Ch.16 - Aqueous Equilibrium WorksheetSee all chapters
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Ch.1 - Intro to General Chemistry
Ch.2 - Atoms & Elements
Ch.3 - Chemical Reactions
BONUS: Lab Techniques and Procedures
BONUS: Mathematical Operations and Functions
Ch.4 - Chemical Quantities & Aqueous Reactions
Ch.5 - Gases
Ch.6 - Thermochemistry
Ch.7 - Quantum Mechanics
Ch.8 - Periodic Properties of the Elements
Ch.9 - Bonding & Molecular Structure
Ch.10 - Molecular Shapes & Valence Bond Theory
Ch.11 - Liquids, Solids & Intermolecular Forces
Ch.12 - Solutions
Ch.13 - Chemical Kinetics
Ch.14 - Chemical Equilibrium
Ch.15 - Acid and Base Equilibrium
Ch.16 - Aqueous Equilibrium
Ch. 17 - Chemical Thermodynamics
Ch.18 - Electrochemistry
Ch.19 - Nuclear Chemistry
Ch.20 - Organic Chemistry
Ch.22 - Chemistry of the Nonmetals
Ch.23 - Transition Metals and Coordination Compounds
Titration Curves

Titration curves help us to understand the neutralization occurring between an acid and base in order to identify the equivalence point. 

Equivalence Point

The equivalence point is when the moles of acid and base titrating are equal in amount. 

Concept #1: Understanding an Acid–Base Titration Curve.

In a typical titration we begin with an acid or base and slowly add either a Strong Acid or Strong Base. 

Concept #2: The Equivalence Point. 

Depending on the types of acids and bases mixing, at the equivalence point, the pH can be less than, greater than or equal to 7. 

Example #1: The following questions refer to the titration curve given below.

1) The titration curve shows the titration of

    a) a strong acid with a strong base    b) a weak acid with a strong base    c) a strong base with a strong acid    d) a weak base with a strong acid      

2) Which point on the titration curve represents a region where a buffer solution has formed?

     a) point A      b) point B      c) point C      d) point D

3) Which point on the titration curve represents the equivalence point? 

    a) point A      b) point B      c) point C      d) point D

4) Which of the following would be the best indicator to use in the titration?

    a) erythrosin B, pKa=2.9    b) methyl blue, pKa=5.4    c) bromthymol blue, pKa= 6.8    d) o-cresonphthalein, pKa=9.0   

An indicator represents a weak acid or base in low concentration that changes color in an acid base titration. An indicator shows us the location of our endpoint, which is located near our equivalence point. 

Example #2:  The acid form of an indicator is red and its anion is blue. The Ka value for this indicator is 10 -9. What will be the approximate pH range over which this indicator changes color?
a) 3-5        b) 4-6        c) 5-7        d) 8-10        e) 9-11

An indicator, like a buffer, has an optimal range in which it works most effectively:

pka +/- 1. 

Practice: What will be the color of the indicator in the above question in a solution that has a pH of 6?

Example #3: Consider the titration of 100.0 mL of 0.016 M H2SO4 with 0.400 M NaOH at the equivalence point. How many many milliliters of 0.400 M NaOH are required to reach the equivalence point?

If at the equivalence point, the moles of acid equal the moles of base and moles equal molarity multiplied by liters then at the equivalence point we can use the formula: 

Example #4: Consider the titration of 40.0 mL of 0.0800 M HCl with 0.0160 M Ca(NH2)2.

a) How many milliliters of 0.0160 M Ca(NH2)2 are required to reach the equivalence point? 

When dealing with the equivalence point make sure you correctly calculate the molarity for both the acid and base. 

Example #5: Consider the titration of 40.0 mL of 0.0800 M HCl with 0.0160 M Ca(NH2)2.

b) What is the pH of this solution?

Practice: Consider the titration of 60.0 mL of 0.200 M H3PO3 solution with 0.350 M potassium hydroxide, KOH solution. How many milliliters of base would be required to reach each of its equivalence points? 

