Calculate the pH of each of the following strong acid solutions: (a) 8.5 * 10^-3 M HBr, (b) 5.00 mL of 0.250 M HClO4 diluted to 50.0 mL, (c) a solution formed by mixing 10.0 mL of 0.100 M HBr with 20.0 mL of 0.200 M HCl.

Verified step by step guidance

1. Step 1: Understand that strong acids like HBr and HClO4 dissociate completely in water. Therefore, the concentration of hydrogen ions [H⁺] is equal to the concentration of the acid.
2. Step 2: For part (a), the concentration of HBr is given as 8.5 * 10^-3 M. Since HBr is a strong acid, [H⁺] = 8.5 * 10^-3 M. Use the formula for pH: pH = -log([H⁺]).
3. Step 3: For part (b), first calculate the new concentration of HClO4 after dilution. Use the dilution formula: C1V1 = C2V2, where C1 is the initial concentration (0.250 M), V1 is the initial volume (5.00 mL), C2 is the final concentration, and V2 is the final volume (50.0 mL). Solve for C2 to find the new [H⁺]. Then, calculate the pH using pH = -log([H⁺]).
4. Step 4: For part (c), calculate the total moles of H⁺ from each acid before mixing. For HBr: moles = concentration * volume = 0.100 M * 10.0 mL. For HCl: moles = concentration * volume = 0.200 M * 20.0 mL. Add the moles from both acids to find the total moles of H⁺.
5. Step 5: Calculate the total volume of the mixed solution (10.0 mL + 20.0 mL = 30.0 mL). Find the concentration of H⁺ in the mixed solution by dividing the total moles of H⁺ by the total volume in liters. Finally, calculate the pH using pH = -log([H⁺]).

Key Concepts

Strong Acids

Strong acids are substances that completely dissociate in water, releasing all of their hydrogen ions (H+). This means that the concentration of H+ ions in a strong acid solution is equal to the concentration of the acid itself. For example, a 0.01 M HCl solution will have a pH of 2, as it fully dissociates to produce 0.01 M H+.

pH Calculation

pH is a measure of the acidity or basicity of a solution, calculated using the formula pH = -log[H+]. For strong acids, since they fully dissociate, the pH can be directly determined from the molarity of the acid. For example, if the concentration of H+ is 0.0085 M, the pH can be calculated as pH = -log(0.0085).

Dilution of Solutions

Dilution involves reducing the concentration of a solute in a solution, typically by adding more solvent. The dilution formula, C1V1 = C2V2, relates the concentrations and volumes before and after dilution. For example, if 5.00 mL of 0.250 M HClO4 is diluted to 50.0 mL, the new concentration can be calculated to find the resulting pH.