Question

Choose the answer that best completes the following statement and defend your answer. When \(100.0 \mathrm{mL}\) of water is added to \(100.0 \mathrm{mL}\) of \(1.00 \mathrm{M} \mathrm{HCl}\) a. the pH decreases because the solution is diluted. b. the pH does not change because water is neutral. c. the \(\mathrm{pH}\) is doubled because the volume is now doubled. d. the pH increases because the concentration of \(\mathrm{H}^{+}\) decreases. e. the solution is completely neutralized.

Short answer

The correct answer is (d). The pH of the solution increases from 0 to approximately 0.3 because the concentration of H+ ions decreases from 1.00 M to 0.50 M when 100.0 mL of water is added to the 100.0 mL of 1.00 M HCl, diluting the solution.

Step-by-step solution

Calculate the initial concentration of H+ ions in the HCl solution

Since the initial HCl solution is 1.00 M and HCl is a strong acid, it will completely dissociate into H+ and Cl- ions. So, the initial concentration of H+ ions is also 1.00 M.

Calculate the final concentration of H+ ions after dilution

When 100.0 mL of water is added to 100.0 mL of the HCl solution, the total volume of the solution becomes 200.0 mL. The moles of H+ ions in the solution will not change, so we can use the formula for dilution: C1V1 = C2V2. C1 = initial concentration of H+ ions = 1.00 M V1 = initial volume of the HCl solution = 100.0 mL V2 = final volume of the solution after adding water = 200.0 mL C2 = final concentration of H+ ions (this is what we want to find) 1.00 M × 100.0 mL = C2 × 200.0 mL C2 = 0.50 M

Calculate the initial and final pH of the solution

The initial pH of the HCl solution can be calculated using the formula: pH = -log[H+] Initial pH = -log(1.00) = 0 The final pH of the diluted solution can be calculated similarly: Final pH = -log(0.50) ≈ 0.3

Analyze the result and choose the correct answer

Comparing the initial and final pH values, we can see that the pH of the solution has increased because the concentration of H+ ions has decreased due to the dilution. Therefore, the correct answer is: d. the pH increases because the concentration of H+ decreases.

Key concepts

Dilution and Its Effects

Dilution refers to the process of adding more solvent, usually water, to a solution without adding more solute. This process decreases the concentration of the solute, in this case, hydrogen ions (H\(^+\)) from hydrochloric acid (HCl).
When you dilute an acidic solution, like HCl, by adding water, the overall number of H\(^+\) ions spread over a larger volume than before. However, this doesn't affect the total number of moles of H\(^+\) present—just their concentration.

• The formula to calculate dilution is: \( C_1V_1 = C_2V_2 \), where \( C_1 \) and \( C_2 \) are the initial and final concentrations, and \( V_1 \) and \( V_2 \) are the initial and final volumes of the solution.
• For instance, if you start with 1.00 M HCl and add an equal volume of water, the concentration drops to 0.50 M because the volume doubles while the amount of H\(^+\) ions stays the same.

Understanding HCl Concentration

The concentration of hydrochloric acid (HCl) in a solution indicates how many moles of HCl are dissolved in a given volume of solvent. In this scenario, the initial concentration of HCl is 1.00 M, meaning there is 1 mole of HCl per liter of solution.

• HCl is a strong acid, which implies it completely dissociates in water. Hence, the concentration of HCl initially equals the concentration of H\(^+\) ions.
• To find how much the concentration of HCl affects pH, we perform calculations using the dilution formula mentioned previously, adjusting for any change in volume as water is added.

Acid Dissociation of HCl

Acid dissociation describes the process by which an acid, like HCl, releases hydrogen ions (H\(^+\)) into a solution.
HCl is a strong acid, which means it dissociates completely in water:

Complete Dissociation:

- HCl → H\(^+\) + Cl\(^-\)
This means each mole of HCl originally in the solution yields a mole of H\(^+\) ions. Because this process is complete, we can accurately predict changes in pH when the acid is diluted.
Understanding dissociation is key because it underlines why the concentration of HCl directly translates to the concentration of H\(^+\) ions before any dilution occurs.

Impacts of Solution Volume

The volume of a solution is crucial in understanding how its concentration changes upon dilution. When the volume of a solution increases, while the solute quantity remains the same, the concentration decreases.
In our exercise, adding 100.0 mL of water to 100.0 mL of HCl solution doubles the solution's volume to 200.0 mL.

• The change in volume doesn't alter the amount of solute (i.e., H\(^+\) ions), but the ions now occupy a greater space, reducing their concentration.
• This reduced concentration leads to a higher pH value, indicating a less acidic solution.

By assessing the initial and final volumes, we can understand how dilution affects pH and why adding water doesn't neutralize the solution but makes it less acidic instead.