Homework: Calculate the value of pH of 25 gm, 300 ml NaOH solution.
Answers
Answer:
pH = 1.222
EXPLANATION:
Explanation:
As you know, sodium hydroxide and hydrochloric acid neutralize each other in a
1
:
1
mole ratio as described by the balanced chemical equation
NaOH
(
a
q
)
+
HCl
(
a
q
)
→
NaCl
(
a
q
)
+
H
2
O
(
l
)
This means that a complete neutralization, which would result in a neutral solution, i.e. a solution that has
pH
=
7
at room temperature, requires equal numbers of moles of sodium hydroxide and hydrochloric acid.
Notice that your two solutions have equal molarities, but that the volume of the hydrochloric acid solution is
100
.
mL
25.0
mL
=
4
times larger than the volume of the sodium hydroxide solution. This implies that the number of moles of hydrochloric acid is
4
times bigger than the number of moles of sodium hydroxide.
This means that after the reaction is complete, you will be left with excess hydrochloric acid
→
the
pH
of the resulting solution will be
<
7
.
Now, the number of moles of hydrochloric acid that will not take part in the reaction is given by
moles of HCl added
100
.
mL
⋅
0.100 moles HCl
10
3
mL
−
moles of NaOH added
25.0
mL
⋅
0.100 moles NaOH
10
3
mL
=
(
75
⋅
0.100
10
3
)
.
moles HCl
what is not consumed by the reaction
The total volume of the resulting solution will be
25.0 mL + 100. mL = 125 mL
As you know, the
pH
of the solution is given by
pH
=
−
log
(
[
H
3
O
+
]
)
Since hydrochloric acid is a strong acid that ionizes in a
1
:
1
mole ratio to produce hydronium cations, you can say that the concentration of hydronium cations in the resulting solution will be
[
H
3
O
+
]
=
(
75
⋅
0.100
10
3
)
.
moles H
3
O
+
125
⋅
10
3
.
L
=
(
75
⋅
0.100
125
)
mol L
−
1
This means that you have
pH
=
−
log
(
75
⋅
0.100
125
)
=
1.222
−−−−−
The answer is rounded to three decimal places, the number of sig figs you have for your values.
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