Final answer:
Approximately 4.14 mL of 7.6 M HI is required to prepare 500 mL of solution with a pH of 3.20. The calculation is done by converting pH to hydrogen ion concentration and using the dilution formula to find the volume needed from the concentrated solution.
Step-by-step explanation:
To calculate the volume of a 7.6 M HI solution needed to make 500.0 mL of a solution with a pH of 3.20, we must first understand the relationship between pH and molarity. The pH is defined as the negative logarithm (base 10) of the hydrogen ion concentration ([H+]). A pH of 3.20 implies a hydrogen ion concentration of 10-3.20 M.
The required molarity (M) of the solution can be calculated using the formula: M = 10-pH, which for a pH of 3.20 gives: M = 10-3.20 M = 0.00631 M.
Using the dilution equation M1V1 = M2V2 where M1 is the molarity of the concentrated solution (7.6 M), V1 is the volume of the concentrated solution needed, M2 is the molarity of the diluted solution (0.00631 M), and V2 is the final volume of the diluted solution (500.0 mL or 0.500 L), we can solve for V1:
V1 = (M2 * V2) / M1
V1 = (0.00631 M * 0.500 L) / 7.6 M
V1 = 0.00414 L
Converting liters to milliliters: V1 = 0.00414 L * 1000 mL/L
V1 ≈ 4.14 mL
You would need approximately 4.14 mL of the 7.6 M HI solution to make 500.0 mL of a solution with a pH of 3.20.