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Equivalence Point

Analytical chemistry is a branch of chemistry which mainly deals with the quantitative and qualitative analysis of given substances. For example; gravimetric analysis is used to measure the quantity of compound formed during any chemical reactions. It helps in the determination of yield percentage. Similarly, chromatography helps in the separation of components of a mixture on the basis of adsorption of it on a certain medium.

Another analytical technique is a volumetric analysis which is used to measure the concentration of a chemical substance in a certain solution. Titration is one of the most common volumetric analysis techniques which involves 2 samples; titrant and analyte. We know the concentration of titrant and the solution of unknown concentration is called as an analyte. The volumetric measurement requires certain glassware like burette which is filled with titrant, conical flask for analyte solution. The pipette is used to use to measure a certain volume of solution.

In some of the titration,  the indicator is used to show  equivalence point of the titration. It is a point at which the moles of the titrant and analyte are equal. Sometimes we use end point which is almost same as equivalence point.

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Equivalence Point Definition

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The equivalence point or stoichiometric point of a chemical reaction in titration is the point or concentration of added titrant which is stoichiometrically equal to the number of moles of analyte in given sample.

Or at the equivalence point is a point the fraction added the stoichiometric amount of titrant to the titrated substance equals exactly. 

$\frac{Stoichiometric\ Amount\ of\ Titrant}{Titrated\ Substance}$ =1

The best way to figure out the equivalence point is titration curve which is a plot of the pH as a function of added titrant.

At the equivalence point, the curve shows inflection point. 

Equivalence Point 

There are various methods for the determination of the equivalence point. The use of a particular method depends upon the type of reaction involved in the titration.

pH indicator

Indicator plays an important role in the acid-base titration. They show a color change at the equivalence point. They can be used in Redox Titration. pH indicators give an approximation of the equivalence point.

  • Potentiometer: It is an instrument which can measure the electrode potential of the given solution and generally used in redox titration as the potential gets change at equivalence point in redox reactions.
  • pH meter: Just like pH indicators, they also show a variation in potential at a change in pH.
  • Conductance: In an acid-base titration, the equivalence point reached neutralization point. Due to neutralization reaction, the concentration of ions changes which associates with the change in conductance. Hence the change in conductance is the measurement of equivalence point.
  • Color change: Some reaction show color change at equivalence point without any added indicator.
  • Precipitation: In some titration process, a precipitate forms at equivalence point. For example; white precipitate of silver chloride formed because of reaction between Ag+ and Cl- at the equivalence point.
  • Isothermal titration calorimeter: This is used to measure the heat produced or consumed by the reaction for the determination the equivalence point.
  • Thermometric titrimetry: In this technique, the equivalence point is determined by using the rate of temperature change.
  • Spectroscopy: This method is based on the spectrum of the reactant, titrant or product. By using the spectrum the relative amounts of the product and reactant determine which used to calculate the equivalence point.
  • Amperometry: This technique is only can be used for amperometry titration.

End Point

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Below are the points of Endpoint titration:
  1. From the name only, we can conclude that endpoint is related to the end of titration in practice.
  2. The accuracy of titration will be high when the end point is quite close to the equivalence point.
  3. For example in the acid-base titration of a strong acid with a strong base, the equivalence point is at pH 7.00.
  4. The indicator used for this titration is phenolphthalein which starts the color change at pH slightly above 8.
  5. Hence, in this reaction, the color change is noticed only when small excess amount added of titrant which introduces small positive error in the titration.
  6. In other words, both equivalence point and the end point is different as equivalence point corresponds to the theoretical completion of the reaction while the endpoint is related to the actually measured physical change in the solution determined by an indicator or an instrument mentioned above.

The difference between the endpoint and the equivalence point of the titration is called as an indicator error.
End Point and Equivalence Point

For example, when we add strong base like sodium hydroxide with strong acid like hydrochloric acid of same concentration and same volume, the neutral point will reach at pH =7.

So equivalence point will comes at pH seven when both solutions have been mixed in exactly the right proportions.

While at the end point indicator will show the color change , that will happen when the concentration of one the solution will more than other one.

Half Equivalence Point

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When a reaction in titration reaches the halfway, at this point the value of equivalence point is termed as the half-equivalence point. For example, the titration of 2M monoprotic acid reaches to the half-equivalence point when 1 M of the acid has been made into its corresponding base, and 1 M is still left by Stoichiometric. 

