Question

A student is required to prepare 40.0 mL of ethanol using a sucrose fermentation technique. How many mL of carbon dioxide can be expected to fill a balloon used as a trap in the fermentation? Conditions: 22.1°C and 1.05 atm, the enzymatic system works at 65.0 % efficiency, and the solubility of CO2 in water can be obtained from the following table:

(ml of CO2/100 mL of H2O at 760 mm Hg)

Temperature 0°C 20°C 60°C

Solubility (mL) 171 88 36

The sucrose solution used in the fermentation was 0.750 M. Assume solubility of CO2 in water equivalent to the solubility in the sucrose solution. Hint: some of the CO2 obtained from the fermentation dissolves in the solution; the rest goes to the balloon. Disregard water vapor pressure.

Answer 1

The balanced equation for the fermentation of sucrose can be written as shown below.

i.e. The fermentation of 1 mole of sucrose at 100% efficiency produces 4 moles of CO₂.

Therefore, the fermentation of 1 mole of sucrose at 65% efficiency produces (65/100)*4 = 2.6 moles of CO₂.

The concentration of sucrose solution = 0.75 M, i.e. 0.75 mol/L

Then the no. of moles of CO₂ that can be produced at 65% efficiency = 0.75*2.6, i.e. 1.95 mol

Volume of the ethanol required to prepare = 40 mL

From ideal gas equation, PV = nRT

i.e. P = 1.05 atm, R = 0.0821 L atm mol^-1 K^-1 and T = 22.1 + 273.15, i.e. 295.25 K and n = 1.95

Therefore, the no. volume of CO₂ = 1.95 mol*0.0821 L atm mol^-1 K^-1 * 295.25 K / 1.05 atm, i.e. ~ 45 L

Solubility of CO2 = 88 mL/100 mL water

i.e. Calculate accordingly.