In the "Methode Champenoise," grape juice is fermented in a...

In the "Methode Champenoise," grape juice is fermented in a wine bottle to produce sparkling wine. The reaction is $$\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(a q) \longrightarrow 2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(a q)+2 \mathrm{CO}_{2}(g)$$ Fermentation of $750 .$ mL grape juice (density $=1.0 \mathrm{g} / \mathrm{cm}^{3} )$ is allowed to take place in a bottle with a total volume of 825 $\mathrm{mL}$ until 12$\%$ by volume is ethanol $\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)$ . Assuming that the $\mathrm{CO}_{2}$ is insoluble in $\mathrm{H}_{2} \mathrm{O}$ (actually, a wrong assumption), what would be the pressure of $\mathrm{CO}_{2}$ inside the wine bottle at $25^{\circ} \mathrm{C} ?$ (The density of ethanol is $0.79 \mathrm{g} / \mathrm{cm}^{3} . )$

In the "Methode Champenoise," grape juice is fermented in a wine bottle to produce sparkling wine. The reaction is
$$\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(a q) \longrightarrow 2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(a q)+2 \mathrm{CO}_{2}(g)$$
Fermentation of $750 .$ mL grape juice (density $=1.0 \mathrm{g} / \mathrm{cm}^{3} )$ is allowed to take place in a bottle with a total volume of 825 $\mathrm{mL}$ until 12$\%$ by volume is ethanol $\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)$ . Assuming that the $\mathrm{CO}_{2}$ is insoluble in $\mathrm{H}_{2} \mathrm{O}$ (actually, a wrong assumption), what would be the pressure of $\mathrm{CO}_{2}$ inside the wine bottle at $25^{\circ} \mathrm{C} ?$ (The density of ethanol is $0.79 \mathrm{g} / \mathrm{cm}^{3} . )$

Key Concepts

Ideal Gas Law

The ideal gas law (PV = nRT) is a fundamental principle in physical chemistry that relates the pressure, volume, temperature, and mole quantity of a gas. This law is used to determine the pressure exerted by the carbon dioxide generated during the fermentation process in a closed container.

Volume, Density, and Concentration Conversions

Conversions between volume, density, and concentration are critical when transitioning from mass or volume measurements of liquids to molar quantities. This manipulation of units enables the application of stoichiometric relationships and subsequent use of the ideal gas law to calculate properties such as gas pressure in a system.

Fermentation

Fermentation is a biological process where sugars are converted into ethanol and carbon dioxide by the action of yeast or bacteria. This reaction is central to a variety of processes including food and beverage production, serving as an essential example of biochemical transformations that yield both alcohol and gas as products.

Stoichiometry of Chemical Reactions

Stoichiometry involves using a balanced chemical equation to determine the quantitative relationships between reactants and products. In this context, it is used to relate the consumption of sugar to the production of ethanol and carbon dioxide, allowing one to calculate the molar yields from known amounts of starting materials.

Transcript

00:01 For this problem, we are looking at grape juice fermentation in a wine bottle to produce sparkling wine.

00:09 And we're told that the reaction is c6h12 .06 yields 2.

00:15 C2h5oh, which is ethanol plus 2 co2.

00:20 We are told that the volume of the grape juice to start off is 750 milliliters.

00:29 We are told that the density of grape juice is one gram per centimeter cubed.

00:41 We're told that the volume of the bottle equals 825 milliliters, and that it's going to be fermenting until the volume of the ethanol is 12 %, or the ethanol is 12 % by volume, assuming, and then assuming that co2 is insoluble in water, which is an incorrect assumption, but the assumption that we're going to make, we're trying to find what the pressure of co2 inside the wine bottle at a temperature of 25 degrees celsius will be.

01:19 And we're also told that the density of ethanol is 0 .79 ,000, grams per centimeter cubed.

01:30 So this is all of our known information.

01:32 We might as well go ahead and convert some of this stuff right off the bat.

01:37 So for instance, 750 milliliters is 0 .750 liters.

01:44 One gram per centimeter cubed is equivalent to one gram per millimeter millimeter because one centimeter cubed is one millimeter.

01:54 We can turn this into liters as well, so 8 .25 liters.

02:00 12 percent ethanol, we're going to do 12 percent of the volume of grape juice.

02:08 So we're going to do 0 .12 times our 750 milliliters of grape juice, which will give us a volume of 90 milliliters.

02:25 And we're going to change our temperature into kelvin.

02:28 So 25 plus 273 gives us a temperature of 298 kelvin.

02:37 And then, of course, we can change this density as well to 0 .79 grams per milliliter.

02:44 Now, some other information we're also going to need right off the bat is going to be the molar masses of both our ethanol as well as our glucose.

02:59 So for ethanol, so to find our molar mass of ethanol, come over here, okay, we can find the molar mass.

03:11 So if we have c2h50h, then we have 2 times 12 .01 plus 6 times 1 .008 plus 16.

03:29 And we get that our molar mass of ethanol is going to be 46 .068 grams.

03:39 And then we can do the same thing for glucose.

03:41 So we have c6h1206.

03:45 So we have 6 times 12 .01 plus 12 .008.

03:53 Plus 6 times 16, and that gives us a total mass of 180 .156 grams.

04:04 So we have our molar masses now.

04:08 All right, so first thing we have is we're going to figure out how many moles of ethanol we produced during the fermentation process.

04:20 So to start it off, let's go ahead.

04:23 And we know that we produced 90 milliliters of ethanol.

04:31 We know that the density of ethanol is 0 .79 grams per milliliter, and we know that one mole of it is equal to 46 .068 grams.

04:49 So putting that all together, we end up with 1 .4 .4 .5 grams...

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