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Calculate or sketch titration curves for the following acid-base titrations. a. \(25.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{NaOH}\) with \(0.0500 \mathrm{M} \mathrm{HCl}\) b. \(50.0 \mathrm{~mL}\) of \(0.0500 \mathrm{M} \mathrm{HCOOH}\) with \(0.100 \mathrm{M} \mathrm{NaOH}\) c. \(50.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{NH}_{3}\) with \(0.100 \mathrm{M} \mathrm{HCl}\) d. \(50.0 \mathrm{~mL}\) of \(0.0500 \mathrm{M}\) ethylenediamine with \(0.100 \mathrm{M} \mathrm{HCl}\) e. \(50.0 \mathrm{~mL}\) of \(0.0400 \mathrm{M}\) citric acid with \(0.120 \mathrm{M} \mathrm{NaOH}\) f. \(50.0 \mathrm{~mL}\) of \(0.0400 \mathrm{M} \mathrm{H}_{3} \mathrm{PO}_{4}\) with \(0.120 \mathrm{M} \mathrm{NaOH}\)

Short Answer

Expert verified
Sketch and solve step-by-step using the identified acid-base reactions for each titration.

Step by step solution

01

Understanding the Acid-Base Reaction

For each titration, identify the type of acid-base reaction (strong acid-strong base, weak acid-strong base, or weak base-strong acid). This determines the shape and points on the titration curve.
02

Calculate the Initial pH

Determine the pH of the solution before any titrant is added. For example, use appropriate formulas for weak acids/bases (like the Henderson-Hasselbalch equation) or straightforward calculations for strong acids and bases.
03

Find the Equivalence Point

Use stoichiometry to find the volume of titrant required to fully react with the analyte, determining the equivalence point. This is where the moles of acid equal the moles of base.
04

Sketch the Titration Curve

Plot the starting pH, equivalence point, and post-equivalence region based on the reaction types. For weak acids and bases, also plot the buffer region and half-equivalence point where applicable.
05

Verify by Calculating the pH at Key Points

Calculate the pH at different points (half-equivalence, equivalence, and past equivalence). Use these points to verify the accuracy of the sketch.

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Key Concepts

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

Acid-Base Reactions
Acid-Base Reactions are essential in understanding titration because they reveal how acids and bases react with each other. In a titration involving acids and bases, you typically mix a solution of known concentration, the titrant, with an analyte solution of unknown concentration. There are three primary types of reactions you may encounter in titration:
  • Strong Acid-Strong Base: An example would be titrating hydrochloric acid (HCl) with sodium hydroxide (NaOH). These reactions quickly lead to a dramatic change in pH.
  • Weak Acid-Strong Base: A titration like formic acid (HCOOH) with NaOH results in a gradual change in pH until the very end.
  • Weak Base-Strong Acid: This involves titrations like ammonia (NH3) with HCl, leading to more buffer regions and gradual pH changes.
Understanding which category your titration falls into helps predict how the pH will change as more titrant is added, aiding in sketching the titration curve.
Equivalence Point
The Equivalence Point is a critical concept in titrations. It represents the point at which the amount of titrant added is chemically equivalent to the amount of substance in the sample. In other words, the moles of acid are equal to the moles of base. Depending on the acids and bases involved, reaching the equivalence point is accompanied by a sharp change in pH. This is a crucial point because it indicates that your titration reaction is complete. In a strong acid-base titration, the equivalence point is often near a pH of 7. However, in weak acid-strong base or weak base-strong acid titrations, the equivalence point may be below or above the neutral pH of 7. Calculating the exact volume of titrant needed to reach this point involves stoichiometry, helping ensure an accurate titration process.
Henderson-Hasselbalch Equation
The Henderson-Hasselbalch Equation is essential when dealing with weak acids or bases during titration. It provides a straightforward way to calculate the pH of a solution when the concentrations of the acid and its conjugate base are known. The equation is expressed as:\[pH = pK_a + \log\left( \frac{[A^-]}{[HA]} \right)\]Here, - \(pH\) is what we want to find,- \(pK_a\) is the known ionization constant of the acid or base, - \([A^-]\) is the concentration of the conjugate base, and - \([HA]\) is the concentration of the acid.This equation is invaluable for determining the pH in the buffer region of a titration. It helps to estimate the pH reasonably accurately during titrations of weak acids or bases, especially as you approach the equivalence point.
Buffer Region
The Buffer Region of a titration curve is where the solution resists changes in pH. It occurs because the acid and conjugate base (or base and conjugate acid) coexist, maintaining a balance. This unique aspect of a titration happens most noticeably in weak acid-strong base or weak base-strong acid titrations. In this region, adding small amounts of titrant will not result in significant pH changes, offering a buffer effect. The buffer capacity is highest at the half-equivalence point, where the amounts of acid and conjugate base are approximately equal. This point is calculated using the Henderson-Hasselbalch Equation, which simplifies evaluating the pH during this stable phase. Understanding the buffer region is crucial for recognizing its effect on the overall shape of a titration curve and for employing it effectively in laboratory experiments, where pH stability is desired.

