if 500 ml of 0.2 mole HCL is mixed with 500 ml of 0.4 mole NaOH. find the amount of heat liberated
Answers
Answer:
Notice that the solution goes from being acidic at
pH
=
3
to being basic at
pH
=
10
, so the first thing that comes to mind here is that you need to add more sodium hydroxide than the number of moles of hydrochloric acid present in the initial solution.
As you know, the concentration of hydronium cations is equal to
[
H
3
O
+
]
=
10
−
pH
−−−−−−−−−−−−−−−
This means that the initial solution contains
[
H
3
O
+
]
=
10
−
3
M
Now, use the volume of the solution to calculate the number of moles of hydronium cations it contains.
500
mL solution
⋅
10
−
3
moles H
3
O
+
10
3
mL solution
=
0.00050 moles H
3
O
+
Sodium hydroxide and hydrochloric acid react in a
1
:
1
mole ratio to produce aqueous sodium chloride and water
HCl
(
a
q
)
+
NaOH
(
a
q
)
→
NaCl
(
a
q
)
+
H
2
O
(
l
)
so you know that in order to completely neutralize the acid and make the solution neutral, you need to add
0.0005
moles of sodium hydroxide.
So you can say that at
25
∘
C
, you will have
0.0005 moles NaOH added
→
pH
=
7
Now, you want the target solution to have
pH
=
10
which implies that it must have
pOH
=
14
−
10
=
4
This means that the concentration of hydroxide anions in the final solution must be equal to
[
OH
−
]
=
10
−
4
M
Since you are told to assume that the volume of the solution does not change upon the addition of the salt, you can use it to find the number of moles of hydroxide anions present in the final solution.
500
mL solution
⋅
10
−
4
moles OH
−
10
3
mL solution
=
0.000050 moles OH
−
Therefore, you can say that if you add
0.00050
moles of sodium hydroxide to the initial solution, you will completely neutralize the acid and get the
pH
to
7
.
At that point, adding an additional
0.000050
moles of sodium hydroxide will increase the
pH
of the solution from
7
to
10
.
The total number of moles of sodium hydroxide that you must add--remember that sodium hydroxide delivers hydroxide anions to the solution in a
1
:
1
mole ratio--will thus be equal to
0.00050 moles + 0.000050 moles = 0.00055 moles NaOH
Finally, to convert the number of moles to grams, use the molar mass of the salt.
0.00055
moles NaOH
⋅
40 g
1
mole NaOH
=
0.02 g
−−−−−
The answer is rounded to one significant figure.