Two Antacid Tablets and 50 mL of Gastric Acid
A patient with reflux chews two antacid tablets, each containing 500 mg of calcium carbonate as the only active ingredient, and asks the nurse, 'Does this get rid of all the acid in my stomach?' A unit reference states that the fasting stomach holds about 50 mL of gastric fluid with hydrochloric acid at roughly 0.10 M. The nurse decides to answer quantitatively, using molar masses of 100.09 g/mol for CaCO3, 36.46 g/mol for HCl, and 44.01 g/mol for CO2. The patient has also been told to limit sodium, and the label lists 2 mg of sodium per tablet from inactive ingredients. The nurse's note must include a balanced equation, identification of the limiting reactant, the mass of carbon dioxide the tablets can generate in this simplified model, and a plain-language answer for the patient. Assume the acid concentration stays at 0.10 M and ignore other stomach contents.
1. Write the balanced equation for calcium carbonate reacting with hydrochloric acid and classify the reaction.
Read the worked answer
Balanced equation:
CaCO₃(s) + 2 HCl(aq) → CaCl₂(aq) + H₂O(l) + CO₂(g)
Atom check: Ca 1/1; C 1/1; O 3/(1 + 2) = 3; H 2/2; Cl 2/2. The coefficient 2 in front of HCl is required by both the chlorine and hydrogen balances. Without it the equation is unbalanced, and the resulting mole ratio would be wrong.
Classification: this is an acid–base neutralization that is simultaneously a double-replacement (metathesis) reaction and a gas-evolving reaction. The carbonate ion accepts two protons, forming carbonic acid, which decomposes to water and carbon dioxide. The pattern to recognize is carbonate + acid → salt + water + CO₂; that pattern lets you predict the fizzing before writing anything down.
Naming the type matters practically: it tells you the products, it tells you a gas leaves the system, and it tells you the 2:1 acid-to-carbonate ratio that controls the next two steps.
2. Determine the limiting reactant given 1.000 g of CaCO3 (two tablets) and 50 mL of 0.10 M HCl.
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Moles available:
- CaCO₃: 1.000 g ÷ 100.09 g/mol = 9.99 × 10⁻³ mol (two 500 mg tablets).
- HCl: 0.050 L × 0.10 mol/L = 5.00 × 10⁻³ mol.
Stoichiometric requirement: the balanced equation calls for 2 mol HCl per 1 mol CaCO₃. Consuming all the CaCO₃ would require 2 × 9.99 × 10⁻³ = 2.00 × 10⁻² mol HCl, but only 5.00 × 10⁻³ mol is present. Equivalently, the available HCl can consume only 5.00 × 10⁻³ ÷ 2 = 2.50 × 10⁻³ mol CaCO₃.
Conclusion: HCl is the limiting reactant, and CaCO₃ is in excess by 9.99 × 10⁻³ − 2.50 × 10⁻³ = 7.49 × 10⁻³ mol, about 0.750 g left unreacted.
The intuitive answer - that two large tablets must overwhelm a small volume of acid - is wrong. The mole ratio, not the tablet size, decides, and the 2:1 ratio is what makes the acid run out first.
3. Calculate the mass of CO2 produced, answer the patient's question, and note the clinical caveat and the sodium detail.
Read the worked answer
CO₂ produced: the HCl-to-CO₂ ratio is 2:1, so n(CO₂) = 5.00 × 10⁻³ ÷ 2 = 2.50 × 10⁻³ mol.
Mass = 2.50 × 10⁻³ mol × 44.01 g/mol = 0.110 g CO₂ (about 56 mL of gas at STP).
Plain-language answer: in this simplified model the acid is the limiting reactant, so the tablets do neutralize all 50 mL of acid present, with excess calcium carbonate left over. The fizzing stops when the acid is spent, not when the tablet is spent - which is why a partly used tablet can still fizz later.
Caveats the note must carry: the stomach secretes new acid continuously, so 'all the acid' is true only for the acid present at that moment; the excess CaCO₃ can act as a buffer; and the model ignores food, mucus, and other buffers. The 2 mg of sodium per tablet, 4 mg total, is negligible chemically and does not change the limiting reactant, but it belongs in the note because the patient was told to watch sodium.