Question

fermentation of 750. ml grape juice (density 5 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 258c? (the density of ethanol is 0.79 g/cm3.)

Answer 1

The pressure of CO2 inside the wine bottle at 258°C would be approximately 4.13 atm.

Step-by-step explanation:

To calculate the pressure of CO2 inside the wine bottle, we need to consider the amount of ethanol produced during fermentation and the ideal gas law.

Firstly, we need to convert the volume of ethanol to moles by dividing it by the molar volume.

The molar volume at standard temperature and pressure is 22.4 L/mol.

Next, we can use the ideal gas law, PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin.

By rearranging the equation, we can solve for P.

Given:

V = 825 mL = 0.825 L (volume of the bottle)

n = 0.12 x 0.825 L / 22.4 L/mol (moles of ethanol)

R = 0.0821 L·atm/(mol·K) (ideal gas constant)

T = 258°C + 273.15 = 531.15 K (temperature in Kelvin)

Plugging these values into the equation, we get:

P * 0.825 = (0.12 * 0.825) * 0.0821 * 531.15

Solving for P, we find:

P = (0.12 * 0.825) * 0.0821 * 531.15 / 0.825

≈ 4.13 atm

Therefore, the pressure of CO2 inside the wine bottle at 258°C would be approximately 4.13 atm.