Question

For the titration of \(25.00 \mathrm{~mL}\) of \(0.1000 \mathrm{M} \mathrm{HCl}\) with \(0.1000 \mathrm{M} \mathrm{NaOH},\) calculate the \(\mathrm{pH}\) of the reaction mixture after each of the following total volumes of base have been added to the original solution. (Remember to take into account the change in total volume.) Construct a graph showing the titration curve for this experiment. (d) \(24.99 \mathrm{~mL}\) (g) \(25.10 \mathrm{~mL}\) (b) \(10.00 \mathrm{~mL}\) (e) \(25.00 \mathrm{~mL}\) (h) \(26.00 \mathrm{~mL}\) (c) \(24.90 \mathrm{~mL}\) (f) \(25.01 \mathrm{~mL}\) (i) \(50.00 \mathrm{~mL}\)

Short answer

To calculate the pH: (d, c, f, g, e) Subtract moles of NaOH added from initial moles of HCl, use resulting moles to find new concentration and pH; (h, i) Subtract initial moles of HCl from moles of NaOH added, use resulting moles to find concentration and pOH, then subtract pOH from 14 for pH; (b) Calculate pH based on moles of HCl with no titration. pH at equivalence (25.00 mL NaOH) is 7.

Step-by-step solution

Calculate the moles of HCl initially present

Calculate the initial moles of HCl using the given concentration and volume. The formula to calculate moles is concentration (M) times volume (L). For 0.1000 M HCl and 25.00 mL, you have: \(0.1000 \text{ M} * 25.00 \times 10^{-3} \text{ L} = 0.002500 \text{ moles of HCl}\).

Determine the moles of NaOH added

For each subpart, calculate the moles of NaOH added using the given volume added and the concentration of NaOH (which is the same as the concentration of HCl, 0.1000 M). Multiply the volume of NaOH added (in liters) by the concentration to find the moles of NaOH added.

Calculate the moles of HCl and NaOH after addition

Subtract the moles of NaOH added from the moles of HCl initially present to find the remaining amount of HCl for cases where NaOH is less than or equal to the equivalence point (25.00 mL). For volumes of NaOH greater than 25.00 mL, subtract the initial moles of HCl from the moles of NaOH added to find the remaining moles of NaOH.

Calculate the new volume of the solution

Add the volume of NaOH added to the initial volume of HCl to get the total volume of the solution after the addition for each part.

Calculate the pH for each part

Use the remaining moles of acid or base and the new total volume to calculate the concentration. For acidic solutions (with excess HCl), use the concentration of HCl to find the pH: \(\text{pH} = -\log[\text{H}^{+}]\). For basic solutions (with excess NaOH), use the concentration of NaOH and the formula \(\text{pOH} = -\log[\text{OH}^{-}]\), and then calculate pH using the formula: \(\text{pH} = 14 - \text{pOH}\). At the exact point of equivalence, the solution is neutral, so the pH is 7.

Construct the titration curve graph

Plot the calculated pH values on the y-axis against the corresponding volumes of NaOH added on the x-axis. The curve should start with a low pH, show a steep rise in pH at the equivalence point, and then plateau after the equivalence point.

Key concepts

Titration Curve

The titration curve is a graph that illustrates how the pH of a solution changes as a titrant is added during an acid-base titration. It is a powerful visual tool that shows the relationship between the amount of titrant added and the pH level at each stage of the titration process.

To construct a titration curve, one measures the pH of a solution after successive additions of a titrating agent. In our example, we are adding a strong base (NaOH) to a strong acid (HCl). The curve will begin at a low pH value since HCl is a strong acid. As NaOH is added, the pH will gradually increase until it approaches the equivalence point, which is marked by a sharp increase in pH. This rapid change is due to the neutralization of the acid by the base. Beyond this point, the curve will level off as the solution becomes increasingly basic.

Understanding the shape of the titration curve is essential, not only for determining the equivalence point but also for understanding buffer regions and predicting the pH at various points of the titration. It is important to note that the shape of the curve can vary depending on the strength of the acids and bases involved in the titration.

Equivalence Point

The equivalence point, also known as the stoichiometric point, is a pivotal moment in any titration process. It is the point at which the amount of titrant added is chemically equivalent to the amount of substance initially present in the solution.

In the context of our example titration of a strong acid with a strong base, the equivalence point is reached when the moles of HCl originally present in the solution have reacted exactly with an equal number of moles of NaOH added. It's the point at which the chemical reaction between the titrant and the analyte is complete. At the equivalence point in a strong acid-strong base titration, the solution is neutral, and the pH is 7. However, it's crucial to realize that the equivalence point is not always at pH 7; it can vary depending on the nature of the titration, and in the case of weak acids or weak bases, the equivalence point pH may be above or below 7.

Finding the equivalence point is critical for accurate titrations as it helps in determining the concentration of the unknown solution. In laboratory settings, indicators or pH meters are often used to detect the equivalence point. A well-practiced analyst will look for the section of the titration curve that shows a vertical, almost perpendicular increase in pH; this indicates the equivalence point has been reached.

pH Calculation

pH calculation is a key stage of the titration process that enables us to determine the acidity or basicity of a solution at any given point. pH is a logarithmic scale that represents the hydrogen ion concentration \( [H^+] \) of a solution and is defined by the formula \( \text{pH} = -\log[H^+] \).

In a titration, calculating the pH provides insight into the progress of the reaction. Before the equivalence point, the pH can be found by calculating the concentration of unneutralized acid. After the equivalence point, the pH is determined by the concentration of excess base. At the exact equivalence point in a strong acid-strong base titration, the pH is neutral at 7.

In our example, when NaOH is added to HCl, the number of moles of HCl and NaOH in the solution determines whether the solution is acidic, neutral, or basic. By using the formula for pH or pOH and the known concentrations of the acid or base in the solution, one can calculate the pH at different stages of the titration. It's important to include the change in total volume after each addition to accurately calculate the concentration. This step-by-step understanding of pH is crucial for interpreting the titration curve and predicting the outcome of the titration process.