carbon dioxide pressure over wine

[smit0452]

Hello, everyone. This is my first post.

 

I'm having trouble with a problem from my general chemistry homework. Everytime I work it out, I end up with a ridiculously large pressure. Any suggestions will be greatly appreciated. The problem is written as follows:

 

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

 

C6H12O6(aq)---> 2 C2H5OH(aq) + 2 CO2(g)

 

Fermentation of 750. mL of grape juice (density=1.0g/mL) is allowed to take place in a bottle with a total volume of 825mL until 12% by volume is ethanol (C2H5OH). Assuming that the CO2 is insoluble in water (actually, a wrong assumption), what would be the pressure of CO2 inside the wine bottle at 25 degrees Celsius? (density of ethanol is 0.79g/mL)

[hermanntrude]

how rediculously large? you said yourself that the assumption isn't true, and have you ever seen a champagne cork go off? it really moves. that's because of high pressure.

[John Cuthber]

If you show us how you came up with a ridiculously large answer then we can tell you where you went wrong (if you did) or reasssure you that you got it right.

[feign_ignorence]

Hmm... this is what i did:

 

Set x as an independent variable representing the volume of grape juice that reacts to produce ethanol.

 

Use the given volume percentage with stoichometric ratio, density, molar mass, etc to solve for x.

 

Verify that x gives y such that (in mL [ethanol volume]) y*100/(750-x) =~ 12%

 

Convert x to moles of CO2 and use PV=nRT to solve for pressure. (V=825-(750-x)-y???)

 

I got 0.29 atm but that isn't large so i'm assuming i did something wrong...

 

(Is this reasoning correct?)