The solubility of the oxidizing agent potassium permanganate is 7.1 g per 100.0 g of water at 25° C. What is the mole fraction of potassium permanganate (KMn04) in this saturated solution? What is the molality of the potassium permanganate solution?

0.00803

Why did the potassium permanganate go to the party? Because it heard there would be a lot of water to dissolve in!

To find the mole fraction of potassium permanganate (KMnO4) in the saturated solution, we need to calculate the number of moles of KMnO4 and the number of moles of water.

The molar mass of KMnO4 is:
K (atomic mass) + Mn (atomic mass) + 4O (atomic mass) = 39.10 + 54.94 + 4(16.00) = 158.03 g/mol

So, the number of moles of KMnO4 is:
7.1 g / 158.03 g/mol = 0.045 moles

Next, let's calculate the number of moles of water:
100.0 g / 18.02 g/mol = 5.55 moles

The mole fraction (X) of KMnO4 can be calculated using the formula:
X = moles of KMnO4 / (moles of KMnO4 + moles of water)

X = 0.045 moles / (0.045 moles + 5.55 moles) = 0.008 (rounded to three decimal places)

So, the mole fraction of potassium permanganate (KMnO4) in this saturated solution is approximately 0.008.

Now, let's move on to the molality of the potassium permanganate solution.

Molality is defined as the number of moles of solute per kilogram of solvent.

The mass of 100.0 g of water is 100.0 g.

The molality (m) of the potassium permanganate solution can be calculated using the formula:
m = moles of solute / kilogram of solvent

m = 0.045 moles / 0.100 kg = 0.45 mol/kg (rounded to two decimal places)

So, the molality of the potassium permanganate solution is approximately 0.45 mol/kg.

To find the mole fraction of potassium permanganate (KMnO4) in the saturated solution, we first need to calculate the moles of solute (KMnO4) and solvent (water), and then use the formula for mole fraction.

Step 1: Calculate the moles of KMnO4:
Molar mass of KMnO4 = (39.1 g/mol for K) + (54.9 g/mol for Mn) + (16.0 g/mol for O) x 4
= 39.1 + 54.9 + 64 = 158 g/mol

Number of moles of KMnO4 = mass of KMnO4 / molar mass of KMnO4
= 7.1 g / 158 g/mol
≈ 0.045 mol

Step 2: Calculate the moles of water:
Molar mass of H2O = (1.0 g/mol for H) x 2 + (16.0 g/mol for O)
= 2.0 + 16.0 = 18.0 g/mol

Number of moles of water = mass of water / molar mass of H2O
= 100.0 g / 18.0 g/mol
≈ 5.56 mol

Step 3: Calculate the mole fraction of KMnO4:
Mole fraction of KMnO4 = moles of KMnO4 / (moles of KMnO4 + moles of water)
= 0.045 mol / (0.045 mol + 5.56 mol)
≈ 0.008

Therefore, the mole fraction of potassium permanganate (KMnO4) in this saturated solution is approximately 0.008.

Now, let's move on to calculating the molality of the potassium permanganate solution.

Step 4: Calculate the molality of KMnO4:
Molality = moles of solute (KMnO4) / mass of solvent (water) in kg
= 0.045 mol / (100.0 g / 1000)
= 0.45 mol/kg

Therefore, the molality of the potassium permanganate solution is 0.45 mol/kg.

To find the mole fraction of potassium permanganate (KMnO4) in the saturated solution, we need to calculate the moles of KMnO4 and the moles of water present.

Step 1: Calculate the moles of KMnO4:
The molecular weight of KMnO4 is:
K (1 atom) + Mn (1 atom) + O (4 atoms) = 39.10 g/mol + 54.94 g/mol + (16.00 g/mol × 4) = 158.04 g/mol

The number of moles of KMnO4 in the 7.1 g of the compound is:
moles of KMnO4 = mass of KMnO4 / molecular weight of KMnO4
moles of KMnO4 = 7.1 g / 158.04 g/mol

Step 2: Calculate the moles of water:
Given that the mass of water is 100.0 g, we can use the molar mass of water to convert this mass to moles:
The molecular weight of water (H2O) is:
H (2 atoms) + O (1 atom) = (1.01 g/mol × 2) + 16.00 g/mol = 18.02 g/mol

The number of moles of water in 100.0 g is:
moles of water = mass of water / molecular weight of water
moles of water = 100.0 g / 18.02 g/mol

Step 3: Calculate the mole fraction of KMnO4:
The mole fraction (X) of KMnO4 is defined as the moles of KMnO4 divided by the total number of moles in the solution (moles of KMnO4 + moles of water).
mole fraction (XMnO4) = moles of KMnO4 / (moles of KMnO4 + moles of water)

Step 4: Calculate the molality of the solution:
The molality (m) of a solution is defined as the moles of solute (KMnO4) divided by the mass of the solvent (water) in kilograms.
molality (m) = moles of KMnO4 / mass of water (in kg)

To convert the mass of water (100.0 g) to kilograms, divide it by 1000:
mass of water (kg) = mass of water (g) / 1000

Now you can substitute the calculated values into the formulas to find the mole fraction and the molality of the potassium permanganate solution.