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Acid-base titration curves

Before we start discussing about titration and titration curves, we should quickly refresh the concept of a weak/strong acid and weak/strong base.

A strong acid dissociates (or ionizes) completely in aqueous solution to form hydronium ions (H

_{3}

^{+}

)

A weak acid does not dissociate completely in aqueous solution to form hydronium ions (H

_{3}

^{+}

)

A strong base dissociates completely in aqueous solution to form hydroxide ions (OH

^{-}

)

A weak base does not dissociate completely in aqueous solution to form hydroxide ions (OH

^{-}

)

Examples of weak/strong acids and bases

Type	Examples
Strong Acids	hydrochloric acid (HCl), sulfuric acid (H $_{2}$ ‍SO $_{4}$ ‍), nitric acid (HNO $_{3}$ ‍)
Weak Acids	acetic acid (CH $_{3}$ ‍COOH), hydrofluoric acid (HF), oxalic acid (COOH) $_{2}$ ‍
Strong Bases	sodium hydroxide (NaOH), potassium hydroxide (KOH), lithium hydroxide (LiOH)
Weak Bases	ammonium hydroxide (NH $_{4}$ ‍OH), ammonia (NH $_{3}$ ‍)

Weak acids and weak bases always exist as conjugate acid-base pairs in an aqueous solution as represented below

Here, HA is the acid and A

^{-}

is termed as the conjugate base of HA

In the above reaction, A

^{-}

is a base and HA is the conjugate acid of A

^{-}

Rule of thumb is: Weak acids have strong conjugate bases, while weak bases have strong conjugate acids. As shown in the above two reactions, if HA is a weak acid, then its conjugate base A $^{-}$ ‍ will be a strong base. Similarly, if A $^{-}$ ‍ is a weak base, then its conjugate acid HA will be a strong acid.

How do we define ‘titration’?

Titration is a technique to determine the concentration of an unknown solution. As illustrated in the titration setup above, a solution of known concentration (titrant) is used to determine the concentration of an unknown solution (titrand or analyte).

Typically, the titrant (the solution of known concentration) is added through a burette to a known volume of the analyte (the solution of unknown concentration) until the reaction is complete. Knowing the volume of titrant added allows us to determine the concentration of the unknown analyte. Often, an indicator is used to signal the end of the reaction, the endpoint. Titrant and analyte is a pair of acid and base. Acid-base titrations are monitored by the change of pH as titration progresses.

Let us be clear about some terminologies before we get into the discussion of titration curves.

Titrant: solution of a known concentration, which is added to another solution whose concentration has to be determined.
Titrand or analyte: the solution whose concentration has to be determined.
Equivalence point: point in titration at which the amount of titrant added is just enough to completely neutralize the analyte solution. At the equivalence point in an acid-base titration, moles of base = moles of acid and the solution only contains salt and water.
Diagram of equivalence point

Acid-base titrations are monitored by the change of pH as titration progresses

Indicator: For the purposes of this tutorial, it’s good enough to know that an indicator is a weak acid or base that is added to the analyte solution, and it changes color when the equivalence point is reached i.e. the point at which the amount of titrant added is just enough to completely neutralize the analyte solution. The point at which the indicator changes color is called the endpoint. So the addition of an indicator to the analyte solution helps us to visually spot the equivalence point in an acid-base titration.

Endpoint: refers to the point at which the indicator changes color in an acid-base titration.

What is a titration curve?

A titration curve is the plot of the pH of the analyte solution versus the volume of the titrant added as the titration progresses.

Let’s attempt to draw some titration curves now.

1) Titration of a strong acid with a strong base

Suppose our analyte is hydrochloric acid HCl (strong acid) and the titrant is sodium hydroxide NaOH (strong base). If we start plotting the pH of the analyte against the volume of NaOH that we are adding from the burette, we will get a titration curve as shown below.

Point 1: No NaOH added yet, so the pH of the analyte is low (it predominantly contains H

_{3}

^{+}

from dissociation of HCl).

As NaOH is added dropwise, H

_{3}

^{+}

slowly starts getting consumed by OH

^{-}

produced by dissociation of NaOH. Analyte is still acidic due to predominance of H

_{3}

^{+}

ions.

Point 2: This is the pH recorded at a time point just before complete neutralization takes place.

Point 3: This is the equivalence point (halfway up the steep curve). At this point, moles of NaOH added = moles of HCl in the analyte. At this point, H

_{3}

^{+}

ions are completely neutralized by OH

^{-}

ions. The solution only has salt (NaCl) and water and therefore the pH is neutral i.e. pH = 7.

Point 4: Addition of NaOH continues, pH starts becoming basic because HCl has been completely neutralized and now excess of OH

^{-}

ions are present in the solution (from dissociation of NaOH).

2) Titration of a weak acid with a strong base

Let’s assume our analyte is acetic acid CH

_{3}

COOH (weak acid) and the titrant is sodium hydroxide NaOH (strong base). If we start plotting the pH of the analyte against the volume of NaOH that we are adding from the burette, we will get a titration curve as shown below.

