Calculating pH of Polyprotic Acid Buffers: 1:1 and Non-1:1 Examples - Prof. James B. Condo, Study notes of Chemistry

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pH of Polyprotic acid

buffers

1:1 buffers and non-1:1 buffers

plus the pH of the first weak acid proton.

pH of Polyprotic 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.

pH of Polyprotic acid buffers Answers to the question, “What is the pH of each of the acidsif they are made up to be 0.

M

H

2

SO

4

pH = 1.

(Recall it’s a strong acid.)

H

2

SO

3

pH = 1.

(Missed this one? Note

x

is not valid)

H

3

PO

4

pH = 1.

H

2

CO

3

pH = 3.

pH of Polyprotic acid buffers Recall that for the 1:1 buffer, the pH

p

K

a

pH of Polyprotic acid buffers Recall that for the 1:1 buffer, the pH

p

K

a

The two reactions associated with H

2

SO

3

are:

H

2

SO

3

+ H

2

O

H

3

O

+ HSO

3

and

HSO

3

+ H

2

O

H

3

O

+ SO

3

2–

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

M

in NaHSO

3

and 0.

M

in Na

2

SO

3

pH of Polyprotic acid buffers Recall that for the 1:1 buffer, the pH

p

K

a

The two reactions associated with H

2

SO

3

are:

H

2

SO

3

+ H

2

O

H

3

O

+ HSO

3

and

HSO

3

+ H

2

O

H

3

O

+ SO

3

2–

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

M

in NaHSO

3

and 0.

M

in Na

2

SO

3

Notice that it is the HSO

3

and the SO

3

2–

that are relevant.

(Na

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!)

pH of Polyprotic acid buffers Recall that for the 1:1 buffer, the pH

p

K

a

The two reactions associated with H

2

SO

3

are:

H

2

SO

3

+ H

2

O

H

3

O

+ HSO

3

and

HSO

3

+ H

2

O

H

3

O

+ SO

3

2–

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

M

in NaHSO

3

and 0.

M

in Na

2

SO

3

Since this is a 1:1 buffer, one need only set the pH to the p

K

a

K

a

= 6.24 × 10

Notice that it is the HSO

3

and the SO

3

2–

that are relevant.

pH of Polyprotic acid buffers Recall that for the 1:1 buffer, the pH

p

K

a

The two reactions associated with H

2

SO

3

are:

H

2

SO

3

+ H

2

O

H

3

O

+ HSO

3

and

HSO

3

+ H

2

O

H

3

O

+ SO

3

2–

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

M

in NaHSO

3

and 0.

M

in Na

2

SO

3

Since this is a 1:1 buffer, one need only set the pH to the p

K

a

K

a

= 6.24 × 10

pH = 7.

Notice that it is the HSO

3

and the SO

3

2–

that are relevant.

pH of Polyprotic acid buffers

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

M

in KH

2

PO

4

and 0.

M

in K

2

HPO

4

Answer: pH = p

K

a

2

pH = 7.

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

M

in K

2

HPO

4

and 0.

M

in K

3

PO

4

Answer: pH = p

K

a

3

pH = 11.

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

M

in Li

2

CO

3

and 0.

M

in LiHCO

3

Answer: pH = p

K

a

2

pH = 10.

These are all 1:1 buffer so pH

p

K

a

is OK.

pH of Polyprotic 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 KH

2

PO

4

and 0.

M

in K

2

HPO

4

pH of Polyprotic 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 KH

2

PO

4

and 0.

M

in K

2

HPO

4

So, which of these reactions is relevant?H

3

PO

4

+ H

2

O

H

3

O

+ H

2

PO

4

!

K

a

= 1.1 × 10

H

2

PO

4

!

+ H

2

O

H

3

O

+ HPO

4

2

!

K

a

= 7.5 × 10

HPO

4

!

+ H

2

O

H

3

O

+ PO

4

3

!

K

a

= 4.8 × 10

It is the second one.

pH of Polyprotic 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 KH

2

PO

4

and 0.

M

in K

2

HPO

4

H

2

PO

4

!

+ H

2

O

H

3

O

+ HPO

4

2

!

K

a

= 7.5 × 10

2

3

4

2

4

H O

HPO

H PO

a

K

−

−

⎡

⎤ ⎡

⎤

⎣

⎦ ⎣

⎦

=

⎡

⎤

⎣

⎦

pH of Polyprotic 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 KH

2

PO

4

and 0.

M

in K

2

HPO

4

H

2

PO

4

!

+ H

2

O

H

3

O

+ HPO

4

2

!

K

a

= 7.5 × 10

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

after equilibrium

before equilibrium

0.50 +

x

0.10 0.

x

!

x

[H

3

O

]

[HPO

4

2–

]

[H

2

PO

4

]

x

Fill in theequilibriumexpression:

8

10

x

x

x

−

×

=

−

pH of Polyprotic 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 KH

2

PO

4

and 0.

M

in K

2

HPO

4

H

2

PO

4

!

+ H

2

O

H

3

O

+ HPO

4

2

!

K

a

= 7.5 × 10

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

after equilibrium

before equilibrium

0.50 + x

0.10 0.

x

!

x

[H

3

O

]

[HPO

4

2–

]

[H

2

PO

4

]

x

Fill in theequilibriumexpression: