What is the van't Hoff factor for K2SO4 in an aqueous solution that is 5.00 % K2SO4 by mass and freezes at -1.21 ∘C?

You don't believe 3? That's the right answer.

My Home work is online. When I gave that answer it said 3 is wrong.

This is college chem 132

The theoretical number is 3 for K2SO4. Since all of that other information is included you must want the actual factor for this particular solution.

5% K2SO4 = 5g K2SO4/100 g solution which is 5g K2SO4/95 g solvent.
mol K2SO4 = 5/molar mass K2SO4
m K2SO4 = mols K2SO4/0.095 kg solvent. Plug in and solve for m K2SO4.
Then dT = i*Kf*m
1.21 = i*1.86*m
Solve for i. It should be close to 3 but not exactly 3.

2.15

bhag yaha se

To determine the van't Hoff factor for K2SO4 in an aqueous solution, we need to consider the colligative properties of the solution, specifically the freezing point depression.

The van't Hoff factor (i) accounts for the number of particles that an ionic compound dissociates into when it dissolves in a solvent. For K2SO4, each formula unit dissociates into three ions: 2 K+ ions and 1 SO4^2- ion. Thus, the van't Hoff factor for K2SO4 is 3.

Now, let's calculate the molality of the K2SO4 solution and use it to find the degree of freezing point depression (ΔTf). We can then use the equation ΔTf = Kf * i * molality to find the van't Hoff factor.

First, we need to calculate the molality (m) of the solution:

Molar mass of K2SO4:
K = 39.10 g/mol (potassium)
S = 32.07 g/mol (sulfur)
O = 16.00 g/mol (oxygen)
Total molar mass = 2 * 39.10 + 32.07 + 4 * 16.00 = 174.27 g/mol

Given that the solution is 5.00% K2SO4 by mass, we can calculate the mass of K2SO4 in the solution:

Mass of solution = 100 g
Mass of K2SO4 = 5.00% * 100 g = 5.00 g

Now, let's calculate the number of moles of K2SO4:

Number of moles = mass / molar mass = 5.00 g / 174.27 g/mol = 0.0287 mol

Next, we need to calculate the molality of the solution:

Molality (m) = moles of solute / mass of solvent (in kg)
Assuming the mass of the solvent to be 100 g - 5.00 g = 95.00 g (since K2SO4 is dissolved in water), we can convert it to kg:

Mass of solvent (in kg) = 95.00 g / 1000 = 0.095 kg

Molality (m) = 0.0287 mol / 0.095 kg = 0.302 mol/kg

Now, let's use the equation ΔTf = Kf * i * molality to find the van't Hoff factor:

ΔTf = -1.21 ∘C (the freezing point depression)

The cryoscopic constant (Kf) is specific to the solvent and can be looked up in a reference book. For water, its value is 1.86 ∘C/m.

ΔTf = Kf * i * molality
-1.21 ∘C = 1.86 ∘C/m * 3 * 0.302 mol/kg

Simplifying the equation:

-1.21 ∘C = 1.86 ∘C/m * 0.906 mol/kg

Finally, let's solve for the van't Hoff factor (i):

i = -1.21 ∘C / (1.86 ∘C/m * 0.906 mol/kg)

Calculating this expression, we find that the van't Hoff factor for K2SO4 in the given solution is approximately 2.08.