Point 1: No NaOH added yet, so the pH of the analyte is low (it predominantly contains H

_{3}

^{+}

from dissociation of CH

_{3}

COOH). But acetic acid is a weak acid, so the starting pH is higher than what we noticed in case 1 where we had a strong acid (HCl).

As NaOH is added dropwise, H

_{3}

^{+}

slowly starts getting consumed by OH

^{-}

(produced by dissociation of NaOH). But analyte is still acidic due to predominance of H

_{3}

^{+}

ions.

Point 2: This is the pH recorded at a time point just before complete neutralization takes place.

Point 3: This is the equivalence point (halfway up the steep curve). At this point, moles of NaOH added = moles of CH

_{3}

COOH in the analyte. The H

_{3}

^{+}

ions are completely neutralized by OH

^{-}

ions. The solution contains only CH

_{3}

COONa salt and H

_{2}

Let me pause here for a second - can you spot a difference here as compared to case 1 (strong acid versus strong base titration)??? In the case of a weak acid versus a strong base, the pH is not neutral at the equivalence point. The solution is basic (pH ~ 9) at the equivalence point. Let’s reason this out.

As you can see from the above equation, at the equivalence point the solution contains CH

_{3}

COONa salt. This dissociates into acetate ions CH

_{3}

COO

^{-}

and sodium ions Na

^{+}

. As you will recall from the discussion of strong/ weak acids in the beginning of this tutorial, CH

_{3}

COO

^{-}

is the conjugate base of the weak acid CH

_{3}

COOH. So, CH

_{3}

COO

^{-}

is relatively a strong base (weak acid CH

_{3}

COOH has a strong conjugate base), and will thus react with H

_{2}

O to produce hydroxide ions (OH

^{-}

) thus increasing the pH to ~ 9 at the equivalence point.

Point 4: Beyond the equivalence point (when sodium hydroxide is in excess) the curve is identical to HCl-NaOH titration curve (1) as shown below.

3) Titration of a strong acid with a weak base

Suppose our analyte is hydrochloric acid HCl (strong acid) and the titrant is ammonia NH

_{3}

(weak base). If we start plotting the pH of the analyte against the volume of NH

_{3}

that we are adding from the burette, we will get a titration curve as shown below.

Point 1: No NH

_{3}

added yet, so the pH of the analyte is low (it predominantly contains H

_{3}

^{+}

from dissociation of HCl).

As NH

_{3}

is added dropwise, H

_{3}

^{+}

slowly starts getting consumed by NH

_{3}

. Analyte is still acidic due to predominance of H

_{3}

^{+}

ions.

Point 2: This is the pH recorded at a time point just before complete neutralization takes place.

Point 3: This is the equivalence point (halfway up the steep curve). At this point, moles of NH

_{3}

added = moles of HCl in the analyte. The H

_{3}

^{+}

ions are completely neutralized by NH

_{3}

. But again do you spot a difference here??? In the case of a weak base versus a strong acid, the pH is not neutral at the equivalence point. The solution is in fact acidic (pH ~ 5.5) at the equivalence point. Let’s rationalize this.

At the equivalence point, the solution only has ammonium ions NH

_{4}

^{+}

and chloride ions Cl

^{-}

. But again if you recall, the ammonium ion NH

_{4}

^{+}

is the conjugate acid of the weak base NH

_{3}

. So NH

_{4}

^{+}

is a relatively strong acid (weak base NH

_{3}

has a strong conjugate acid), and thus NH

_{4}

^{+}

will react with H

_{2}

O to produce hydronium ions making the solution acidic.

Point 4: After the equivalence point, NH

_{3}

addition continues and is in excess, so the pH increases. NH

_{3}

is a weak base so the pH is above 7, but is lower than what we saw with a strong base NaOH (case 1).

4) Titration of a weak base with a weak acid

Suppose our analyte is NH

_{3}

(weak base) and the titrant is acetic acid CH

_{3}

COOH (weak acid). If we start plotting the pH of the analyte against the volume of acetic acid that we are adding from the burette, we will get a titration curve as shown below.

If you notice there isn’t any steep bit in this plot. There is just what we call a ‘point of inflexion’ at the equivalence point. Lack of any steep change in pH throughout the titration renders titration of a weak base versus a weak acid difficult, and not much information can be extracted from such a curve.

To summarize

In an acid-base titration, a known volume of either the acid or the base (of unknown concentration) is placed in a conical flask.
The second reagent (of known concentration) is placed in a burette.
The reagent from the burette is slowly added to the reagent in the conical flask.
A titration curve is a plot showing the change in pH of the solution in the conical flask as the reagent is added from the burette.
A titration curve can be used to determine:
1) The equivalence point of an acid-base reaction (the point at which the amounts of acid and of base are just sufficient to cause complete neutralization).
2) The pH of the solution at equivalence point is dependent on the strength of the acid and strength of the base used in the titration.
-- For strong acid-strong base titration, pH = 7 at equivalence point
-- For weak acid-strong base titration, pH > 7 at equivalence point
-- For strong acid-weak base titration, pH < 7 at equivalence point

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MCAT

Kurs: MCAT > Rozdział 9

Acid-base titration curves

How do we define ‘titration’?

What is a titration curve?

To summarize

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