Question

Identify each type of titration curve. Note that the analyte Is stated first, followed by the titration. Drag each graph to the appropriate bin. A 50.0-mL volume of 0.15 M HBr is titrated with 0.25 M KOH. Calculate the pH after the addition of 17.0mL of KOH. A 75.0-mL volume of 0.200 M NH3 (Kb = 1.8 x 10-5) is titrated with 0.500 M HN03. Calculate the pH after the addition of 21.0mL of HN03. A 52.0-mL volume of 0.35 M CH3COOH (Ka = 1.8 x 10-5) is titrated with 0.40 M NaOH. Calculate the pH after the addition of 31.0mL of NaOH- To calculate the pH at the equivalence point for Consider the titration of 50.0 mL of 0.20 M NH3 (K b= 1.8x 10-5) with 0.20 M HN03. Calculate the pH after addition of 50.0 mL of the titrant. A 30.0-mL volume of 0.50 M CH3COOH (Ka = 1.8 x 10-5) was titrated with 0.50 M NaOH- Calculate the pH after addition of 30.0 mL of NaOH-

Answer 1

Concepts and reason

The concepts used here are based on acid-base titrations, molarity, and . dissociation constant of acid and base, ionic product of water

Start by identifying the type of titration curves based on the nature of analyte and titrant. Then, the concentration of hydrogen ions remained after neutralization of hydrobromic acid by the used amount of potassium hydroxide is calculated which is then used to determine the value of the solution. Then, the value of is calculated by using of ammonia and ionic product of water which is then used along with concentrations and the Henderson-Hasselbalch equation to calculate the value of for the solution. A similar procedure is followed for acetic acid and acetate ions where the value of is given. Then, the value of is calculated from the determined concentration of hydrogen ions from the ionization of ammonium ions at the equivalence point. Further, the value of is calculated from the determined concentration of hydroxide ions from the ionization of acetate ions at the equivalence point. Finally, the value of is determined by using this value of .

Fundamentals

Polyprotic acid:

Acids which contain more than one ionizable hydrogens are known as polyprotic acids. The number of equivalence points is equal to the number of ionizable protons for titration of these acids.

Titration:

Quantitative experimental technique carried out by slowly adding titrant to a solution of the analyte to determine its concentration.

The solution with known concentration used in titration is called titrant.

The solution whose concentration is unknown and has to be determined by titration is called analyte.

Acid-base titration:

Titration involving acid-base is performed by monitoring the value of the solution as titrant is added to reach the equivalence point where neutralization reaction between acid-base is complete.

Acid-base titrations involve the neutralization reactions to give salt and water.

Depending on the type of acid-base, titrations are classified into the following categories.

1.Strong acid-strong base titration

2.Weak acid-strong base titration

3.Strong acid-weak base titration

4.Weak acid-weak base titration

The plot of against volume of titrant is called titration curve and can be used to identify the type of acid-base titration.

The initial value of when no titrant is added indicates the nature of the analyte, the value of at the equivalence point indicates the nature of the salt, and the final value of when an excess of titrant is added indicates the nature of titrant.

When the value of is less than , it represents the acidic solution, when it is more than , it represents a basic solution and represents a neutral solution.

Molarity: The number of moles per liter of the solution is called its molarity. It can be expressed by the following formula.

…… (1)

For a solution, the value of is calculated by using the following formula.

…… (2)

Here, is the equilibrium concentration of hydrogen ions.

Dissociation constant of acid: The equilibrium constant for the dissociation of acid is called its dissociation constant and is denoted by

The general expression for dissociation of acid is given as follows.

The equilibrium constant is given as follows.

…… (3)

Here, is the equilibrium concentration of the acid, is the equilibrium concentration of the conjugate base and is the equilibrium concentration of hydrogen ions.

Dissociation constant of base: The equilibrium constant for the dissociation of a base is called its dissociation constant and is denoted by .

The general expression for dissociation of the base is given as follows.

The equilibrium constant is given as follows.

…… (4)

Here, is the equilibrium concentration of the base, is the equilibrium concentration of the conjugate acid and is the equilibrium concentration of hydroxide ions.

For a solution, the value of can be calculated by using the following formula.

…… (5)

Here, is the equilibrium concentration of hydroxide ions.

For a solution, is related to by the following expression.

…… (6)

Ionic product of water: It is related to the dissociation constants of conjugate acid-base by the following expression.

…… (7)

At it has a value of .

For any given value of , the value of can be calculated by using the following formula.

…… (8)

Henderson-Hasselbalch equation:

It is expressed as shown below.

…… (9)

Here, is the equilibrium concentration of the acid and is the equilibrium concentration of the conjugate base.

