If you want to increase the pH of the stomach from 1 to 2 using an antacid tablet, how many grams of CaCO3 will be required to change the pH value? Assume the acid is HCl and you have a 1L stomach value
1 = -log (H^+) so for pH 1, (H^+) = 0.1M and for 1 L of that, mols HCl = M x L = 0.1 x 1 = 0.1 mol.
2 = -log (H^+)
(H^+) = 0.01 M and mols HCl = 0.01M x 1 L = 0.01 mols.
Then 0.1 mol HCl - 0.01 mol HCl = 0.09 mols HCl to be removed.
2HCl + CaCO3 ==> CaCl2 + H2O + CO2
mols HCl = 0.09.
mols CaCO3 = 1/2 that or 0.045
g CaCO = mols CaCO3 x molar mass CaCO3 = ?
To determine the amount of CaCO3 required to increase the pH of the stomach from 1 to 2, we need to calculate the number of moles of HCl that needs to be neutralized and then use stoichiometry to find the corresponding amount of CaCO3.
Step 1: Calculate the number of moles of HCl present in 1L of stomach acid.
The pH value of 1 corresponds to a concentration of HCl of 0.1 M (since pH = -log[H+]). Therefore, for 1L of stomach acid, we have:
Moles of HCl = (Concentration of HCl) x (Volume of solution)
= 0.1 M x 1L
= 0.1 moles of HCl
Step 2: Determine the stoichiometric ratio between HCl and CaCO3.
According to the balanced chemical equation for the reaction between HCl and CaCO3:
CaCO3 + 2HCl → CaCl2 + CO2 + H2O
The ratio shows that 1 mole of CaCO3 reacts with 2 moles of HCl.
Step 3: Calculate the number of moles of CaCO3 needed to neutralize the HCl.
Since the ratio is 1:2 (CaCO3:HCl), we need double the moles of HCl to neutralize the solution. Therefore:
Moles of CaCO3 = 2 x (Moles of HCl)
= 2 x 0.1 moles (calculated in step 1)
= 0.2 moles of CaCO3
Step 4: Convert moles of CaCO3 to grams.
To determine the mass, we can use the molar mass of CaCO3, which is approximately 100.09 g/mol.
Mass of CaCO3 = (Moles of CaCO3) x (Molar mass of CaCO3)
= 0.2 moles x 100.09 g/mol
= 20.018 g
Therefore, approximately 20.018 grams of CaCO3 would be required to change the pH value from 1 to 2 in a 1L stomach.
To solve this problem, we need to calculate the number of moles of HCl in the stomach, determine the number of moles of HCl that can be neutralized by CaCO3, and then convert the moles of CaCO3 to grams using the molar mass of CaCO3.
Step 1: Calculate the number of moles of HCl in the stomach.
The pH scale is logarithmic, which means that a decrease of one unit in pH indicates a tenfold increase in acidity. So, to increase the pH of the stomach from 1 to 2, we need to neutralize the amount of HCl present in the stomach by a factor of 10.
HCl is a strong acid, so its concentration is equal to its molarity. Since we have a 1L stomach volume and a pH of 1, we can assume the HCl concentration is 10^(-1) M.
To calculate the number of moles of HCl in the stomach, we use the formula:
moles of acid = concentration of acid × volume of solution
moles of HCl = (10^(-1) mol/L) × 1 L = 0.1 mol
Step 2: Determine the number of moles of HCl that can be neutralized by CaCO3.
CaCO3 reacts with 2 moles of HCl to form 1 mole of CaCl2, 1 mole of CO2, and 1 mole of H2O. This means that 1 mole of CaCO3 can neutralize 2 moles of HCl.
Since we have 0.1 moles of HCl in the stomach, we can determine the number of moles of CaCO3 required as follows:
moles of CaCO3 = (2/1) × 0.1 mol = 0.2 mol
Step 3: Convert moles of CaCO3 to grams using the molar mass of CaCO3.
The molar mass of CaCO3 is calculated by adding up the atomic masses of calcium (Ca), carbon (C), and three oxygen (O) atoms.
Molar mass of CaCO3 = (1 × atomic mass of Ca) + (1 × atomic mass of C) + (3 × atomic mass of O)
Using the atomic masses from the periodic table, we find:
Molar mass of CaCO3 = (1 × 40.08 g/mol) + (1 × 12.01 g/mol) + (3 × 16.00 g/mol) ≈ 100.09 g/mol
Finally, we can calculate the mass of CaCO3 required to neutralize the HCl in the stomach:
mass of CaCO3 = moles of CaCO3 × molar mass of CaCO3
mass of CaCO3 = 0.2 mol × 100.09 g/mol ≈ 20.02 g
Therefore, approximately 20.02 grams of CaCO3 will be required to increase the pH of the stomach from 1 to 2 using an antacid tablet.