Problem 59 - Chemistry

Question

How would you prepare \(1600 \mathrm{~mL}\) of a \(\mathrm{pH}=1.50\) solution using concentrated \((12 M) \mathrm{HCl} ?\)

Step-by-Step Solution

Answer

To prepare 1600 mL of a pH 1.50 solution using concentrated 12 M HCl, mix 4.213 mL of concentrated HCl with 1595.787 mL of water.

Step 1: Calculate the concentration of H+ ions required for the desired pH

: We can use the pH formula to determine the concentration of H+ ions in the solution: \[ pH = -\log[H^+] \] Where \(pH\) is the desired pH (1.50) and \([H^+]\) is the required concentration of H+ ions. Rearrange the formula and solve for \([H^+]\): \[ [H^+] = 10^{-pH} \] Plug in the desired pH (1.50) and calculate the required H+ concentration: \[ [H^+] = 10^{-1.50} \] \[ [H^+] = 0.0316 \ \mathrm{M} \]

Step 2: Calculate the moles of H+ ions required to achieve the desired concentration

: Now that we have the concentration of H+ ions required, we can calculate the moles of H+ ions needed for the entire solution. Use the formula: \[ moles\ of\ H^+ = [H^+] \times \ volume\ of\ solution \] Plug in the H+ concentration (0.0316 M) and the volume of solution (1600 mL, converting to L for the calculation): \[ moles\ of\ H^+ = 0.0316\ \mathrm{M} \times 1.6\ \mathrm{L} \] \[ moles\ of\ H^+ = 0.05056 \]

Step 3: Calculate the volume of 12 M HCl needed to provide the required number of H+ moles

: Now we will determine the volume of 12 M HCl needed to provide the required number of moles of H+ ions. Use the formula: \[ volume\ of\ HCl = \frac{moles\ of\ H^+}{concentration\ of\ HCl} \] Plug in the moles of H+ (0.05056) and the concentration of HCl (12 M): \[ volume\ of\ HCl = \frac{0.05056}{12\ \mathrm{M}} \] \[ volume\ of\ HCl = 0.004213\ \mathrm{L} \] Convert the volume to milliliters for practical use: \[ volume\ of\ HCl = 4.213\ \mathrm{mL} \]

Step 4: Mix the calculated volume of concentrated HCl with the appropriate amount of water

: Finally, mix the calculated volume of concentrated HCl (4.213 mL) with the appropriate amount of water to achieve a total volume of 1600 mL. Subtract the HCl volume from the desired total volume to find the volume of water needed: \[ volume\ of\ water = 1600\ \mathrm{mL} - 4.213\ \mathrm{mL}\] \[ volume\ of\ water = 1595.787\ \mathrm{mL} \] To prepare 1600 mL of a pH 1.50 solution using concentrated 12 M HCl, mix 4.213 mL of concentrated HCl with 1595.787 mL of water.