The new pH after adding NaC6H5CO2 and HCl to the benzoic acid solution is approximately 9.75.
To find the new pH after adding 10.5 grams of NaC6H5CO2 to a 100 ml 1.0 M benzoic acid solution, and then adding 5 ml of 1.35 M HCl, the following steps should be taken:
Adding NaC6H5CO2:
Calculate the moles of NaC6H5CO2 using its molar mass.
Use the stoichiometry in moles to find the change in concentration of the benzoic acid and its conjugate base.
Apply the Henderson-Hasselbalch equation to find the new pH.
Adding HCl:
Use the stoichiometry of the reaction between HCl and the benzoate ion to find the change in concentration of the acid and its conjugate base.
Apply the Henderson-Hasselbalch equation again to find the final pH.
The detailed calculations involve the use of the Henderson-Hasselbalch equation and stoichiometry to account for the changes in the concentrations of the acid and its conjugate base due to the addition of the NaC6H5CO2 and HCl. The final pH can be found using these steps.
To find the new pH after adding 10.5 grams of NaC6H5CO2 to a 100 ml 1.0 M benzoic acid solution, and then adding 5 ml of 1.35 M HCl, follow these steps:
Adding NaC6H5CO2
Calculate the moles of NaC6H5CO2 using its molar mass:
Molar mass of NaC6H5CO2 = 122.0 g/mol
Moles of NaC6H5CO2 = (10.5 g / 122.0 g/mol) = 0.08825 moles
Calculate the moles of benzoic acid (C6H5CO2H) and its conjugate base (C6H5CO2−) using the stoichiometry of the acid-base reaction:
For each mole of benzoic acid that reacts, 2 moles of its conjugate base are produced.
Moles of C6H5CO2H = 0.08825 moles * 2 = 0.1765 moles
Moles of C6H5CO2− = 0.1765 moles * 2 = 0.353 moles
Calculate the new concentration of benzoic acid and its conjugate base:
New concentration of benzoic acid = Initial concentration of benzoic acid / (Initial concentration of benzoic acid + Moles of C6H5CO2H)
= 1.0 M / (1.0 M + 0.1765 M) ≈ 0.55 M
New concentration of the conjugate base = Moles of C6H5CO2− / (Initial concentration of benzoic acid + Moles of C6H5CO2H)
= 0.353 M / (1.0 M + 0.1765 M) ≈ 0.225 M
Apply the Henderson-Hasselbalch equation to find the new pH:
pH = 10 - log((Initial concentration of benzoic acid * Initial concentration of the conjugate base) / (New concentration of the conjugate base)^2)
= 10 - log((1.0 M * 0.1765 M) / (0.225 M)^2) ≈ 9.75
Adding HCl
Calculate the moles of HCl:
Molar mass of HCl = 36.0 g/mol
Moles of HCl = (5 ml * 1000 ml/L * 36.0 g/mol) = 180 moles
Calculate the new concentration of HCl:
New concentration of HCl = Moles of HCl / Volume of solution
= 180 moles / 100 ml = 1.8 M
Apply the Henderson-Hasselbalch equation again to find the final pH:
pH = 10 - log((Initial concentration of benzoic acid * Initial concentration of the conjugate base) / (New concentration of the conjugate base * New concentration of HCl))
= 10 - log((0.1765 M * 0.225 M) / (0.225 M * 1.8 M)) ≈ 9.75.