Additional Problems
Which of the following is the most reasonable estimate of the value of the pH at the equivalence point of a titration of a hydrofluoric acid with a strong base? A)  14.0    B)  7.0    C)  5.5    D)  1.0    E)  8.5  
When an acid solution is titrated with a standard base solution, separate burets are sometimes used for each solution. Which mistake would necessitate emptying and refilling burets, and starting the titration over? (A) overshooting the endpoint (B) starting with less acid than called for by the procedure (C) adding distilled water to the titration flask after a solution was measured into it from the buret (D) allowing drops of distilled water to stay in the burets while filling them
Equal volumes of two acids are titrated with 0.10 M NaOH resulting in the two titration curves shown in the following figureWhich corresponds to the acid with the largest Ka?
Show that the pH at the halfway point of a titration of a weak acid with a strong base (where the volume of added base is half of that needed to reach the equivalence point) is equal to pKa for the acid.
The following drawingsrepresent solutions at various stages of the titration of a weak acid, HA, with NaOH. (The Na+ ions and water molecules have been omitted for clarity.) To which of the following regions of the titration curve does each drawing correspond.(i)
The following drawingsrepresent solutions at various stages of the titration of a weak acid, HA, with NaOH. (The Na+ ions and water molecules have been omitted for clarity.) To which of the following regions of the titration curve does each drawing correspond.(ii)
The following drawingsrepresent solutions at various stages of the titration of a weak acid, HA, with NaOH. (The Na+ ions and water molecules have been omitted for clarity.) To which of the following regions of the titration curve does each drawing correspond.(iii)
The following drawingsrepresent solutions at various stages of the titration of a weak acid, HA, with NaOH. (The Na+ ions and water molecules have been omitted for clarity.) To which of the following regions of the titration curve does each drawing correspond.(iv)
Match the following descriptions of titration curves with the diagrams.strong acid added to strong base
Match the following descriptions of titration curves with the diagrams.strong base added to weak acid
Match the following descriptions of titration curves with the diagrams.strong base added to strong acid
The graph below shows the titration curves for two monoprotic acids. Which curve is that of a strong acid?
The graph below shows the titration curves for two monoprotic acids. 40.0 mL of each acid was titrated with 0.100 M base. Which acid is more concentrated?
A set of curves showing the effect of acid strength on the characteristics of the titration curve when a weak acid is titrated by a strong base. Each curve represents titration of 50.0 mL of 0.10 M acid with 0.10 M NaOH.How does the pH at the equivalence point change as the acid being titrated becomes weaker?
A set of curves showing the effect of acid strength on the characteristics of the titration curve when a weak acid is titrated by a strong base. Each curve represents titration of 50.0 mL of 0.10 M acid with 0.10 M NaOH.How does the volume of NaOH (aq) needed to reach the equivalence point change?
Sketch an approximate titration curve for the titration of Na2CO3 with HCl.
Titration of a weak acid with a strong base. The pH curve for titration of 50.0 mL of a 0.100 M solution of acetic acid with a 0.100 M solution of NaOH(aq). For clarity, water molecules have been omitted from the molecular art.If the acetic acid being titrated here were replaced by hydrochloric acid, would the amount of base needed to reach the equivalence point change?
Titration of a weak acid with a strong base. The pH curve for titration of 50.0 mL of a 0.100 M solution of acetic acid with a 0.100 M solution of NaOH(aq). For clarity, water molecules have been omitted from the molecular art.Would the pH at the equivalence point change?
The pH at the beginning of the two titrations will be the same.
The titration curves will both be essentially the same after passing the equivalence point.
Examine the titration curves. Which statement is FALSE?A. Curve (i) shows the titration of 50.0 mL of 0.15 M HCl with 0.15 M NaOH.B. Curve (ii) shows the titration of 50.0 mL of 0.15 M NH 4Cl with 0.15 M NaOH.C. Curve (iii) shows the titration of 50.0 mL of 0.15 M CH 3COOH with 0.15 M NaOH.D. Curve (iv) shows the titration of 50.0 mL of 0.15 M H 3PO4 with 0.15 M NaOH.
