Final answer:
To increase stomach pH from 1.00 to 2.00 with a volume of 1.00 L, 1.45 grams of calcium carbonate (CaCO3) is needed to neutralize the excess hydrochloric acid (HCl).
Step-by-step explanation:
To increase the pH of the stomach from 1.00 to 2.00 using an antacid tablet which contains calcium carbonate (CaCO3), we need to first calculate the amount of hydrochloric acid (HCl) in the stomach that requires neutralization. The pH of a solution is the negative logarithm of the hydrogen ion concentration ([-H+]).
As the pH increases from 1.00 to 2.00, the concentration of hydrogen ions decreases by a factor of 10 (from 10-1 M to 10-2 M).
Assuming the stomach contains 0.03 M HCl over a volume of 1.00 L, the moles of HCl originally present are 0.03 mol. To reach a pH of 2.00, the concentration should be 0.001 M, which means a decrease of 0.029 mol of HCl is necessary.
Since the reaction between calcium carbonate and hydrochloric acid is:
CaCO3(s) + 2HCl(aq) → CaCl₂(aq) + H₂O(l) + CO₂(g)
The reaction shows that 1 mole of CaCO3 reacts with 2 moles of HCl.
Therefore, 0.029 mol HCl requires 0.0145 mol of CaCO3 to be neutralized.
Knowing that the molar mass of CaCO3 is approximately 100 g/mol, we can calculate the mass needed:
(0.0145 mol) × (100 g/mol) = 1.45 g
Therefore, 1.45 grams of CaCO3 is required to change the pH value of the stomach acid from 1.00 to 2.00 in a 1.00 L volume.