pH of the Polybasic Acid Buffers - Lecture Slides | CHEM 1110, Study notes of Chemistry

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pH of Polybasic bases and

their buffers

1:1 buffers and non-1:1 buffers

plus the pH of the first weak base proton.

pH of Polybasic acid buffers The concept of the equilibriums involve with polyprotic acidsand amphoteric bases has been presented in a previous slideshow titled “

Amphoteric (amphiprotic) acids and bases

Please review this before continuing if you have not masteredthe subject.

Answers to the question, “What is the pH of each of thebases if they are made up to be 0.

M

H

2

NNH

2

pOH = 3.

Y

pH =10.

H

2

N(CH

6

NH

2

pOH = 1.

Y

pH =12.

H

2

N(CH

2

NH

2

pOH = 2.

Y

pH =11.

H

2

N(CH

3

NH

2

pOH = 2.

Y

pH =11.

pH of Polybasic acid buffers

Recall that for the 1:1 buffer, the pOH

p

K

b

pH of Polybasic acid buffers

Recall that for the 1:1 buffer, the pH

p

K

a

The two reactions associated with H

2

NNH

2

are:

H

2

NNH

2

+ H

2

O

H

2

NNH

3

+ OH

!

and

H

2

NNH

3

+ H

2

O

H

3

NNH

3

2+

+ OH

!

Example 1: Calculate the pH of the buffer solution made up tobe 0.10 Which one should be used?

M

in H

2

NNH

2

and 0.

M

in H

2

NNH

3

Cl.

pH of Polybasic acid buffers

Recall that for the 1:1 buffer, the pH

p

K

a

Notice that H

2

NNH

2

and H

2

NNH

3

are relevant.

(Cl

ions are spectator ions. If this is mysterious to you (tish,

tish), see the CHEM 1110 slide show “

Overall versus Net

Ionic Reactions

” for a review!)

The two reactions associated with H

2

NNH

2

are:

H

2

NNH

2

+ H

2

O

H

2

NNH

3

+ OH

!

and

H

2

NNH

3

+ H

2

O

H

3

NNH

3

2+

+ OH

!

Example 1: Calculate the pH of the buffer solution made up tobe 0.10 Which one should be used?

M

in H

2

NNH

2

and 0.

M

in H

2

NNH

3

Cl.

pH of Polybasic acid buffers

Recall that for the 1:1 buffer, the pH

p

K

a

Since this is a 1:1 buffer, one need only set the pOH to thep

K

b

K

b

= 1.2 × 10

The two reactions associated with H

2

NNH

2

are:

H

2

NNH

2

+ H

2

O

H

2

NNH

3

+ OH

!

and

H

2

NNH

3

+ H

2

O

H

3

NNH

3

2+

+ OH

!

Example 1: Calculate the pH of the buffer solution made up tobe 0.10 Which one should be used?

M

in H

2

NNH

2

and 0.

M

in H

2

NNH

3

Cl.

Notice that H

2

NNH

2

and H

2

NNH

3

are relevant.

pH of Polybasic acid buffers

Recall that for the 1:1 buffer, the pH

p

K

a

Since this is a 1:1 buffer, one need only set the pOH to thep

K

b

K

b

= 1.2 × 10

pOH = 5.

Y

pH = 8.

The two reactions associated with H

2

NNH

2

are:

H

2

NNH

2

+ H

2

O

H

2

NNH

3

+ OH

!

and

H

2

NNH

3

+ H

2

O

H

3

NNH

3

2+

+ OH

!

Example 1: Calculate the pH of the buffer solution made up tobe 0.10 Which one should be used?

M

in H

2

NNH

2

and 0.

M

in H

2

NNH

3

Cl.

Notice that H

2

NNH

2

and H

2

NNH

3

are relevant.

pH of Polybasic acid buffers

Here’s some more examples, determine the answers: Example 2: Calculate the pH of a solution made up to be0.

M

in H

2

N(CH

6

NH

3

Cl and 0.