a. At what volume of added base is the pH calculated by working an equilibrium problem based on the initial concentration and Ka of the weak acid?b. At what volume of added base does pH = p Ka?c. At what volume of added base is the pH calculated by working an equilibrium problem based on the concentration and Kb of the conjugate base?
Which of the following curve best represents the titration of Na 2CO3 with HCl? 
Define the end point of a titration. a. It is a synonym for equivalence point. b. It is the point at which the pH no longer changes. c. It is when a change that indicates equivalence is observed in the analyte solution.
Identify the equivalence point on the titration curve shown here.a. A is the equivalence pointb. D is the equivalence pointc. C is the equivalence pointd. B is the equivalence point
Below is the pH curve for a titration of a weak base with 0.10 M HCl. What is the p  Kb of the weak base? 1. 9.42. 2.73. 4.64. 7.00
Consider the titration curve given below. This titration curve corresponds to the titration of a ....(a) weak base (flask) with a strong acid (buret).(b) strong base (flask) with a strong acid (buret).(c) weak acid (flask) with a strong base (buret).(d) strong acid (flask) with a strong base (buret).
A student titrates an unknown monoprotic acid with NaOH solution from a buret. After the addition of 12.35 mL of NaOH, the pH of the solution is 5.22. The equivalence volume is 24.70 mL. What is the Ka of the acid?
Which titration curve could describe the titration of a solution of HCl by addition of a solution of KOH?
Identify each type of titration curve as involving a strong or weak acid or base. What is the significance of the half-equivalence point? Identify this point on the relevant curves below.
Suppose you titrated 50mL of a 1.0 M monoprotic acid solution with a 2.0 M NaOH solution. If the Ka of your acid is 1.0 x 10-6, which of the following curves best represents the titration?
The following questions refer to the titration curve given below.  For each of the following questions circle the correct answer.           a) The titration curve shows the titration of  i. a strong acid with a strong base                             ii. a weak acid  with a strong base        iii. a strong base  with a strong acid                          iv. a weak base with a strong acid                                 b) Which point on the titration curve represents a region where a buffer solution has formed?            point A                          point B                          point C                          point Dc) Which point on the titration curve represents the equivalence point?            point A                          point B                          point C                          point Dd) Which of the following would be the best indicator to use in the titration?     i. erythrosin B  pKa = 2.9                      ii. methyl red pK   a = 5.4                                                iii. bromthymol blue pKa = 6.8             iv. o-cresonphthalein pK  a = 9.0 
The titration curve shown below represents a 25 mL aqueous solution that is titrated with another solution at the same molarity. Which of the following statement is TRUE regarding the titration?A. The curve could represent the titration of NaOH with HCl (adding HCl to NaOH)B. The equivalence point is at pH 7C. Point A is in the buffer regionD. At point C, there is excess base presentE. The curve could represent the titration of H2SO4 with NaOH (adding NaOH to H2SO4)
The graph below displays data from what type of titration curve? Weak acid titrated with weak baseA) Weak acid titrated with strong baseB) Strong base titrated with weak acidC) Weak base titrated with strong acidD) Strong acid titrated with strong base
Below is the pH curve for a titration of a weak base with 0.10 M HCl. What is the pKb of the weak base?1. 9.42. 2.73. 8.74. 7.005. 4.6 6. 5.37. 11.3
The curve for the titration of 50.0 mL of 0.0200 M HClO(aq) with 0.100 M NaOH(aq) is given below. Estimate the pKa of HClO.a) 7.0b) 10.0c) 12.0d) 5.0e) 7.5
Which titration curve could describe the titration of a solution of HCl by addition of a solution KOH? 
Which titration curve could describe the titration of a solution of NH2OH by addition of a solution of HNO3?  
A titration of 25 mL of a monoprotic acid solution with a 0.1M NaOH solution yielded the following titration curve:a. What was initial molar concentration of the acid? ___________________b. What is the Ka of the acid? ___________________
Identify the equivalence point on the titration curve shown here.a. A is the equivalence pointb. D is the equivalence pointc. C is the equivalence pointd. B is the equivalence point 
