When Bubbling Stops: Equilibrium or Limiting Reagent?
During a demonstration, a student adds 5.00 g of solid sodium bicarbonate to 100.0 mL of 1.00 M acetic acid at 25 °C. The mixture bubbles vigorously, then the bubbling stops after several minutes. The student writes: 'The reaction has reached equilibrium because the bubbles stopped. The pH is 4.8, which proves the system is at equilibrium.' The teacher knows the reaction produces CO2, water, and sodium acetate. The lab has a gas syringe that collected 1.15 L of CO2 at 25 °C and 1.00 atm. The molar volume of an ideal gas at these conditions is 24.5 L/mol. The student asks why the reaction stopped if acid is still present. The class has studied limiting reagents, weak acids, and Le Châtelier's principle.
1. Evaluate the student's equilibrium claim using the amounts of reactants and the observed gas volume. Determine the limiting reagent and the theoretical volume of CO2.
Read the worked answer
mol NaHCO3 = 5.00 g / 84.01 g/mol = 0.0595 mol. mol CH3COOH = 0.100 L × 1.00 mol/L = 0.100 mol. The balanced reaction is NaHCO3 + CH3COOH → NaCH3COO + H2O + CO2, a 1:1 mole ratio. NaHCO3 is limiting because 0.0595 mol < 0.100 mol. Theoretical CO2 = 0.0595 mol × 24.5 L/mol = 1.46 L. The collected 1.15 L corresponds to 0.0469 mol CO2, or about 79% of theoretical. The reaction stops when bicarbonate is used up, not because equilibrium is reached; excess acetic acid remains.
2. Explain why the escape of CO2 makes this reaction effectively irreversible, and describe one experimental test that would distinguish 'equilibrium' from 'limiting reagent consumed.'
Read the worked answer
CO2 is a gas that escapes from the solution. As CO2 leaves, the reverse reaction (CO2 + H2O → H2CO3 → HCO3− + H+) is starved of reactant, so the system cannot establish a true equilibrium with the gas phase in the open beaker. The net reaction is driven essentially to completion by gas evolution. A simple test: after bubbling stops, add a small amount of solid NaHCO3. If fizzing resumes, acid is still present and the original stop was due to limiting bicarbonate, not equilibrium. If no fizzing occurs, the acid has been consumed. Another test is to collect gas over time; a plateau with unreacted acid confirms the limiting-reagent explanation.
3. The student measures pH 4.8 after the reaction. Calculate the approximate ratio of acetate to acetic acid using Ka = 1.8e-5, and explain whether this ratio supports the idea that acid remains.
Read the worked answer
Henderson–Hasselbalch: pH = pKa + log([CH3COO−]/[CH3COOH]). pKa = −log(1.8×10^−5) = 4.74. At pH 4.8, log ratio = 4.8 − 4.74 = 0.06, so ratio = 10^0.06 ≈ 1.15. After reaction, acetate ≈ 0.0595 mol and remaining acetic acid ≈ 0.100 − 0.0595 = 0.0405 mol, giving ratio 1.47 and pH ≈ 4.91. The measured 4.8 is close to this buffer prediction. The presence of roughly comparable amounts of acetic acid and acetate shows that acid remains and that the pH is set by a buffer, not by a simple equilibrium with CO2. This supports the limiting-reagent explanation.