Final answer:
To find the pH of the solution, calculate the molarity of HClO₄ by dividing the mass by the molar mass and then by the volume in liters. Since HClO₄ fully dissociates, the molarity equals the [H+]. The pH, calculated as the negative logarithm of [H+], is approximately 1.05.
Step-by-step explanation:
The question is asking to calculate the pH of a solution made by dissolving 2.250 grams of HClO₄ (perchloric acid) in 250 mL of water. Perchloric acid is a strong acid, meaning it fully dissociates in water. To calculate the pH, first, we need to find the molarity (M) of the solution, which is defined as the number of moles of solute per liter of solution.
To find the molarity, divide the mass of HClO₄ by its molar mass to get the number of moles:
- Number of moles = mass (g) / molar mass (g/mol)
The molar mass of HClO₄ is approximately 100.46 g/mol. Calculate the moles of HClO₄:
- Number of moles = 2.250 g / 100.46 g/mol
- Number of moles ≈ 0.0224 mol
Now, convert 250 mL to liters and calculate the molarity:
- Volume in liters = 250 mL * 0.001 L/mL
- Volume in liters = 0.250 L
- Molarity (M) = Number of moles / Volume in liters
- Molarity (M) = 0.0224 mol / 0.250 L
- Molarity (M) ≈ 0.0896 M
Since HClO₄ is a strong acid, it fully dissociates to produce H+ ions in a 1:1 ratio:
[H+] = Molarity of HClO₄ = 0.0896 M
The pH is then calculated by taking the negative logarithm (base 10) of the hydrogen ion concentration:
- pH = -log[H+]
- pH = -log(0.0896)
- pH ≈ 1.05
Therefore, the pH of the solution is approximately 1.05.