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pH Calculation for Monoprotic Acids and Bases: Strong, Weak, and Buffers, Study notes of Chemistry

A comprehensive guide on calculating ph values for monoprotic acids and bases, including strong acids and bases, weak acids and bases, and acid-base conjugates. It covers the conditions for neutral systems, strong acid and base solutions, and weak acid and base solutions. The document also explains the concepts of degree of dissociation and buffer capacity.

Typology: Study notes

2021/2022

Uploaded on 09/12/2022

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Calculation of pH for monoprotic acids and bases
Acid/base
system Examples Calculation of pH / pOH Conditions
Pure water
and neutral
salts
H
2
O, KCl, NaNO
3,
CsClO
4
... [H
+
] = [OH
] =
W
K
under any
conditions
[H
+
] = c
strong acid
c
strong acid
> 10
–6
M Strong acids HCl, HNO
3
,
H
2
SO
4
(only the
first deprotonation
step), HClO
4
,
CF
3
SO
3
H
][H
c][H
W
acid strong +
+
+= K under any
conditions
[OH
] = c
strong base
c
strong base
> 10
–6
M
Strong bases NaOH, KOH,
RbOH, CsOH...
][OH
c][OH
W
base strong
+=
K
under any
conditions
][H
][Hc
][H
acidweak
a+
+
+
= K
under any
conditions
Monoprotic
weak acids
and acidic
salts
CH
3
COOH,
HNO
2
, HCOOH,
NH
4
Cl (NH
4+
)...
any monoprotic
acid with a
K
a
[H
+
] =
acidweak a
c
K
c
weak acid
>>>
K
a
][OH
][OHc
][OH
baseweak
b
= K
under any
conditions
Monoprotic
weak bases
and basic
salts
NH
3
, (CH
3
)
3
N,
CH
3
COONa
(CH
3
COO
)...
any monoprotic
base with a
K
b
[OH
] =
baseweak b
cK c
weak base
>>> K
b
[H
+
] = c
strong acid
c
strong acid
>> c
weak
acid
Strong and
weak acid in
the same
solution
][H
][Hc
c][H
acidweak
aacid strong
+
+
+
+= K under any
conditions
[OH
] = c
strong base
c
strong base
>> c
weak
base
Strong and
weak base in
the same
solution
][OH
][OHc
c][OH
baseweak
bbase strong
+= K
under any
conditions
Acidic
buffers CH
3
COOH +
CH
3
COONa
together
Basic
buffers NH
3
+ NH
4
Cl
together
[H
+
] = K
a
baseweak
acidweak
c
c
= K
a
baseweak
acidweak
n
n
...
pH = pK
a
+ log
acid acid/weak conjugate
base gatebase/conjuweak
c
c
pf2

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Calculation of pH for monoprotic acids and bases

Acid/base system

Examples Calculation of pH / pOH Conditions

Pure water and neutral salts

H 2 O, KCl, NaNO3, CsClO 4 ...

[H+] = [OH–] = K (^) W under any conditions

Strong acids HCl, HNO 3 , [H+] = cstrong acid cstrong acid > 10–6^ M H 2 SO 4 (only the first deprotonation step), HClO 4 , CF 3 SO 3 H [H ]

[H +^ ]= cstrong acid+ W+

K under any conditions

Strong bases NaOH, KOH, [OH–] = cstrong base cstrong base > 10–6^ M RbOH, CsOH...

[OH ]

[OH −^ ]= cstrong base+ W−

K under any conditions

[H ]

c [H ] [H ] a weakacid+

  • (^) = K ⋅ − under any conditions

Monoprotic weak acids and acidic salts

CH 3 COOH,

HNO 2 , HCOOH,

NH 4 Cl (NH 4 +)... any monoprotic acid with a K a

[H+] = K (^) a ⋅cweakacid cweak acid^ >>>^ K a

[OH ]

c [OH ] [OH ] b weakbase −

− − (^) = K ⋅ − under any conditions

Monoprotic weak bases and basic salts

NH 3 , (CH 3 ) 3 N,

CH 3 COONa (CH 3 COO–)... any monoprotic base with a K b

[OH–] = K (^) b ⋅cweakbase cweak base^ >>>^ K b

[H+] = cstrong acid cstrong acid >> cweak acid

Strong and weak acid in the same solution [H ]

c [H ] [H ] cstrong acid a weakacid+

  • (^) = + K ⋅ − under any conditions

[OH–] = cstrong base cstrong base >> cweak base

Strong and weak base in the same solution [OH]

c [OH ] [OH ] cstrong base b weakbase −

− − (^) = + K ⋅ − under any conditions

Acidic buffers

CH 3 COOH +

CH 3 COONa together Basic buffers

NH 3 + NH 4 Cl together

[H+] = K a weak base

weakacid c

c ⋅ = K a weak base

weakacid n

n ⋅ ...

pH = p K a + log conjugateacid/weak acid

weakbase/conjugatebase c

c

General equations for pH calculations:

pH = –log[H+] pOH = –log[OH–] [H+] = 10–pH^ [OH–] = 10–pOH

[H+][OH–] = K W in any aqueous solution pH + pOH = p K W = –log K W

K a K b = K W for any conjugate acid-base pair p K a + p K b = p K W

Some other concepts:

The concept of degree of dissociation (α) is used when only a weak acid or base are present in the solution, no other chemicals affecting the pH.

Degree of dissociation = totalnumberofmoles

numberofmolesofthedissoc. form

Buffer capacity (unit: mol, mol/dm^3 , dm^3 or cm^3 ) is the amount of H+^ and OH–^ ions (i.e. the amount of strong acid and strong base) which should be added to 1 dm^3 of buffer solution to change its pH by 1 unit.

Calculation of buffer capacity for strong acid (nstrong acid):

[H+]buffer – 1 = K a weakbase strong acid

weakacid strongacid n n

n n −

Calculation of buffer capacity for strong base (nstrong base):

[H+]buffer + 1 = K a weakbase strong base

weakacid strongbase n n

n n