Question

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

Short answer

The concentration of H+ ions in the stomach is \(0.01M\). There are \(0.004\) moles of H+ ions present in the stomach's contents. According to the balanced equation, 1 mole of HCl reacts with 1 mole of NaHCO₃. Therefore, \(0.004\) moles of NaHCO₃ are needed to neutralize the stomach acid. The molar mass of NaHCO₃ is \(84 g/mol\), so the mass of NaHCO₃ required to neutralize the stomach acid is \(0.336 g\).

Step-by-step solution

1. Find the concentration of H+ ions from the pH value

To find the concentration of H+ ions in the stomach, we can use the formula: pH = -log[H+] Rearranging the formula to solve for the H+ concentration: [H+] = 10^(-pH) Substitute the given pH value (2) into the formula: [H+] = 10^(-2) = 0.01M

2. Calculate the number of moles of H+ ions

To find the number of moles of H+ ions, we can use the formula: moles = concentration × volume Make sure the volume is in liters: Volume in liters = 400 mL / 1000 = 0.4 L Substitute the H+ concentration (0.01M) and volume (0.4 L) into the formula: moles of H+ = (0.01M) × (0.4 L) moles of H+ = 0.004 mol

3. Write the balanced chemical equation for the acid-base reaction

In this step, we need to write a balanced equation for the reaction between stomach acid (HCl) and sodium hydrogen carbonate (NaHCO₃) to neutralize the acid. The balanced equation is: HCl (aq) + NaHCO₃ (s) → NaCl (aq) + H₂O (l) + CO₂ (g) From the balanced equation, we can see that 1 mole of HCl reacts with 1 mole of NaHCO₃.

4. Calculate the mass of sodium hydrogen carbonate needed to neutralize the acid

Since the mole ratio of HCl to NaHCO₃ is 1:1, we will need the same number of moles of NaHCO₃ to neutralize the acid. moles of NaHCO₃ = moles of H+ = 0.004 mol Now, find the molar mass of NaHCO₃. The molar mass of sodium (Na) is approximately 23 g/mol, hydrogen (H) is approximately 1 g/mol, carbon (C) is approximately 12 g/mol, and oxygen (O) is approximately 16 g/mol. Molar mass of NaHCO₃ = (1 × 23) + (1 × 1) + (1 × 12) + (3 × 16) = 84 g/mol Now, use the formula to find the mass of NaHCO₃: mass = moles × molar mass Substitute the moles of NaHCO₃ (0.004 mol) and the molar mass (84 g/mol) into the formula: mass of NaHCO₃ = (0.004 mol) × (84 g/mol) = 0.336 g Thus, 0.336 grams of sodium hydrogen carbonate will be needed to totally neutralize the stomach acid.