The analysis depends on the particular indicator used. If we use methyl orange, then we know that it can detect completion of reaction of HCl with either of two basic compounds. Hence,

volume of HCl used
=
volume acid required for neutralization of NaOH and
N
a
2
C
O
3
volume of HCl used
=
volume acid required for neutralization of NaOH and
N
a
2
C
O
3

This means that :

geq of HCl
=
geq of NaOH
+
geq of
N
a
2
C
O
3
(indicator : methyl orange)
geq of HCl
=
geq of NaOH
+
geq of
N
a
2
C
O
3
(indicator : methyl orange)

If we use phenolphthalein, then we know that it can detect completion of reaction of HCl with NaOH. However, it can detect only half of the completion of reaction of HCl with sodium carbonate.

volume of HCl used
=
volume acid required for neutralization of NaOH
+
1
2
volume acid required for neutralization of
N
a
2
C
O
3
volume of HCl used
=
volume acid required for neutralization of NaOH
+
1
2
volume acid required for neutralization of
N
a
2
C
O
3

This means that :

geq of HCl
=
geq of NaOH
+
1
2
X
geq of
N
a
2
C
O
3
(indicator : phenolphthalein)
geq of HCl
=
geq of NaOH
+
1
2
X
geq of
N
a
2
C
O
3
(indicator : phenolphthalein)

Q. A volume of 25 ml of 0.2 N HCl is titrated to completely neutralize 25 ml mixture of NaOH and
N
a
2
C
O
3
N
a
2
C
O
3
, using phenolphthalein as indicator. On the other hand, 60 ml of 0.1 N HCl is required to neutralize the equal volume of mixture, using methyl orange as indicator. Find the strengths of NaOH and
N
a
2
C
O
3
N
a
2
C
O
3
in the mixture.

Answer : Strength is expressed in terms of gm/litre. Thus, we need to know the mass of each component in the mixture. First titration uses phenolphthalein, which detects completion of reaction with NaOH and half of reaction with
N
a
2
C
O
3
N
a
2
C
O
3
. Hence,

meq of acid
=
meq of NaOH
+
1
2
X
meq of
N
a
2
C
O
3
meq of acid
=
meq of NaOH
+
1
2
X
meq of
N
a
2
C
O
3

Clearly, it is helpful to assume unknowns in terms of milli-equivalents (meq) instead of mass. Once, meq are calculated, we convert the same finally in mass terms and strength of solution as required. Let x and y be the meq of NaOH and
N
a
2
C
O
3
N
a
2
C
O
3
in the mixture.

Putting values in the equation, we have :

⇒
N
a
V
a
=
x
+
0.5
y
⇒
N
a
V
a
=
x
+
0.5
y

⇒
x
+
0.5
y
=
0.2
X
25
=
5
⇒
x
+
0.5
y
=
0.2
X
25
=
5

Second titration uses methyl orange, which detects completion of reaction with both NaOH and
N
a
2
C
O
3
N
a
2
C
O
3
. Hence,

meq of acid
=
meq of NaOH
+
meq of
N
a
2
C
O
3
meq of acid
=
meq of NaOH
+
meq of
N
a
2
C
O
3

⇒
N
a
V
a
=
x
+
y
⇒
N
a
V
a
=
x
+
y

⇒
x
+
y
=
0.1
X
60
=
6
⇒
x
+
y
=
0.1
X
60
=
6

Solving two equations (subtracting first from second equation), we have

⇒
0.5
y
=
1
⇒
0.5
y
=
1

⇒
y
=
2
⇒
y
=
2

and

⇒
x
=
6
−
2
=
4
⇒
x
=
6
−
2
=
4

Now, we need to convert meq into strength of solution. For that, we first convert meq to mass of solute (B) in gram.

meq
=
valence factor
X
milli-moles
meq
=
valence factor
X
milli-moles

⇒
meq
=
valence factor
X
g
B
X
1000
M
B
⇒
meq
=
valence factor
X
g
B
X
1000
M
B

⇒
g
B
=
M
B
X
meq
valence factor
X
1000
⇒
g
B
=
M
B
X
meq
valence factor
X
1000

Thus, strength of component in 25 ml solution is :

⇒
S
=
g
B
X
1000
25
=
M
B
X
meq
X
1000
25
X
valence factor
X
1000
=
M
B
X
meq
25
X
valence factor
⇒
S
=
g
B
X
1000
25
=
M
B
X
meq
X
1000
25
X
valence factor
X
1000
=
M
B
X
meq
25
X
valence factor

Putting values, strength of NaOH is :

⇒
S
=
M
B
X
meq
25
X
valence factor
=
40
X
4
25
X
1
=
6.4
g
m
/
l
⇒
S
=
M
B
X
meq
25
X
valence factor
=
40
X
4
25
X
1
=
6.4
g
m
/
l

Similarly, strength of
N
a
2
C
O
3
N
a
2
C
O
3
is :

⇒
S
=
M
B
X
meq
25
X
valence factor
=
106
X
4
25
X
2
=
4.24
g
m
/
l
⇒
S
=
M
B
X
meq
25
X
valence factor
=
106
X
4
25
X
2
=
4.24
g
m
/
l