(1.A)

The first titration curve is shown below.

The value of at the start is , at the equivalence point is and at the end point is .

The sharp increase in the value of further implies that this titration curve is for strong acid-strong base titration.

The second titration curve is given as follows.

The value of at the start is , at the two equivalence point is and at the end point is .

The presence of two equivalence points implies that this titration curve is for polyprotic acid-strong base titration.

The third titration curve is shown below.

The value of at the start is , at the equivalence point is and at the end point is .

The initial slow increase in the value of further implies that this titration curve is for weak acid-strong base titration.

The fourth titration curve is given as follows.

The value of at the start is , at the equivalence point is and at the end point is .

The initial slow decrease in the value of further implies that this titration curve is for weak base-strong acid titration.

(1.B)

Conversion of to liter is done as shown below.

Convert the units of volume for by using the conversion factor for volume as shown below.

Convert the units of volume for by using the conversion factor for volume as shown below.

Rewrite the formula of molarity for number of moles by using equation (1) as shown below.

Calculate the initially taken number of moles of ions by substituting for volume and for molarity in the above expression as shown below.

Calculate the used number of moles of by substituting for volume and for molarity in the above expression as shown below.

Calculate the remaining number of moles of ions by substituting for initial number of moles and for neutralized number of moles as shown below

Calculate the total volume of the solution by adding by the used volume of acid and base as shown below.

Calculate the final concentration of ions in the solution by substituting for number of moles and for volume in the equation (1) as shown below.

Calculate the value of by substituting for in the equation (2) as shown below.

(1.C)

Rewrite the expression of the ionic product of water from equation (7) for as shown below.

Calculate the value of at by substituting for and for in the above expression as shown below.

Calculate the value of by substituting for , in the equation (8) as shown below.

Calculate the initially taken number of moles of by substituting for volume and for molarity and using the conversion factor for volume in the derived expression as shown below.

Calculate the used number of moles of by substituting for volume and for molarity and using the conversion factor for volume in the derived expression as shown below.

Calculate the remaining number of moles of conjugate acid-base for neutralization of ammonia by nitric acid as shown below.

Write the Henderson-Hasselbalch equation for this solution according to the equation (9) as shown below.

Here, is the equilibrium concentration of ammonia and is the equilibrium concentration of the ammonium ions.

Calculate the value of for this solution by substituting for , for and for in the above expression as shown below.

(1.D)

Calculate the value of by substituting for , in the equation (8) as shown below.

Calculate the initially taken number of moles of by substituting for volume and for molarity and using the conversion factor for volume in the derived expression as shown below.

Calculate the used number of moles of by substituting for volume and for molarity and using the conversion factor for volume in the derived expression as shown below.

Calculate the remaining number of moles of conjugate acid-base for neutralization of ammonia by nitric acid as shown below.

Write the Henderson-Hasselbalch equation for this solution according to the equation (9) as shown below.

Here, is the equilibrium concentration of sodium acetate and is the equilibrium concentration of the acetic acid.

Calculate the value of for this solution by substituting for , for and for in the above expression as shown below.

(2.C)

Calculate the initially taken number of moles of and used number of moles of by substituting for volume and for molarity and using the conversion factor for volume in the derived expression as shown below.

Calculate the total volume of the solution by adding by the used volume of acid and base as shown below.

Calculate the initial concentration of ions in the solution by substituting for number of moles and for volume in the equation (1) as shown below.

Write the ICE table for the dissociation of ammonium ions as shown below.

Calculate the concentration of hydrogen ions by substituting for and the concentrations from ICE table in the expression for the equilibrium constant according to the equation (3) and assuming that ionization is small so denominator can be approximated accordingly as shown below.

Calculate the value of by substituting for in equation (2) as shown below:

(2.D)

Rewrite the expression of the ionic product of water from equation (7) for as shown below.

Calculate the value of at by substituting for and for in the above expression as shown below.

Calculate the initially taken number of moles of and used number of moles of by substituting for volume and for molarity and using the conversion factor for volume in the derived expression as shown below.

Calculate the total volume of the solution by adding by the used volume of acid and base as shown below.

Calculate the initial concentration of ions in the solution by substituting for number of moles and for volume in the equation (1) as shown below.

Write the ICE table for the ionization of acetate ions as shown below.

Calculate the concentration of hydroxide ions by substituting for and the concentrations from ICE table in the expression for the equilibrium constant according to the equation (4) and assuming that ionization is small so denominator can be approximated accordingly as shown below.

Calculate the value of by substituting for in equation (5) as shown below.

Calculate the value of by substituting for in equation (6) as shown below.

Ans: Part 1.A

The given titration curves are identified as shown below.