Answer:
The pressure inside the wine bottle at 21 °C is 4.8 · 10² atm
Explanation:
Hi there!
We know that 1 mol of CO₂ is produced per mol of produced ethanol.
If the final concentration of ethanol is 13%, let´s calculate how many moles of ethanol are present at that concentration.
A concentration of 13% means that in 100 ml of solution, 13 ml is dissolved ethanol. We have 754 ml of solution, then, the volume of ethanol will be:
754 ml solution · (13 ml ethanol/100 ml solution) = 98 ml ethanol
With the density, we can calculate the mass of ethanol present:
density = mass/ volume
0.79 g/ml = mass / 98 ml
mass = 0.79 g/ml · 98 ml
mass = 77 g
The molar mass of ethanol is 46.07 g/mol, then 77 g of ethanol is equal to:
77 g · (1 mol/46.07 g) = 1.7 mol
Then, the number of moles of CO₂ produced will be 1.7 mol.
Using the equation of the ideal gas law, we can calculate the pressure of CO₂:
P = nRT/V
Where:
P = pressure
n = number of moles
R = ideal gas constant
T = temperature
V = volume
The volume will be the headspace of the bottle (840 ml - 754 ml) 86 ml = 0.086 l.
The temperature in kelvin will be: 21 + 273 = 294 K
The gas constant is 0.082 l atm / K mol
Then:
P = (1.7 mol · 0.082 l atm/K mol · 294 K)/ 0.086 l
P = 4.8 · 10² atm
The pressure inside the wine bottle at 21 °C is 4.8 · 10² atm
