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Chapter 17: Problem 31

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 pH at the beginning of the titration and at the equivalence point. What is the total solution volume at the equivalence point?

Short Answer

Expert verified
Initial pH is 13, equivalence point pH is 7, total volume at equivalence is 60 mL.

Step by step solution

01

Identify Initial Conditions

The solution starts with the titration of 30.0 mL of 0.10 M NaOH. Initially, only NaOH is present, which is a strong base. The initial pH of the solution is estimated using the concentration of NaOH, which can be calculated as follows: \[\text{pH} = 14 - \text{pOH} = 14 - \log(0.10) = 13.\] Thus, at the start, the pH is around 13.
02

Determine the Equivalence Point

In a strong acid-strong base titration, the equivalence point occurs when equal moles of acid and base have reacted. This point is where 30.0 mL of 0.10 M NaOH is neutralized by 30.0 mL of 0.10 M HCl, making the total volume 60.0 mL. At the equivalence point, the solution will be neutral, having a pH of 7 because both NaOH and HCl are strong and fully dissociate.
03

Sketch the Titration Curve

When sketching the titration curve, start with a high pH at the initial point (pH = 13), decrease towards the equivalence point showing a steep drop in pH, and reach pH = 7 at the equivalence point at 60.0 mL total volume. After the equivalence point, the pH will drop further as excess HCl is added, reaching closer to a lower pH value.

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Key Concepts

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

Equivalence Point
In a titration involving a strong acid and a strong base, the equivalence point is a crucial moment. It is the point at which the number of moles of hydrogen ions ( H^+ ) from the acid equals the number of moles of hydroxide ions ( OH^- ) from the base. This means that the acid has fully neutralized the base.
For a titration of 30.0 mL of 0.10 M NaOH with 0.10 M HCl , you will reach the equivalence point when you've added an equal volume of the HCl solution (30.0 mL). At this point:
  • All NaOH has reacted with HCl resulting in a neutral solution.
  • The total volume is 60.0 mL, accounting for the added acid.
  • The pH of the solution at the equivalence point is neutral (pH 7), as both reactants are strong and fully dissociate.
Understanding this step is key because it allows us to predict and verify the behavior of the solution as the titration progresses.
Titration Curve Sketching
Sketching a titration curve provides a visual representation of the pH changes during the titration process. For the titration of a strong base with a strong acid, the curve typically starts at a high pH due to the initial base in the solution.
When sketching, keep the following steps in mind:
  • Begin at the initial pH determined by the NaOH , which is around pH 13.
  • As HCl is gradually added, the pH will decrease precipitously until it reaches the equivalence point.
  • The equivalence point is depicted as a sharp drop on the curve, indicating a rapid pH change around a volume of 60.0 mL total solution volume.
  • Beyond the equivalence point, as more HCl is added, the pH will continue to decrease, indicating excess acid.
This curve is typically S-shaped, and the steep section indicates the rapid transition at the equivalence point, making it a vital part of understanding the titration process.
pH Calculation
Calculating the pH at different stages of the titration allows for a clearer understanding of the solution's behavior. Before any HCl is added, the pH can be calculated using the initial concentration of NaOH, which is a strong base. To find the initial pH, you can use NaOH's concentration in the formula:
\[\text{pOH} = -\log(0.10)\;\text{and thus,}\;\text{pH} = 14 - \text{pOH} = 13.\]
During and after the addition of HCl, the pH changes, particularly around the equivalence point:
  • At the equivalence point, the solution is neither basic nor acidic, making the pH equal to 7.
  • Before reaching the equivalence point, as HCl is added, the solution's pH gradually decreases.
  • After surpassing the equivalence point, further addition of HCl results in a decrease in pH as the solution becomes acidic.
A solid grasp of pH calculations involves acknowledging how these transitions affect the overall outcome of the titration.
Neutralization Reaction
A neutralization reaction is at the heart of a titration process, especially between a strong acid and a strong base. In such a reaction, the acid and base react to form water and a salt, leading to a balance between the H^+and OH^- ions, effectively neutralizing the solution.
For the given titration:
  • The NaOH (strong base) reacts with HCl (strong acid) to form NaCl (salt) and water.
  • This specific reaction can be represented as: \[\text{NaOH} (aq) + \text{HCl} (aq) \rightarrow \text{NaCl} (aq) + \text{H}_2\text{O} (l)\]
  • The point of neutralization is the equivalence point where the solution achieves a pH of 7.
This neutralization is significant as it determines when the titration reaches its balance point, illustrating the dynamic interplay between the reacting substances.

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Most popular questions from this chapter

You dissolve \(0.425 \mathrm{g}\) of \(\mathrm{NaOH}\) in \(2.00 \mathrm{L}\) of a buffer solution that has \(\left[\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\right]=\left[\mathrm{HPO}_{4}^{2-}\right]= 0.132 \mathrm{M} .\) What is the \(\mathrm{pH}\) of the solution before adding NaOH? After adding NaOH?

Calcium hydroxide, \(\mathrm{Ca}(\mathrm{OH})_{2},\) dissolves in water to the extent of 1.78 g per liter. What is the value of \(K_{\mathrm{sp}}\) for \(\mathrm{Ca}(\mathrm{OH})_{2} ?\) $$\mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{s}) \rightleftharpoons \mathrm{Ca}^{2+}(\mathrm{aq})+2 \mathrm{OH}^{-}(\mathrm{aq})$$

When \(1.55 \mathrm{g}\) of solid thallium(I) bromide is added to 1.00 L of water, the salt dissolves to a small extent. $$\operatorname{TiBr}(\mathrm{s}) \rightleftharpoons \mathrm{Tl}^{+}(\mathrm{aq})+\mathrm{Br}^{-}(\mathrm{aq})$$ The thallium(I) and bromide ions in equilibrium with TIBr each have a concentration of \(1.9 \times 10^{-3} \mathrm{M} .\) What is the value of \(K_{\mathrm{sp}}\) for TIBr?

What volume of 0.120 M NaOH must be added to \(100 .\) mL of \(0.100 \mathrm{M} \mathrm{NaHC}_{2} \mathrm{O}_{4}\) to reach a \(\mathrm{pH}\) of \(4.70 ?\)

What is the pH change when \(20.0 \mathrm{mL}\) of \(0.100 \mathrm{M}\) NaOH is added to \(80.0 \mathrm{mL}\) of a buffer solution consisting of 0.169 \(\mathrm{M} \mathrm{NH}_{3}\) and \(0.183 \mathrm{M} \mathrm{NH}_{4} \mathrm{Cl} ?\)
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