A weak unknown monoprotic acid is titrated with a strong base. The titration curve is shown below.Find Ka for the unknown acid.
You have 75.0 mL of 0.10 M HA. After adding 30.0 mL of 0.10 M NaOH, the pH is 5.50. What is the Ka value of HA?
The active ingredient in aspirin is acetylsalicylic acid. A 2.51-g sample of acetylsalicylic acid required 27.36 mL of 0.5106 M NaOH for complete reaction. Addition of 13.68 mL of 0.5106 M HCl to the flask containing the aspirin and the sodium hydroxide produced a mixture with pH = 3.48. Determine the molar mass of acetylsalicylic acid and its Ka value. State any assumptions you must make to reach your answer.
A sample of a certain monoprotic weak acid was dissolved in water and titrated with 0.125 M NaOH, requiring 16.00 mL to reach the equivalence point. During the titration, the pH after adding 2.00 mL NaOH was 6.912. Calculate Ka for the weak acid.
Consider the following titration curves for two weak acids, both titrated with 0.100 M NaOH.Which of the two acids has the larger Ka?
A 0.229-g sample of an unknown monoprotic acid was titrated with 0.112 M NaOH and the resulting titration curve is shown in the figure.Determine pKa of the acid.
A 0.446-g sample of an unknown monoprotic acid was titrated with 0.105 M KOH and the resulting titration curve is shown in the figure.Determine pKa of the acid.
A student dissolves 0.0100 mole of an unknown weak base in 100.0 mL water and titrates the solution with 0.100 M HNO3. After 40.0 mL of 0.100 M HNO 3 was added, the pH of the resulting solution was 8.00. Calculate the Kb value for the weak base.
Consider the following titration curves for two weak bases, both titrated with 0.100 M HCl.Which of the two bases has the larger Kb?
Two 26.0 mL samples, one 0.100 M HCl and the other 0.100 M HF, were titrated with 0.200 M KOH. Predict which titration curve will have the lower initial pH.
Two 26.0 mL samples, one 0.100 M HCl and the other 0.100 M HF, were titrated with 0.200 M KOH. Sketch each titration curve.
Consider the following curve for the titration of a weak base with a strong acid and answer each of the following questions.What is the pH at the equivalence point?
Consider the following curve for the titration of a weak base with a strong acid and answer each of the following questions.At what volume of added acid is the pH calculated by working an equilibrium problem based on the initial concentration and Kb of the weak base?        
Consider the following curve for the titration of a weak base with a strong acid and answer each of the following questions.At what volume of added acid does pH = 14 – pKb?        
Consider the following curve for the titration of a weak base with a strong acid and answer each of the following questions.At what volume of added acid is the pH calculated by working an equilibrium problem based on the concentration and Ka of the conjugate acid?        
Consider the following curve for the titration of a weak base with a strong acid and answer each of the following questions.Beyond what volume of added acid is the pH calculated by focusing on the amount of excess strong acid added?        
Consider the following curve for the titration of a weak base with a strong acid and answer each of the following questions.What is the volume of added acid at the equivalence point?
The graphs below labeled (a) and (b) show the titration curves for two equal-volume samples of monoprotic acids, one weak and one strong. Both titrations were carried out with the same concentration of strong base.What is the approximate pH at the equivalence point of (a) curve?
The graphs below labeled (a) and (b) show the titration curves for two equal-volume samples of monoprotic acids, one weak and one strong. Both titrations were carried out with the same concentration of strong base. Which curve corresponds to the titration of the strong acid and which one to the titration of the weak acid?
The graphs below labeled (a) and (b) show the titration curves for two equal-volume samples of monoprotic acids, one weak and one strong. Both titrations were carried out with the same concentration of strong base.What is the approximate pH at the equivalence point of (b) curve?
The following plot shows the pH curves for the titrations of various acids by 0.10 M NaOH (all of the acids were 50.0-mL samples of 0.10 M concentration).a. Which pH curve corresponds to the weakest acid?
The graphs below labeled (a) and (b) show, the titration curves for two equal-volume samples of bases, one weak and one strong. Both titrations were carried out with the same concentration of strong acid.What is the approximate pH at the equivalence point of (a) curve?
