The volume of an adult's stomach ranges from about 50 mL when empty to 1 L when full. If the stomach volume is 400 mL and its contents have a pH of 2, how many moles of H+ does the stomach contain? Assuming that all the H+ comes from HCl, how many grams of sodium hydrogen carbonate will totally neutralize the stomach acid?

Verified step by step guidance

1. Convert the stomach volume from milliliters to liters: 400 mL = 0.4 L.
2. Use the pH to find the concentration of \( \text{H}^+ \) ions: \( \text{pH} = -\log[\text{H}^+] \), so \([\text{H}^+] = 10^{-\text{pH}} = 10^{-2} \text{ M}\).
3. Calculate the moles of \( \text{H}^+ \) ions using the formula: \( \text{moles of } \text{H}^+ = [\text{H}^+] \times \text{volume in L} = 10^{-2} \text{ M} \times 0.4 \text{ L} \).
4. Write the balanced chemical equation for the neutralization reaction: \( \text{HCl} + \text{NaHCO}_3 \rightarrow \text{NaCl} + \text{H}_2\text{O} + \text{CO}_2 \).
5. Calculate the mass of \( \text{NaHCO}_3 \) needed using stoichiometry: 1 mole of \( \text{HCl} \) reacts with 1 mole of \( \text{NaHCO}_3 \), then use the molar mass of \( \text{NaHCO}_3 \) to find the grams needed.

Key Concepts

pH and Hydrogen Ion Concentration

pH is a measure of the acidity or basicity of a solution, defined as the negative logarithm of the hydrogen ion concentration. A pH of 2 indicates a high concentration of H+ ions, specifically 0.01 moles per liter. To find the total moles of H+ in a given volume, you multiply the concentration by the volume in liters.

Neutralization Reaction

A neutralization reaction occurs when an acid reacts with a base to produce water and a salt. In this case, hydrochloric acid (HCl) in the stomach reacts with sodium hydrogen carbonate (NaHCO3) to neutralize the acid. The balanced equation for this reaction is HCl + NaHCO3 → NaCl + H2O + CO2, which helps determine the stoichiometric relationships between the reactants.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the balanced chemical equation. It allows us to determine how much of a substance is needed to completely react with another. By knowing the moles of H+ from the stomach acid, we can use stoichiometry to calculate the grams of sodium hydrogen carbonate required for neutralization, using its molar mass.