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 724 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 the co2 is insoluble in h2o (actually, a wrong assumption), what would be the pressure of co2 inside the wine bottle at 29°c? (the density of ethanol is 0.79 g/cm3.)

So you have 724 mL (cm3) of C2H12O6, but during the reaction 12% turns to C2H2OH giving you about 87.6mL of ethanol (C2H2OH) 

Since the density of ethanol is given we can find the about of moles produced and use the balanced equation to find the amount of CO2 produced and then use the gas laws to determine the pressure of the gas in atm. 

86.88mL ethanol * 0.79 g/cm3 =  68.6352g ethanol 

ethanol has a molar mass of 46.068 g/mole so, 

68.6352g ethanol / 46.068 g/mole = 1.489867 moles ethanol 

the share of ethanol to CO2 is given as 1:1 per the reaction equation so the similar amount of CO2 is formed. 

using the gas laws we can now find the pressure of co2 

P=(nRT)/V 

plugging in we get the following: 

((0.0821 L*atm/K*mol)*(1.489867 moles CO2)*(273+29 K)/(.825L) 

since the equation requires consistency in units we convert degrees C to K by adding 273, and dividing our volume of the bottle by 1000 to get the amount of liters. 

the answer should be 44.7758308 atms. 

the density of gold = 19.3 g/cm3

the relation between density and mass and volume is

density = mass / volume

given :

mass of gold = 13 g

density = 13g / volume = 19.3

volume = 13 /19.3 = 0.67 cm^3

thus volume of gold nugget = 0.67 cm^3