Finding molarity and molality(best answer)?

An aqueous solution is prepared by diluting 3.30 mL acetone,(d= 0.789g/mL) with water to a final volume of 75.0 mL. The density of the solution is 0.993 g/mL. What is the molarity, molality and mole fraction of acetone in this solution?

molality = moles/kg solvent. Ac2O is acetone.

First the moles Ac2O.
grams = 3.30 mL x 0.789 g/mL = 2.604 g Ac2O.
moles = g/molar mass = 2.604/58.08 = 0.045 g (approximate--you should do it more carefully).

Next for solvent (H2O)
grams soln = 75.0mL x 0.993 g/mL = about 74 grams
We had 2.6 g Ac2O in that ; therefore, g H2O = 74-2.6 = about 71 g or 0.071 kg
Then molality = moles/kg solvent.
I assume you can convert from molality to M and mole fraction.
M = moles/L soln
mole fraction = moles Ac2O/total moles.

To find the molarity, molality, and mole fraction of acetone in the solution, we can follow these steps:

Step 1: Calculate the mass of acetone used.
The mass of acetone used can be calculated using the density and volume of acetone.
Mass of acetone = Volume of acetone * Density of acetone
Mass of acetone = 3.30 mL * 0.789 g/mL

Step 2: Calculate the mass of the solution.
The mass of the solution can be calculated using the density of the solution and the final volume.
Mass of solution = Volume of the solution * Density of the solution
Mass of solution = 75.0 mL * 0.993 g/mL

Step 3: Calculate the moles of acetone.
The moles of acetone can be calculated using the mass of acetone and the molar mass of acetone.
Molar mass of acetone = 58.08 g/mol
Moles of acetone = Mass of acetone / Molar mass of acetone

Step 4: Calculate the molarity.
Molarity is defined as moles of solute divided by the volume of the solution in liters.
Molarity = Moles of solute / Volume of the solution (in liters)
Note: Convert the volume of the solution from mL to L.
Molarity = Moles of acetone / (75.0 mL / 1000)

Step 5: Calculate the molality.
Molality is defined as moles of solute divided by the mass of the solvent in kilograms.
Mass of the solvent = Mass of solution - Mass of acetone
Molality = Moles of acetone / (Mass of the solvent in kg)

Step 6: Calculate the mole fraction.
The mole fraction is defined as the ratio of moles of acetone to the total number of moles.
Mole fraction of acetone = Moles of acetone / Total moles in the solution
Note: Total moles can be calculated by dividing the mass of the solution by the molar mass of the solution.
Total moles = Mass of solution / Molar mass of solution
Mole fraction of acetone = Moles of acetone / Total moles

Now, let's plug in the values and calculate the molarity, molality, and mole fraction of acetone.

Step 1: Calculating the mass of acetone used.
Mass of acetone = 3.30 mL * 0.789 g/mL = 2.6007 g

Step 2: Calculating the mass of the solution.
Mass of solution = 75.0 mL * 0.993 g/mL = 74.475 g

Step 3: Calculating the moles of acetone.
Moles of acetone = 2.6007 g / 58.08 g/mol ≈ 0.0448 mol

Step 4: Calculating the molarity.
Molarity = 0.0448 mol / (75.0 mL / 1000) = 0.5973 M

Step 5: Calculating the molality.
Mass of the solvent = 74.475 g - 2.6007 g = 71.8743 g
Molality = 0.0448 mol / (71.8743 g / 1000) = 0.6236 mol/kg

Step 6: Calculating the mole fraction of acetone.
Molar mass of the solution = Mass of solution / Total moles
Total moles = 74.475 g / (58.08 g/mol + 2.6007 g / 58.08 g/mol)
Total moles ≈ 1.285 mol

Mole fraction of acetone = 0.0448 mol / 1.285 mol ≈ 0.0349

In summary, the molarity of acetone in the solution is 0.5973 M, the molality is 0.6236 mol/kg, and the mole fraction is 0.0349.

To find the molarity, molality, and mole fraction of acetone in the given solution, you will need to follow these steps:

1. Begin by finding the mass of the acetone used in the solution. The mass of acetone can be calculated by multiplying its volume (3.30 mL) by its density (0.789 g/mL):

Mass of acetone = 3.30 mL × 0.789 g/mL = 2.60 g

2. Next, determine the mass of the entire solution. The mass of the solution can be calculated by multiplying its volume (75.0 mL) by its density (0.993 g/mL):

Mass of solution = 75.0 mL × 0.993 g/mL = 74.5 g

3. Now, you can find the molarity of the acetone in the solution. Molarity is defined as the number of moles of solute (acetone) per liter of solution. To calculate it, you need to know the molar mass of acetone, which is 58.08 g/mol. The number of moles of acetone can be calculated using the formula:

Moles of acetone = Mass of acetone / Molar mass of acetone
= 2.60 g / 58.08 g/mol ≈ 0.04476 mol

Molarity = Moles of acetone / Volume of solution (in liters)
= 0.04476 mol / 0.075 L ≈ 0.596 M

Therefore, the molarity of acetone in the solution is approximately 0.596 M.

4. Next, you can calculate the molality of the acetone in the solution. Molality is defined as the number of moles of solute per kilogram of solvent. To calculate it, you need to convert the mass of water used to kilograms:

Mass of water = Mass of solution - Mass of acetone
= 74.5 g - 2.60 g = 71.9 g

Molality = Moles of acetone / Mass of water (in kilograms)
= 0.04476 mol / 0.0719 kg ≈ 0.621 mol/kg

Therefore, the molality of acetone in the solution is approximately 0.621 mol/kg.

5. Lastly, you can calculate the mole fraction of acetone in the solution. The mole fraction is the ratio of moles of acetone to the total moles of all components in the solution. To find the mole fraction, you need to calculate the moles of water:

Moles of water = Mass of water / Molar mass of water
= 71.9 g / 18.015 g/mol ≈ 3.992 mol

Total moles = Moles of acetone + Moles of water
= 0.04476 mol + 3.992 mol ≈ 4.036 mol

Mole fraction of acetone = Moles of acetone / Total moles
= 0.04476 mol / 4.036 mol ≈ 0.0111

Therefore, the mole fraction of acetone in the solution is approximately 0.0111.

To summarize:
- Molarity of acetone in the solution: approximately 0.596 M
- Molality of acetone in the solution: approximately 0.621 mol/kg
- Mole fraction of acetone in the solution: approximately 0.0111