Problem 27 - Chemistry and Chemical Reactivity

Question

Without doing detailed calculations, sketch the curve for the titration of \(30.0 \mathrm{mL}\) of \(0.10 \mathrm{M} \mathrm{NaOH}\) with 0.10 M HCl. Indicate the approximate \(\mathrm{pH}\) at the beginning of the titration and at the equivalence point. What is the total solution volume at the equivalence point?

Step-by-Step Solution

Answer

Initial pH is about 13; pH at equivalence is 7; total volume at equivalence is 60.0 mL.

Step 1: Understanding the Initial Conditions

Initially, we have a solution of 0.1 M NaOH. Sodium hydroxide is a strong base, which means it will have a high pH before any HCl is added. Since it's a 0.1 M solution, the initial pH can be calculated using the formula pH = 14 - pOH. The pOH is -log(0.1), which equals 1. Therefore, the initial pH is approximately 13.

Step 2: Identify Key Points During Titration

During the titration, HCl, a strong acid, is added to the NaOH solution. As we add the acid, the pH of the solution will decrease, moving towards neutral.

Step 3: Calculate Volume at Equivalence Point

At the equivalence point, the moles of NaOH will be equal to the moles of HCl. Since both the NaOH and HCl have the same concentration (0.10 M), it will take an equal volume of 0.10 M HCl to neutralize the NaOH. Thus, 30.0 mL of 0.10 M HCl is required to reach the equivalence point. Therefore, the total volume at equivalence is the initial volume of NaOH plus the volume of HCl added: 30.0 mL + 30.0 mL = 60.0 mL.

Step 4: Determine the pH at Equivalence Point

At the equivalence point, all the NaOH has been neutralized by the HCl, forming water and NaCl, a neutral salt. Hence, the pH at the equivalence point should be approximately 7, as the solution is essentially neutral.

Step 5: Sketching the Titration Curve

The titration curve starts with a high pH near 13, tapering down as HCl is added. The pH sharply decreases as we approach the equivalence point at about 60.0 mL total volume, and the pH will temporarily stabilize around 7 at this point. Beyond the equivalence point, as more HCl is added, the pH will drop further, approaching the pH of the HCl solution.

Key Concepts

pH calculation

In acid-base titrations, understanding how to calculate pH is crucial. We start with a solution of sodium hydroxide (NaOH), a strong base. Before any titrant is added, the initial pH can be determined. NaOH dissociates completely in water, providing hydroxide ions \[\begin{align*}\text{NaOH} &\rightarrow \text{Na}^+ + \text{OH}^-.\end{align*}\]To find the pH, calculate the pOH first since we know the concentration of OH⁻ ions. The formula for pOH is \[\text{pOH} = -\log[\text{OH}^-].\] For a 0.1 M NaOH solution:

• pOH = -\log(0.1) = 1
• pH = 14 - 1 = 13

This means the starting pH is quite high, reflecting the basic nature of the solution.

equivalence point

The equivalence point in a titration is when the amount of titrant added equals the amount of substance present in the solution being titrated. For our reaction, we are using 0.10 M of hydrochloric acid (HCl) as the titrant which reacts with NaOH. Equivalence occurs when the moles of HCl equal the moles of NaOH. Given both solutions are 0.10 M, the reaction is straightforward. Since 30.0 mL of NaOH is given, you will need an equal volume of HCl to reach the equivalence point:

• Volume of HCl required = 30.0 mL

At this point, all NaOH has reacted with HCl to form water and sodium chloride (NaCl), a neutral salt. This explains why the pH at the equivalence point is approximately 7, indicating a neutral solution.

strong acid and base reaction

When a strong acid like HCl reacts with a strong base like NaOH, they combine to form water and a salt. The overall reaction is exothermic and can be expressed simply by: \[\text{HCl (aq)} + \text{NaOH (aq)} \rightarrow \text{NaCl (aq)} + \text{H}_2\text{O (l)}\]The strong nature of both the acid and the base means that they dissociate completely in solution. This results in a complete neutralization reaction once the equivalent amounts have reacted. This is a beautiful demonstration of stoichiometry in action, where the balanced chemical equation leads directly to the conclusions about the amounts required to reach the equivalence point, and the system's behavior around it.

titration curve analysis

A titration curve visually represents how pH changes with the addition of titrant. Initially, for strong base titration like NaOH, the curve starts with a very high pH. As we add HCl, the curve gradually dips due to the neutralizing effect of HCl. Before reaching the equivalence point, the pH drops slowly. However, approaching the equivalence point, the pH falls sharply to reflect a rapid consumption of leftover NaOH. At the equivalence point — 60.0 mL total volume in this example — the curve levels off near pH 7, indicating a neutral solution environment. Beyond this, further addition of HCl causes the titration curve to slope downwards again, as the solution becomes increasingly acidic.

• The curve's shape helps identify the equivalence point clearly.
• The steep drop signals the strong acid and base interaction.

Understanding this graphical representation simplifies pH estimation at various stages of the titration process.