Final answer:
To make a solution with a pH of 3.20, we need 20.0 mL of 15.8 M HNO₃.
Step-by-step explanation:
To calculate the volume of 15.8 M HNO₃ needed to make 500.0 mL of a solution with a pH of 3.20, we need to consider the acid dissociation of HNO₃. HNO₃ is a strong acid, which means that it completely dissociates in water. The pH of a solution is related to the concentration of H₃O⁺ ions, so we can use the equation: pH = -log[H₃O⁺]. From the pH of 3.20, we can calculate the concentration of H₃O⁺ ions, which will be equal to the concentration of HNO₃. Once we have the concentration, we can use the equation: concentration = moles/volume, to calculate the moles of HNO₃ needed. Finally, we can use the equation: moles = Molarity × volume, to calculate the volume of 15.8 M HNO₃ needed to make the solution.
First, let's calculate the concentration of H₃O⁺ ions using the given pH:
pH = -log[H₃O⁺]
3.20 = -log[H₃O⁺]
[H₃O⁺] = 10^(-pH)
[H₃O⁺] = 10^(-3.20)
[H₃O⁺] = 6.31 × 10^(-4) M
Since HNO₃ is a strong acid and it dissociates completely, its concentration will be equal to the concentration of H₃O⁺ ions:
concentration of HNO₃ = 6.31 × 10^(-4) M
Next, let's calculate the moles of HNO₃ needed:
moles = concentration × volume
moles = 6.31 × 10^(-4) M × 500.0 mL
Note: We convert mL to L by dividing by 1000.
moles = 6.31 × 10^(-4) M × 0.500 L
moles = 3.15 × 10^(-4) mol HNO₃
Finally, let's calculate the volume of 15.8 M HNO₃ needed:
moles = Molarity × volume
Volume = moles/Molarity
Volume = 3.15 × 10^(-4) mol / 15.8 M
Note: We convert M to L by dividing by 1000.
Volume = 3.15 × 10^(-4) mol / 0.0158 L
Volume = 0.020 L or 20.0 mL