The half-equivalence point is can be used to determine the acid dissociation and pKa of the acid used in titration. In acid-base titration, the ratio between the acid and corresponding base is exactly 1:1 at the half-equivalence point.

 Weak Acid Titration

The same method can be used to determine the pKb of the base by titrating a weak base against an acid.

 Weak Base Titration           

pH at Equivalence Point

The titration curve also called pH curve as they show a certain change at a particular which is a measure of equivalence point in the titration. 

In any acid-base titration; titration curve based on the concentration of both reactants; acid as well as the base. Let’s plot some titration curve for different acid –base titration and determine the position of equivalence point.

Titration Curve Equivalence Point

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There are total four possibilities with the different strength of acid and base.
  1. Strong acid and strong base
  2. Strong acid and weak base
  3. Weak acid and strong base
  4. Weak acid and weak base
In each combination, there will be two titration curve depends on the titrant.

Strong acid and strong base:

Let’s take an example of hydrochloric acid and sodium hydroxide.
NaOH + HCl $\to$ NaCl + H2O
If we add acid solution by burette in to 25 ml of base solution in titration, in starting of titration the pH decreases to a very small amount until quite near the equivalence point. 

After equivalence point there is a steep plunge in titration curve.

Titration Curve with Equivalence Point
In each combination, there will be two titration curve depends on the titrant.

Strong acid and strong base:

Let’s take an example of hydrochloric acid and sodium hydroxide.
NaOH + HCl $\to$ NaCl + H2O
If we add acid solution by burette into 25 ml of base solution in titration, in starting of titration the pH decreases to a very small amount until quite near the equivalence point. After equivalence point, there is a steep plunge in titration curve. 

On the other hand, if we add base solution to the acid solution, as expected the pH of solution increase. As in the previous curve, here also the pH doesn't change very much until you get close to the equivalence point. Then it surges upwards very steeply.
Methyl orange as well as phenolphthalein both acts as a good indicator for this titration. No doubt, neither indicator changes color at the equivalence point but the curve is so steep for a long pH which covers the range from methyl orange to phenolphthalein.
At equivalence point, phenolphthalein becomes colorless (at pH = 8.3) while with methyl orange solution; color gets change from orange to red which is after equivalence point.
Indicator at Point of Equivalence 

Strong acid and weak base:

  • Titration of hydrochloric acid with ammonia gives ammonium chloride. Since we have a weak base, so when we add acid to weak base the pH value will decrease and once there is an excess of acid in solution, the pH starts by falling quite but after some time the curve gets less steep due to a buffer solution is being set up between ammonia and ammonium chloride.
  • The equivalence point obtained at less than pH = 5 due to ammonium chloride.
  • For this combination, methyl orange is the perfect indicator as phenolphthalein does not show change in color.

Weak acid and strong base:

  • If a weak acid like acetic acid (CH3COOH) titrated with the strong base (NaOH) it forms sodium acetate and water.
  • If titration started with an excess of acid the equivalence point obtained at the formation of buffer solution containing sodium ethanoate and acetic acid results a large fall in pH value.
  • If we started with excess of base the reaction as well as titration curve will be exactly same as in case of strong acid and base. Phenolphthalein is a good indicator for this titration.

Weak acid and weak base:

  • If both acid and base are weak like acetic acid and ammonia, the equivalence point is obtained at pH = 7.
  • There is no suitable indicator for this titration as phenolphthalein gets finish before equivalence point while methyl orange falls off the curve altogether.
  • Hence this titration will continue without indicator only.

Calculate Equivalence Point

Various methods are used to determine the equivalence point,
e.g. pH indicator, Potentiometer, pH meter, Conductance, Color change, Precipitation etc. The most common method used is the pH indicators. The theory behind it is that the indicators change the color when complete neutralization takes place.

The pH of the completely neutralized solution is 7, as it is ideally neutral solution. The common indicators are Phenolphthalein, Litmus etc. Phenolphthalein is colorless when in an acidic solution. However, it would acquire pink color in the basic solution. This transition decides the determination of equivalence point.

Similarly, litmus is red when in an acidic solution. However, it would acquire blue color in the basic solution.

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