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Sketch the titration curve (pH versus volume of \(0.50 M\) \(\mathrm{NaOH} \text { added })\) for a \(25 \mathrm{mL}\) sample of \(0.25 \mathrm{M} \mathrm{FeCl}_{3}\)

Short Answer

Expert verified
Question: Sketch the titration curve for a 25 mL sample of 0.25 M FeCl鈧, with the pH versus the volume of 0.50 M NaOH. Answer: The titration curve for this problem starts with a low (acidic) pH, which gradually increases as NaOH is added. At the equivalence point (37.5 mL of NaOH), there is a steep increase in pH, after which the pH again gradually increases as more NaOH is added. The curve will show the pH as an acidic value throughout the titration.

Step by step solution

01

Determine the balanced chemical equation

First, we need to write the balanced chemical equation for the reaction between FeCl鈧 and NaOH. The reaction can be written as: $$ \underset{\ce{FeCl3}}{\ce{Fe^{3+} + 3Cl^-}} + \underset{\ce{3NaOH}}{\ce{3Na^+ + 3OH^-}} \rightarrow \ce{Fe(OH)3\/ \downarrow} +3\underset{\ce{NaCl}}{\ce{Na^{+}+Cl^-}} $$ The balanced chemical equation shows that one mole of FeCl鈧 reacts with three moles of NaOH.
02

Determine the number of moles of FeCl鈧 and NaOH

Next, calculate the number of moles of FeCl鈧 in the 25 mL sample and the NaOH concentration. Number of moles of FeCl鈧: moles = concentration 脳 volume moles = (0.25 mol/L) 脳 (0.025 L) moles = 0.00625 mol
03

Identify the key points on the titration curve

We will now identify the key points on the titration curve: the initial pH (before any NaOH is added), the equivalence point (where mol of FeCl鈧 = 3 脳 mol of NaOH), and the final pH (after the equivalence point).
04

Calculate the initial pH of FeCl鈧

We can estimate the pH of the 0.25 M FeCl鈧 solution before the titration. The pH value will be dominated by the hydrolysis reaction of the Fe鲁鈦 ion with water: $$ \ce{Fe^3+ + H2O <=> Fe(OH)^2+ + H+} $$ However, given that this is a complex calculation involving multiple equilibria we will not do this in our calculation, instead we will just recognize that before any NaOH is added, the pH of the solution is acidic.
05

Calculate the equivalence point

At the equivalence point, the moles of FeCl鈧 will equal three times the moles of NaOH. We can use this relationship to determine the volume of NaOH needed to reach the equivalence point. $$ \frac{\text{moles of FeCl}_3}{3} = \text{moles of NaOH} $$ $$ \frac{0.00625}{3} = \frac{\text{moles of NaOH}}{0.50 \text{ mol/L}} $$ $$ \text{Volume of NaOH (L)} = 3\times \frac{0.00625}{0.50} = 0.0375 \text{ L} $$ So, the equivalence point occurs at a volume of 37.5 mL of NaOH.
06

Calculate the pH at the equivalence point

At the equivalence point, Fe(OH)鈧 has formed as a solid precipitate. The pH at the equivalence point will be determined by the hydrolysis of the Fe(OH)鈧傗伜 ion: $$ \ce{Fe(OH)^2+ + H2O <=> Fe(OH)2 \downarrow + H+} $$ However, calculating the exact pH value at the equivalence point will also involve a more complex calculation related to hydrolysis. We will not do this calculation here, but we acknowledge that it will be acidic.
07

Draw the titration curve

With the initial pH, the equivalence point volume, and the general shape of the titration curve in mind, we can now sketch the titration curve for this problem. The curve starts with a low (acidic) pH, which gradually increases as NaOH is added. At the equivalence point (37.5 mL of NaOH), there is a steep increase in pH, after which the pH again gradually increases as more NaOH is added. Remember that the curve will show the pH as an acidic value throughout the titration.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

FeCl3 and NaOH reaction
The reaction between Iron(III) chloride, FeCl鈧, and sodium hydroxide, NaOH, is a classic example of an acid-base reaction. FeCl鈧, when dissolved in water, dissociates into Fe鲁鈦 ions and 3 Cl鈦 ions. Similarly, NaOH dissociates into Na鈦 and OH鈦 ions. When combined, these ions react to form a solid precipitate of Fe(OH)鈧 and a salt, NaCl, as shown in the equation:
  • FeCl鈧 + 3NaOH 鉃 Fe(OH)鈧冣啌 + 3NaCl
The formation of Fe(OH)鈧 is a key point, as the precipitate influences the pH of the solution. The stoichiometry of the reaction tells us that one mole of FeCl鈧 will react with three moles of NaOH. This balanced equation helps us calculate how much NaOH is needed to reach the equivalence point in a titration process.
Equivalence point calculation
In titration, the equivalence point is the stage where the amount of titrant (in this case, NaOH) equals the stoichiometric amount needed to completely react with the analyte (FeCl鈧). For our reaction, the equivalence point occurs when the number of moles of FeCl鈧 matches with the moles provided by the NaOH, adjusted by the stoichiometry (1:3) ratio:
  • Moles of FeCl鈧 = 0.00625
  • Moles of NaOH needed = 3 x Moles of FeCl鈧 = 0.01875
We solve for the volume of NaOH using its concentration:
  • Volume = Moles / Concentration = 0.01875 moles / 0.50 M = 0.0375 L
    • This tells us that 37.5 mL of NaOH is required to reach the equivalence point. At this volume, all Fe鲁鈦 ions will have reacted with OH鈦 ions from NaOH to form Fe(OH)鈧.
Hydrolysis reaction
Hydrolysis is a crucial concept to understand when dealing with salts in solution and their effect on pH. When Fe鲁鈦 ions are in water, they can undergo hydrolysis to form Fe(OH)虏鈦 and release H鈦, which contributes to the acidic nature of the solution. The hydrolysis reaction is:
  • Fe鲁鈦 + H鈧侽 鈬 Fe(OH)虏鈦 + H鈦
This equilibrium reaction indicates that even a small amount of Fe鲁鈦 can lower the pH by increasing the concentration of H鈦 ions. In the context of the titration, before any NaOH is added, the solution is acidic due to this hydrolysis process. Even at the equivalence point, the presence of hydrolyzing species means the solution can still exhibit an acidic pH. Hydrolysis influences both the early and late stages of the titration curve.
Acidic pH
FeCl鈧 is known for its acidic properties when dissolved in water. This is due to the hydrolysis of Fe鲁鈦 ions, which results in the release of H鈦 ions, making the solution acidic. Prior to adding NaOH, the initial pH will be low as a result of the prevalent H鈦 ions:
  • Fe鲁鈦 + H鈧侽 鈬 Fe(OH)虏鈦 + H鈦
At the initial stages of titration, given FeCl鈧's significant effect, the pH of the solution is acidic. Even upon reaching the equivalence point, the solution remains acidic because not all hydrolysis effects are neutralized. This trend continues even as we add more NaOH, showcasing the complex interplay of titration with weak bases and the formation of Fe(OH)鈧 precipitate, which maintains an acidified environment. The final titration curve will illustrate a slow rise in pH starting from an acidic environment, though increasing alkalinity after the equivalence point.

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