What mass of HClO₄ must be present in 0.500 L of solution to obtain a solution with each pH value? a. pH = 2.50 b. pH = 1.50 c. pH = 0.50

Verified step by step guidance

1. insert step 1> Calculate the concentration of hydrogen ions \([H^+]\) using the pH formula: \([H^+] = 10^{-\text{pH}}\). For pH = 1.50, find \([H^+]\).
2. insert step 2> Recognize that perchloric acid \(\text{HClO}_4\) is a strong acid and dissociates completely in water, so \([H^+] = [\text{HClO}_4]\).
3. insert step 3> Use the concentration of \([H^+]\) to find the moles of \(\text{HClO}_4\) in the 0.500 L solution. Use the formula: \(\text{moles} = \text{concentration} \times \text{volume}\).
4. insert step 4> Calculate the molar mass of \(\text{HClO}_4\) by adding the atomic masses of hydrogen, chlorine, and oxygen.
5. insert step 5> Convert the moles of \(\text{HClO}_4\) to mass using the formula: \(\text{mass} = \text{moles} \times \text{molar mass}\).

Key Concepts

pH and its Calculation

pH is a measure of the acidity or basicity of a solution, defined as the negative logarithm of the hydrogen ion concentration. The formula pH = -log[H+] allows us to calculate the concentration of hydrogen ions in a solution. For a pH of 1.50, the hydrogen ion concentration can be determined as [H+] = 10^(-1.50), which is essential for further calculations.

Strong Acids and Their Ionization

Strong acids, like HClO4 (perchloric acid), completely dissociate in water, meaning that the concentration of the acid equals the concentration of hydrogen ions produced. This complete ionization simplifies calculations, as the molarity of the acid directly corresponds to the molarity of H+ ions in the solution, which is crucial for determining the mass needed to achieve a specific pH.

Molarity and Mass Calculations

Molarity (M) is defined as the number of moles of solute per liter of solution. To find the mass of HClO4 required, we first calculate the moles needed using the desired hydrogen ion concentration and the volume of the solution. Then, using the molar mass of HClO4, we can convert moles to grams, allowing us to determine the mass of the acid needed to achieve the specified pH.