Solution, Solute and Solvent Problem 7
At 2 0 ∘ C , a 2 0 0 g saturated N a C l solution is heated until 4 0 g of water is evaporated. Then, the solution is cooled down back to 2 0 ∘ C . What is the mass of N a C l that is separated out from the solvent in grams ?
Details and Assumptions :
The solubility of N a C l at 2 0 ∘ C is 3 6 g / 1 0 0 g water
You may refer to Chemistry - Solution, Solute and Solvent Note .
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6 solutions
This is straight forwards. Better than my overall considerations. Just be careful with the equation for the term named solubility.
Let
x
=
the mass of water in the initial solution
Then, clearly,
2
0
0
−
x
=
the mass of
N
a
C
l
in the initial solution
Now,
Solubility of
N
a
C
l
in
1
0
0
g
of water
=
3
6
g
Solubility of
N
a
C
l
in
1
g
of water
=
0
.
3
6
g
Solubility of
N
a
C
l
in
x
g
of water
=
0
.
3
6
x
Therefore, for a saturated solution,
0
.
3
6
x
=
2
0
0
−
x
x
=
the mass of water initially
=
1
4
7
g
⇒
2
0
0
−
x
=
the mass of
N
a
C
l
in the initial solution
=
5
3
g
Now,
4
0
g
of water is lost.
⇒
The mass of water remaining
=
1
4
7
−
4
0
=
1
0
7
g
Therefore, Solubility in 1 0 7 g water = 0 . 3 6 × 1 0 7 = 3 8 . 5 2 g = Final Mass of N a C l in the solution
Finally
,
Mass of
N
a
C
l
separated out
=
the mass of
N
a
C
l
in the initial solution
−
Final Mass of
N
a
C
l
in the solution
⇒
Mass of
N
a
C
l
separated out
=
5
3
−
3
8
.
5
2
=
1
4
.
4
8
g
In the 3rd para,
there is a typo.
The corrected statement is
,
0
.
3
6
x
=
2
0
0
−
x
⇒
x
=
the mass of water initially
=
1
4
7
g
200g of saturated NaCL solution will contain ~53g of NaCl and ~147g of water. Out of 147g, 40g of water is evaporated. Water remained=107g. Now, if 100g of water contains 36g of Nacl, 107g of water will contain 38.52g of NaCl dissolved. Therefore NaCl precipitated out will be 53-38.52=14.48g
136 --> 36
1 --> 36/136
200 --> (36/136)*100=52.94 g
200 - 52.94 = 147.06 g solvent originally
147.06 - 40 = 107.06 g solvent (after evaporation)
100 g Water --> 36 g NaCl
107.06 g --> 38.54 g NaCl
52.94 - 38.54 = 14.4 g NaCl will precipitate
This is very close to what I did. I used fractions for better exactness.
The ratio of the solubility of N a C l is 3 6 : 1 0 0
So, we divide both sides by 2 . 5 so that ratio of the mass : water is x : 4 0
2 . 5 3 6 = 1 4 . 4
In a saturated solution, there are 36 grams of solute in 100 grams of solvent. In other words, 36 grams in 136 grams of solution. There is a 200 gram solution, so the amount of solute is 1 3 6 3 6 × 2 0 0 . After heating, the mass becomes 2 0 0 − 4 0 = 1 6 0 g . And so the amount of solute dissolved becomes 1 3 6 3 6 × 1 6 0 .
The amount of solute that does not get dissolved is the two amounts subtracted (think about it). Which is 1 3 6 3 6 × 4 0 ≈ 1 4 . 4 .
Nacl solubility = 36g/100g
40g of water evaporated means
36/100 =x/40
x=14.4