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Most popular questions from this chapter

The concentration of \(\mathrm{CO}_{2}\) in air is determined by an indirect acid-base titration. A sample of air is bubbled through a solution that contains an excess of \(\mathrm{Ba}(\mathrm{OH})_{2},\) precipitating \(\mathrm{BaCO}_{3} .\) The excess \(\mathrm{Ba}(\mathrm{OH})_{2}\) is back titrated with HCl. In a typical analysis a 3.5-L sample of air is bubbled through \(50.00 \mathrm{~mL}\) of \(0.0200 \mathrm{M} \mathrm{Ba}(\mathrm{OH})_{2} .\) Back titrating with \(0.0316 \mathrm{M} \mathrm{HCl}\) requires \(38.58 \mathrm{~mL}\) to reach the end point. Determine the \(\mathrm{ppm} \mathrm{CO}_{2}\) in the sample of air given that the density of \(\mathrm{CO}_{2}\) at the temperature of the sample is \(1.98 \mathrm{~g} / \mathrm{L}\).

An acid-base titration can be used to determine an analyte's equivalent weight, but it can not be used to determine its formula weight. Explain why.

Calculate or sketch the titration curve for a \(50.0 \mathrm{~mL}\) solution of a \(0.100 \mathrm{M}\) monoprotic weak acid \(\left(\mathrm{p} K_{\mathrm{a}}=8.0\right)\) with \(0.1 \mathrm{M}\) strong base in a nonaqueous solvent with \(K_{\mathrm{s}}=10^{-20}\). You may assume that the change in solvent does not affect the weak acid's \(\mathrm{p} K_{\mathrm{a}}\). Compare your titration curve to the titration curve when water is the solvent.

The concentration of cyanide, \(\mathrm{CN}^{-},\) in a copper electroplating bath is determined by a complexometric titration using \(\mathrm{Ag}^{+}\) as the titrant, forming the soluble \(\mathrm{Ag}(\mathrm{CN})_{2}^{-}\) complex. In a typical analysis a \(5.00-\mathrm{mL}\) sample from an electroplating bath is transferred to a 250 -mL Erlenmeyer flask, and treated with \(100 \mathrm{~mL}\) of \(\mathrm{H}_{2} \mathrm{O}, 5 \mathrm{~mL}\) of \(20 \% \mathrm{w} / \mathrm{v}\) \(\mathrm{NaOH}\) and \(5 \mathrm{~mL}\) of \(10 \% \mathrm{w} / \mathrm{v}\) KI. The sample is titrated with 0.1012 \(\mathrm{M} \mathrm{AgNO}_{3}\), requiring \(27.36 \mathrm{~mL}\) to reach the end point as signaled by the formation of a yellow precipitate of AgI. Report the concentration of cyanide as parts per million of \(\mathrm{NaCN}\).

The amount of calcium in physiological fluids is determined by a complexometric titration with EDTA. In one such analysis a \(0.100-\mathrm{mL}\) sample of a blood serum is made basic by adding 2 drops of \(\mathrm{NaOH}\) and titrated with \(0.00119 \mathrm{M}\) EDTA, requiring \(0.268 \mathrm{~mL}\) to reach the end point. Report the concentration of calcium in the sample as milligrams Ca per \(100 \mathrm{~mL}\).

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