
m is the molality of the solution

First, we need to calculate the molality (m) of the solution. Molality is defined as the number of moles of solute per kilogram of solvent. In this case, we are given the weight of the solute (5.37 g) and the weight of the solution (26.58 g). To find the weight of the solvent, we subtract the weight of the solute from the weight of the solution:

Weight of solvent = Weight of solution - Weight of solute
= 26.58 g - 5.37 g
= 21.21 g

Next, we need to convert the weight of the solvent to kilograms:

Weight of solvent (kg) = Weight of solvent (g) / 1000
= 21.21 g / 1000
= 0.02121 kg

Now we can calculate the molality:

m = moles of solute / weight of solvent (kg)

To find the moles of solute, we use the molar mass formula:

moles of solute = weight of solute / molar mass

We can rearrange the formula to find the molar mass:

molar mass = weight of solute / moles of solute

Now substitute the given values into the formula:

molar mass = 5.37 g / (moles of solute)

Finally, we need to calculate the moles of solute using the freezing point depression formula.

ΔTf = Kf * m
3.6 oC = 1.86 oC.kg/mol * m

Rearrange the equation:

m = ΔTf / Kf
= 3.6 oC / 1.86 oC.kg/mol

Now substitute the value of m into the molar mass formula:

molar mass = 5.37 g / (ΔTf / Kf)

molar mass = 5.37 g / (3.6 oC / 1.86 oC.kg/mol)

Calculate the result:

molar mass = 9.25 g/mol

Therefore, the molar mass of the unknown solute is 9.25 g/mol.