a. To find the pH of a solution that is 5.2x10^-2 M in HClO4 and 5.2x10^-2 M in HCl, we need to first determine the concentration of H+ ions in the solution. Both HClO4 and HCl are strong acids, which means they completely dissociate in water to form H+ and Cl- ions. Therefore, the concentration of H+ ions in the solution will be equal to the concentration of the acids.
[H+] = [HClO4] + [HCl]
[H+] = 5.2x10^-2 M + 5.2x10^-2 M
[H+] = 1.04x10^-1 M
Now we can use the definition of pH to find the pH of the solution:
pH = -log[H+]
pH = -log(1.04x10^-1)
pH ≈ 0.983
Therefore, the pH of the solution is approximately 0.983.
b. To find the pH of a solution with a density of 1.01 g/mL that is 1.04% HCl by mass, we need to first convert the mass percent to molarity. We can assume that the density of the solution is equal to the density of water (1.00 g/mL) for the purpose of this calculation.
The mass of HCl in 100 g of the solution is:
100 g x 1.04/100 = 1.04 g
The molar mass of HCl is 36.5 g/mol, so the number of moles of HCl is:
1.04 g / 36.5 g/mol = 0.0285 mol
The volume of the solution is:
100 g / 1.01 g/mL = 99.01 mL = 0.09901 L
Therefore, the concentration of HCl in the solution is:
[HCl] = 0.0285 mol / 0.09901 L
[HCl] ≈ 0.288 M
Now we can use the definition of pH to find the pH of the solution:
pH = -log[H+]
pH = -log[HCl]
pH = -log(0.288)
pH ≈ 0.540
Therefore, the pH of the solution is approximately 0.540.