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In this problem, we are examining the titration of hydrochloric acid (HCl), a strong acid, with sodium hydroxide (NaOH), a strong base. The key to understanding the pH changes during this titration lies in the concept of the equivalence point, where the amount of acid equals the amount of base in the solution.
Step 1: Understanding the Initial Conditions
Initially, we have 100 mL of 0.1 M HCl in the beaker. The pH of this solution can be calculated using the formula for strong acids, which completely dissociate in solution. The concentration of H+ ions is equal to the concentration of the acid:
$$
\text{pH} = -\log[H^+] = -\log(0.1) = 1
$$
Step 2: Adding NaOH
As we begin to add NaOH in increments of 2 mL, the NaOH will react with the HCl according to the following neutralization reaction:
$$
\text{HCl} + \text{NaOH} \rightarrow \text{NaCl} + \text{H}_2\text{O}
$$
Initially, the pH will remain low as the strong acid is still in excess. However, as we add NaOH, the pH will gradually increase as the acid is neutralized.
Step 3: Approaching the Equivalence Point
As we approach the equivalence point, where the moles of HCl equal the moles of NaOH, the pH will start to rise more rapidly. This is because the solution transitions from being acidic to neutral. At the equivalence point, the solution contains only water and the salt (NaCl), which does not affect the pH significantly. The pH at this point will be around 7.
Step 4: Post-Equivalence Point
After the equivalence point, any additional NaOH will cause the pH to rise sharply, as the solution becomes increasingly basic. The pH can be calculated using the concentration of excess NaOH in the solution.
Step 5: Graphical Representation
The graph depicting the change in pH during this titration will show a gradual increase in pH at first, followed by a steep rise around the equivalence point, and then a plateau as more NaOH is added beyond the equivalence point. This behavior is characteristic of the titration of a strong acid with a strong base.
Thus, the correct graph will illustrate a steep rise in pH around the equivalence point, confirming that the solution transitions from acidic to neutral and then to basic as NaOH is added.
