When excess water is added to a mixture of citric acid and sodium bicarbonate present in a bath bomb, the following reaction takes place C₆H₈O₇(s) + 3 NaHCO₃(s) + H₂O(l) → Na₃C₆H₅O₇(aq)...

Question

When excess water is added to a mixture of citric acid and sodium bicarbonate present in a bath bomb, the following reaction takes place C₆H₈O₇(s) + 3 NaHCO₃(s) + H₂O(l) → Na₃C₆H₅O₇(aq) + 4 H₂O(l) + 3 CO₂(g) Calculate the volume of CO₂ gas collected over water at 38.0 °C when a mixture of 55.5 g of citric acid and excess sodium bicarbonate is added to a tub of water if the total pressure is 725 torr. The vapor pressure of water at 38.0 °C is 49.7 torr.

Answer 1

C₆H₈O₇(s) + 3 NaHCO₃(s) + H₂O(l) → Na₃C₆H₅O₇(aq) + 4 H₂O(l) + 3 CO₂(g)

Since the NaHCO3 is present in excess, the 55.5 g of citric acid will determine the amount of CO2 that can theoretically form.

Theoretical yield of CO2:

55.5 g C₆H₈O₇ x 1 mol C₆H₈O₇ / 192 g x 3 mol CO2 / mol C₆H₈O₇ = 0.867 mols CO2

Volume of CO2:

PV = nRT (since gas collected over water, must subtract vapor pressure of water)

P = pressure = 725 torr - 49.7 torr = 675,3 torr x 1 atm / 760 torr = 0.889 atm

V = volume in liters = ?

n = moles CO2 = 0.867 mols

R = gas constant = 0.0821 Latm/Kmol

T = temperature in K = 38C + 273 = 311K

Solving for V, we have ...

V = nRT / P = (0.867)(0.0821)(311) / 0.889

V = 24.9 L