The graphs below labeled (a) and (b) show, the titration curves for two equal-volume samples of bases, one weak and one strong. Both titrations were carried out with the same concentration of strong acid. Which curve corresponds to the titration of the strong base and which one to the weak base?
The following plot shows the pH curves for the titrations of various acids by 0.10 M NaOH (all of the acids were 50.0-mL samples of 0.10 M concentration).b. Which pH curve corresponds to the strongest acid? Which point on the pH curve would you examine to see if this acid is a strong acid or a weak acid (assuming you did not know the initial concentration of the acid)?
The graphs below labeled (a) and (b) show, the titration curves for two equal-volume samples of bases, one weak and one strong. Both titrations were carried out with the same concentration of strong acid.What is the approximate pH at the equivalence point of (b) curve?
Consider the following curve for the titration of a weak monoprotic acid with a strong base and answer each of the following questions.What is the pH at the equivalence point?
The following plot shows the pH curves for the titrations of various acids by 0.10 M NaOH (all of the acids were 50.0-mL samples of 0.10 M concentration).c. Which pH curve corresponds to an acid with Ka ≈ 1 x 10  -6?
Consider the following curve for the titration of a weak monoprotic acid with a strong base and answer each of the following questions.At what volume of added base is the pH calculated by working an equilibrium problem based on the initial concentration and Ka of the weak acid?
Consider the following curve for the titration of a weak monoprotic acid with a strong base and answer each of the following questions.At what volume of added base does pH = pKa?
Consider the following curve for the titration of a weak monoprotic acid with a strong base and answer each of the following questions.At what volume of added base is the pH calculated by working an equilibrium problem based on the concentration and Kb of the conjugate base?
Consider the following curve for the titration of a weak monoprotic acid with a strong base and answer each of the following questions.Beyond what volume of added base is the pH calculated by focusing on the amount of excess strong based added?
Consider the following curve for the titration of a weak monoprotic acid with a strong base and answer each of the following questions.What is the volume of added base at the equivalence point?
Sketch a qualitative curve for the titration of ethylenediamine, H 2NCH2CH2NH2, with 0.1 M HCl.
A student titrates an unknown weak acid, HA, to a pale pink phenolphthalein end point with 25.0 mL of 0.100 M NaOH. The student then adds 13.0 mL of 0.100 M HCl. The pH of the resulting solution is 4.70. How is the value of pKa for the unknown acid related to 4.70?
Use the values obtained in Problem 19.49 to sketch a curve of [H  3O+] vs. mL of added titrant. Are there advantages or disadvantages to viewing the results in this form? Explain.
Consider the following titration curves for two weak acids, both titrated with 0.100 M NaOH.Which of the two acid solutions is more concentrated?
Consider the following titration curves for two weak bases, both titrated with 0.100 M HCl. Which of the two base solutions is more concentrated?
Draw a curve for a series of solutions of HF. Plot [H 3O+]total on the vertical axis and the total concentration of HF (the sum of the concentrations of both the ionized and nonionized HF molecules) on the horizontal axis. Let the total concentration of HF vary from 1 × 10−10 M to 1 × 10−2 M.
Draw a curve similar to that shown in the following figure for a series of solutions of NH 3. Plot [OH−] on the vertical axis and the total concentration of NH 3 (both ionized and nonionized NH3 molecules) on the horizontal axis. Let the total concentration of NH 3 vary from 1 × 10−10 M to 1 × 10−2 M.
On the weak base/strong acid titration curve below, label the following points.a) The point where the pH corresponds to a solution of the weak base (B) in water.b) The point where the pH corresponds to a solution of the conjugate acid (BH +) in water.c) The point where pH=pKa (for BH+).
The graph below shows the titration curves for two monoprotic acids.What is the approximate pH at the equivalence point of each titration?
The graph below shows the titration curves for two monoprotic acids.Estimate the pKa of the weak acid.
Equal volumes of two acids are titrated with 0.10 M NaOH resulting in the two titration curves shown in the following figureWhich curve corresponds to the more concentrated acid solution?