. Jack Daniels Tennessee whiskey is 40.00% ethanol by volume. However, % alcohol by mass is quite different from % by volume. The molality of ethanol in an aqueous solution that is 40.00 % ethanol by volume is 10.88 molal.

A) Find the % ethanol by MASS, based on the molality. The MM of ethanol, C2H5OH is 46 g.
B. Find the mole fraction of alcohol in the 10.88 molal ethanol solution.
C. The solution has a density of 0.948 g/mL. Find the molarity of the solution.

For A.

Assume you have enough solution to contain 10.88 moles ethanol. Therefore, you will have 1 kg water (1,000 g).
10.88 moles x (46 g/mol) = 500.48 grams ethanol.
Total mass of the solution is 1000 g + 500.48 = 1500.48 grams.
% ethanol = (mass ethanol/mass soln)*100
% ethanol = (500.48/1500.48)*100 = 33.35%.

For B, take enough sample to have 10.88 moles ethanol. That will give you 1,000 g H2O. Convert g H2O to moles and calculate mole fraction of each.

For C. I would use the mass percent and the density to calculate molarity.

Post your work if you get stuck.

A) To find the % ethanol by mass based on the molality, we need to calculate the mass of ethanol present in the solution.

First, let's find the molality of the solution:
Molality (m) = moles of solute / mass of solvent in kg

Given that the molality (m) = 10.88 molal and the molar mass (MM) of ethanol (C2H5OH) is 46 g/mol, we can use these values to calculate the moles of ethanol:
moles of solute = m * (mass of solvent in kg)

Here, the moles of ethanol will be equal to the moles of solute.

Next, we need to find the mass of the solvent. Let's assume we have 1 kg of solvent.

mass of solvent in kg = 1 kg

Now we can calculate the moles of ethanol:
moles of ethanol = 10.88 molal * 1 kg

Now, let's find the mass of ethanol:
mass of ethanol = moles of ethanol * molar mass of ethanol

mass of ethanol = (10.88 molal * 1 kg) * 46 g/mol

Finally, we can calculate the % ethanol by mass:
% ethanol by mass = (mass of ethanol / total mass of solution) * 100

B) To find the mole fraction of alcohol in the 10.88 molal ethanol solution, we can assume that the density of the solution is equal to the density of water (1 g/mL). Therefore, the mass of the solution will be equal to its volume.

Given that the density of the solution is 0.948 g/mL, the mass of the solution will be equal to its volume, which is 1 mL.

mass of solution = 1 mL = 1 g

Next, we need to find the mass of ethanol in the solution. We already calculated this in part A as the moles of ethanol multiplied by the molar mass of ethanol.

mass of ethanol = (10.88 molal * 1 kg) * 46 g/mol

Now, let's find the mole fraction of alcohol in the solution:
mole fraction of alcohol = moles of ethanol / moles of solution

moles of solution = mass of solution / molar mass of solution

Given that the molar mass of water is 18 g/mol, we can calculate the moles of solution:
moles of solution = 1 g / 18 g/mol

C) To find the molarity of the solution, we can use the formula:

Molarity (M) = moles of solute / volume of solution in liters

Here, the moles of solute are the moles of ethanol, which we already calculated in part B.

Now we need to find the volume of the solution. Given that the density of the solution is 0.948 g/mL, we can calculate the volume:

volume of solution = mass of solution / density of solution

volume of solution = 1 g / 0.948 g/mL

Finally, we can calculate the molarity:
Molarity (M) = moles of ethanol / volume of solution in liters

To find the % ethanol by mass based on the molality, we need to calculate the mass of ethanol in the solution.

Step 1: Calculate the mass of 1 liter (1000 mL) of the solution.
The density of the solution is given as 0.948 g/mL. Therefore, the mass of 1 liter of the solution can be calculated as:
Mass of solution = Volume of solution x Density of solution
Mass of solution = 1000 mL x 0.948 g/mL = 948 g

Step 2: Calculate the mass of ethanol in the solution.
The molality of ethanol in the solution is given as 10.88 molal. This means that there are 10.88 moles of ethanol dissolved in 1000 g (1 liter) of water.

The molar mass of ethanol (C2H5OH) is given as 46 g/mol. Therefore, the mass of ethanol in the solution can be calculated as:
Mass of ethanol = Molality x Molar mass
Mass of ethanol = 10.88 molal x 46 g/mol = 500.48 g

Step 3: Calculate the % ethanol by mass.
% ethanol by mass = (Mass of ethanol / Mass of solution) x 100
% ethanol by mass = (500.48 g / 948 g) x 100 = 52.71%

So, the % ethanol by mass, based on the molality, is approximately 52.71%.

To find the mole fraction of alcohol in the 10.88 molal ethanol solution, we need to calculate the moles of ethanol and water.

Step 1: Calculate the moles of ethanol.
The molality of ethanol in the solution is given as 10.88 molal. This means that there are 10.88 moles of ethanol dissolved in 1000 g (1 liter) of water.

So, the moles of ethanol can be calculated as:
Moles of ethanol = Molality x Mass of water in kg
Moles of ethanol = 10.88 molal x 1 kg = 10.88 moles

Step 2: Calculate the moles of water.
The moles of water can be calculated as:
Moles of water = Mass of water in g / Molar mass of water

The mass of water can be calculated as:
Mass of water = Mass of solution - Mass of ethanol
Mass of water = 948 g - 500.48 g = 447.52 g

The molar mass of water (H2O) is 18 g/mol. Therefore, the moles of water can be calculated as:
Moles of water = 447.52 g / 18 g/mol = 24.86 moles

Step 3: Calculate the mole fraction of alcohol.
Mole fraction of alcohol = Moles of ethanol / (Moles of ethanol + Moles of water)
Mole fraction of alcohol = 10.88 moles / (10.88 moles + 24.86 moles)
Mole fraction of alcohol = 0.30

So, the mole fraction of alcohol in the 10.88 molal ethanol solution is 0.30.

To find the molarity of the solution, we need to calculate the moles of ethanol and then convert it to molarity.

Step 1: Calculate the moles of ethanol.
The molality of ethanol in the solution is given as 10.88 molal. This means that there are 10.88 moles of ethanol dissolved in 1000 g (1 liter) of water.

So, the moles of ethanol can be calculated as:
Moles of ethanol = Molality x Mass of water in kg
Moles of ethanol = 10.88 molal x 1 kg = 10.88 moles

Step 2: Calculate the volume of the solution.
The density of the solution is given as 0.948 g/mL. Therefore, the volume of the solution can be calculated as:
Volume of solution = Mass of solution / Density of solution
Volume of solution = 948 g / 0.948 g/mL = 1000 mL

Step 3: Calculate the molarity of the solution.
Molarity = Moles of ethanol / Volume of solution in L
Molarity = 10.88 moles / 1 L = 10.88 M

So, the molarity of the solution is 10.88 M.