A bottle of wine contains 12.5% ethanol by volume. The density of ethanol (C2H5OH) is 0.789 g/cm3. Calculate the concentration of ethanol in wine in terms of mass percent and molality.

12.5% ethanol by volume implies 12.5 mL ethanol

12.5 mL ethanol+87.5 mL water
12.5 mL ethanol x 0.789 g/mL = 9.8625 g ethanol
9.8625 g / 46.068 g/mol = 0.2140857 mol ethanol
87.5 mL water x 1.00 g/mL = 87.5 g water
87.5 g water = 0.0875 kg water
molality = 0.2140857 mol / 0.0875 kg = 2.4466937 m

I dun know

2.45

Why did the wine go to therapy?

Because it had a "proof" complex!

Now, let's tackle your question. To calculate the concentration of ethanol in wine in terms of mass percent, we need to convert the volume percentage to mass percentage. Since the density of ethanol is 0.789 g/cm3, we can say that 1 cm3 of ethanol weighs 0.789 grams.

Now, if the wine contains 12.5% ethanol by volume, that means there are 12.5 cm3 of ethanol in every 100 cm3 of wine. Multiplying by the density, we can say that in every 100 cm3 of wine, there's 0.789 g/cm3 * 12.5 cm3 = 9.86375 grams of ethanol.

So, the mass percentage of ethanol in wine is 9.86375 grams per 100 grams of wine. In percentage form, this is approximately 9.86%.

As for the molality, we need to calculate the amount of ethanol in moles and then divide it by the mass of the solvent (wine) in kilograms.

To do this, we need to know the molar mass of ethanol, which is 46.07 g/mol.

Since the mass of ethanol in the bottle is 9.86375 grams, we can divide that by the molar mass to get the number of moles:

9.86375 g / 46.07 g/mol = 0.214 moles of ethanol.

Now, let's assume that the mass of wine is 1000 grams (1 kilogram).

The molality of ethanol in wine is calculated by dividing the number of moles of ethanol by the mass of the solvent in kilograms:

0.214 moles / 1 kg = 0.214 mol/kg.

So, the molality of ethanol in wine is 0.214 mol/kg.

I hope that's clear! Let me know if you need any more assistance, or if you'd like another joke.

To calculate the concentration of ethanol in wine in terms of mass percent and molality, we'll need to follow these steps:

1. Calculate the mass of ethanol in the bottle of wine.

Given that the volume percentage of ethanol is 12.5%, we can calculate the volume of ethanol in the wine as follows:
Volume of ethanol = (12.5 / 100) * Volume of wine

However, we're not given the volume of wine, so we'll have to assume a specific value. Let's assume the volume of the wine bottle is 750 ml.

Volume of ethanol = (12.5 / 100) * 750 ml = 93.75 ml

Next, we'll calculate the mass of ethanol using its density.

Mass of ethanol = Volume of ethanol * Density of ethanol
Mass of ethanol = 93.75 ml * 0.789 g/cm3 = 73.97 g

2. Calculate the mass percent of ethanol.

Mass percent = (Mass of ethanol / Total mass of wine) * 100

To find the total mass of wine, we need to know the mass of the wine bottle as well. Let's assume the mass of the wine bottle is 500 g.

Total mass of wine = Mass of wine + Mass of bottle
Let's assume the mass of wine is 750 g (same as the volume assumption) and the mass of the bottle is 500 g.

Total mass of wine = 750 g + 500 g = 1250 g
Mass percent = (73.97 g / 1250 g) * 100 = 5.9184%

3. Calculate the molality of ethanol.

Molality is defined as the number of moles of solute (ethanol) per kilogram of solvent (water).

First, we'll need to convert the mass of ethanol to moles.
Moles of ethanol = Mass of ethanol / Molar mass of ethanol

The molar mass of ethanol (C2H5OH) can be calculated as:
(2 * atomic mass of C) + (6 * atomic mass of H) + (1 * atomic mass of O) = 12.01 * 2 + 1.01 * 6 + 16.00 = 46.07 g/mol

Moles of ethanol = 73.97 g / 46.07 g/mol = 1.61 mol

Now, we'll calculate the molality:
Molality = Moles of ethanol / Mass of water (in kg)

To calculate the mass of water, we need to convert the volume assumption (750 ml) to mass.

The density of water is 1 g/cm3, so the mass of 750 ml of water is:
Mass of water = Volume of water * Density of water
Mass of water = 750 ml * 1 g/cm3 = 750 g = 0.75 kg

Molality = 1.61 mol / 0.75 kg = 2.14 mol/kg

Therefore, the concentration of ethanol in wine is approximately 5.9184% mass percent and 2.14 mol/kg molality.

12.5% by volume means 12.5 mL ethanol/100 mL of solution. Don't we need the density of the wine in order to calculate the mass of the 100 mL?

We can estimate if we assume ethanol and water volumes add (and I KNOW they do not).
12.5 mL ethanol in (12.5 mL ethanol+ 87.5 mL water). Using the densities above, calculate volume ethanol and volume water. I get 9.86 g for ethanol and 87.5 g for water for a total of 97.36 grams. The solution is 9.86g/97.36 g = 10.13% by mass (w/w%).

To convert this number to molality, we want to find moles ethanol/kg solvent.
moles ethanol = grams/molar mass which you can do.
moles ethanol/(10.13 g + 89.87 g water), then moles/kg solvent gives molality.