M

in H

3

N(CH

2

6

NH

3

Cl

2

Answer: pH = p

K

b

2

pOH = 3.

Y

pH = 10.

Example 3: Calculate the pH of a solution made up to be0.

M

in H

2

N(CH

2

NH

2

and 0.

M

in H

2

N(CH

2

2

NH

3

Cl

Answer: pH = p

K

b

1

pOH = 3.

Y

pH = 10.

Example 4: Calculate the pH of a solution made up to be0.

M

in H

2

N(CH

3

NH

3

Br and 0.

M

in H

3

N(CH

2

3

NH

3

Br

2

Answer: pH = p

K

b

2

pOH = 4.

Y

pH = 9.

These are all 1:1 buffer so pH

p

K

a

is OK.

pH of Polybasic acid buffers

What if the mixture is not a 1:1 buffer? Example 5: Calculate the pH of a solution made up to be0.

M

in H

2

N(CH

2

NH

3

Cl and 0.

M

in H

3

N(CH

2

2

NH

3

Cl

2

pH of Polybasic acid buffers

Example 5: Calculate the pH of a solution made up to be0.

M

in H

2

N(CH

2

NH

3

Cl and 0.

M

in H

3

N(CH

2

2

NH

3

Cl

2

So, which of these reactions is relevant?H

2

N(CH

2

NH

2

+ H

2

O

H

2

N(CH

2

2

NH

3

+ OH

!

K

b

= 5.2 × 10

H

2

N(CH

2

NH

3

+ H

2

O

H

3

N(CH

2

2

NH

3

2+

+ OH

!

K

b

= 3.7 × 10

It is the second reaction.

What if the mixture is not a 1:1 buffer? pH of Polybasic acid buffers

Example 5: Calculate the pH of a solution made up to be0.

M

in H

2

N(CH

2

NH

3

Cl and 0.

M

in H

3

N(CH

2

2

NH

3

Cl

2

What if the mixture is not a 1:1 buffer? H

2

N(CH

2

NH

3

+ H

2

O

H

3

N(CH

2

2

NH

3

2+

+ OH

!

K

b

= 3.7 × 10

pH of Polybasic acid buffers

2

3

2

2

3

2

2

2

3

OH

H N(CH ) NH

H N(CH ) NH

b

K

−

⎡

⎤ ⎡

⎤

⎣

⎦ ⎣

⎦

=

⎡

⎤

⎣

⎦

Example 5: Calculate the pH of a solution made up to be0.

M

in H

2

N(CH

2

NH

3

Cl and 0.

M

in H

3

N(CH

2

2

NH

3

Cl

2

H

2

N(CH

2

NH

3

+ H

2

O

H

3

N(CH

2

2

NH

3

2+

+ OH

!

K

b

= 3.7 × 10

after equilibrium

0.50 +

x

x

!

x

This then is a normal type II buffer problem. Set up a table: Fill in theequilibriumexpression:

What if the mixture is not a 1:1 buffer?

[H

3

N(CH

2

)

2

NH

3

2+

]

[H

2

N(CH

2

)

2

NH

3

]

[OH

]

pH of Polybasic acid buffers

before equilibrium

0.100.

x

7

10

x

x

x

−

×

=

−

H

2

N(CH

2

NH

3

+ H

2

O

H

3

N(CH

2

2

NH

3

2+

+ OH

!

K

b

= 3.7 × 10

This then is a normal type II buffer problem. Set up a table:

after equilibrium

before equilibrium

0.50 + x

0.100.

x

!

x

Fill in theequilibriumexpression:

[H

3

N(CH

2

)

2

NH

3

2+

]

[H

2

N(CH

2

)

2

NH

3

]

[OH

]

Example 5: Calculate the pH of a solution made up to be0.

M

in H

2

N(CH

2

NH

3

Cl and 0.

M

in H

3

N(CH

2

2

NH

3

Cl

2

What if the mixture is not a 1:1 buffer? pH of Polybasic acid buffers

x