In the "Methode Champenoise," grape juice is fermented in a wine bottle to produce sparkling wine. The reaction is given below.

C6H12O6(aq)--> 2 C2H5OH(aq) + 2 CO2(g)
Fermentation of 746 mL grape juice (density = 1.0 g/cm3) is allowed to take place in a bottle with a total volume of 825 mL until 12% by volume is ethanol (C2H5OH). Assuming that CO2 obeys Henry's law. Calculate the partial pressure of CO2 in the gas phase and the solubility of CO2 in the wine at 25°C. The Henry's law constant for CO2 is 32 L·atm/mol at 25°C with Henry's law in the form P = kC, where C is the concentration of the gas in mol/L. The density of ethanol is 0.79 g/cm3.

Ah, so we're talking about the science of bubbly beverages! Let's pop this question open, shall we?

First, we can calculate the amount of ethanol produced by converting the volume percent to moles. Since the total volume is 825 mL, and we want 12% of it to be ethanol, we have:

825 mL * 0.12 = 99 mL ethanol

Next, we need to convert this volume of ethanol to grams. We know the density of ethanol is 0.79 g/cm3, so:

99 mL * 0.79 g/cm3 = 78.21 g ethanol

Now, let's determine the moles of ethanol using its molar mass. The molar mass of ethanol (C2H5OH) is:

2*(12.01 g/mol) + 6*(1.01 g/mol) + 1*(16.00 g/mol) = 46.07 g/mol

So, the moles of ethanol produced are:

78.21 g / 46.07 g/mol = 1.70 mol ethanol

According to the balanced equation, for every 1 mole of ethanol produced, 2 moles of CO2 are also produced. Therefore, we have:

2 moles CO2 / 1.70 mol ethanol = 1.18 mol CO2

Now, let's calculate the partial pressure of CO2 using Henry's law. Given that the Henry's law constant for CO2 is 32 L·atm/mol, we can use the equation P = kC, where C is the concentration of CO2 in mol/L.

Here, our concentration is:

1.18 mol CO2 / (0.746 L - 0.099 L) = 1.82 mol/L

Plugging it into Henry's law equation gives:

P = (32 L·atm/mol) * (1.82 mol/L) = 58.24 atm

So, the partial pressure of CO2 in the gas phase is approximately 58.24 atm.

Lastly, we need to find the solubility of CO2 in the wine at 25°C. Since Henry's law relates the concentration of the gas to its partial pressure, we can rearrange the equation to find the concentration:

C = P / k

C = 58.24 atm / (32 L·atm/mol) = 1.82 mol/L

So, the solubility of CO2 in the wine at 25°C is approximately 1.82 mol/L.

Cheers to the science behind sparkling wine!

To calculate the partial pressure of CO2 in the gas phase and the solubility of CO2 in the wine, we'll follow the given information and use Henry's law.

Step 1: Calculate the moles of ethanol (C2H5OH) produced
We are given that 12% by volume of the wine is ethanol. Since the total volume of the bottle is 825 mL, the volume of ethanol produced is:

Volume of ethanol = 12% of 825 mL
= (12/100) * 825 mL
= 99 mL

To convert this volume into moles, we'll use the density of ethanol and the molar mass of ethanol.

Density of ethanol = 0.79 g/cm3
Molar mass of ethanol = 46.07 g/mol (C2H5OH)

Moles of ethanol = (Volume of ethanol * Density of ethanol) / Molar mass of ethanol
= (99 mL * 0.79 g/cm3) / 46.07 g/mol
= 1.69 mol

Step 2: Calculate the moles of CO2 produced
From the balanced equation, we know that for every mole of ethanol, 2 moles of CO2 are produced. Therefore,

Moles of CO2 = 2 * Moles of ethanol
= 2 * 1.69 mol
= 3.38 mol

Step 3: Calculate the concentration of CO2 in the wine
The concentration of CO2 can be calculated using the volume of CO2 produced and the total volume of the wine.

Concentration of CO2 = (Volume of CO2 / Volume of wine)
= (Volume of CO2 / Total volume of the bottle)

Since the volume of wine is given as 825 mL and the volume of CO2 is not given, we need to calculate the volume of CO2 by subtracting the volume of ethanol from the total volume.

Volume of CO2 = Total volume of the bottle - Volume of ethanol
= 825 mL - 99 mL
= 726 mL

Concentration of CO2 = (726 mL / 825 mL)
= 0.88 mol/L

Step 4: Use Henry's law to calculate the partial pressure of CO2
Henry's law states that the partial pressure of a gas is directly proportional to its concentration. The proportionality constant is given as the Henry's law constant, which is 32 L·atm/mol for CO2 at 25°C.

Partial pressure of CO2 = Henry's law constant * Concentration of CO2
= 32 L·atm/mol * 0.88 mol/L
= 28.16 atm

Therefore, the partial pressure of CO2 in the gas phase is 28.16 atm, and the solubility of CO2 in the wine is 0.88 mol/L.

To solve this problem, we need to calculate both the partial pressure of CO2 in the gas phase and the solubility of CO2 in the wine at 25°C.

First, let's calculate the moles of ethanol produced in the fermentation reaction. The volume of the grape juice is given as 746 mL. Since the density is 1.0 g/cm^3, the mass of the grape juice is 746 grams.

To calculate the moles of ethanol produced, we can use the molar mass of ethanol, which is 46.07 g/mol.

Moles of ethanol = mass of ethanol / molar mass of ethanol
Moles of ethanol = 746 g / 46.07 g/mol

Next, let's calculate the total volume of the wine once the fermentation is complete. The total volume is given as 825 mL, so we convert it to liters.

Total volume of wine = 825 mL / 1000 mL/L = 0.825 L

To calculate the concentration of ethanol (C2H5OH) in the wine, we divide the moles of ethanol by the total volume of the wine.

Concentration of ethanol = Moles of ethanol / Total volume of wine

Now, let's calculate the partial pressure of CO2 using Henry's law. According to Henry's law, the partial pressure of a gas is equal to the Henry's law constant (k) times the concentration of the gas.

Partial pressure of CO2 = k * concentration of CO2

The given Henry's law constant is 32 L·atm/mol at 25°C.

Finally, let's calculate the solubility of CO2 in the wine at 25°C using the definition of solubility.

Solubility = Concentration of CO2 / Partial pressure of CO2

Now that we have all the necessary information, let's plug in the values and calculate the answers.

1. Calculate the moles of ethanol:
Moles of ethanol = 746 g / 46.07 g/mol = 16.18 mol

2. Calculate the concentration of ethanol in the wine:
Concentration of ethanol = 16.18 mol / 0.825 L = 19.63 mol/L

3. Calculate the partial pressure of CO2:
Partial pressure of CO2 = 32 L·atm/mol * 19.63 mol/L = 628.16 atm

4. Calculate the solubility of CO2:
Solubility = 19.63 mol/L / 628.16 atm = 0.03128 mol/L/atm

Therefore, the partial pressure of CO2 in the gas phase is 628.16 atm, and the solubility of CO2 in the wine at 25°C is 0.03128 mol/L/atm.