Thermodynamics of KNO Solubility

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27 Οκτ 2013 (πριν από 3 χρόνια και 9 μήνες)

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Thermodynamics of KNO
3

Solubility



Theory:

Potassium nitrate, KNO
3
, dissolves in water as described by the equation below:






KNO
3(s)


K
+
(aq)

+ NO
3
-
(aq)


This process may be considered to be at equilibrium when the solid

is in contact with a saturated
solution, the conditions that exist when crystallization begins. The solubility, s, of KNO
3

(in
moles per liter) at a given temperature can be calculated from the mass of KNO
3

and the volume
of H
2
O needed to dissolve it at
that temperature. The equilibrium constant, K
sp

for the reaction is






K
sp

= [K
+
][NO
3
-
] = (s)(s) = s
2


The equilibrium constant, K
(sp)
, can be used to calculate
G for the reaction at each temperature
using the relationship
:





G =
-
RTlnK
sp


where T is the Kelvin temperature and R is the gas law constant (8.31 joules/mol
-
deg.). Because






G =
H
-

T
S






-
RTlnK
sp

=
H
-

T
S








and






lnK
sp

=
-
H/R (1/T) +
S/R


A graph of lnK
sp

vs. 1/T should give a straight line with a slope of
-
H/R and an interc
ept
equal to
S.


Experiment:

Weigh about 7.5 grams of KNO
3

accurately and transfer it to a 25 mL
graduated cylinder. Add 6 mL of water and heat the cylinder in a boiling water bath, with
stirring, until all the KNO
3

dissolved. Re
move the cylinder from the water bath and record the
volume using the graduated scale on the side of the cylinder. Allow the cylinder to cool slowly
while stirring gently. Record the temperature when crystals first appear in the solution.


Add 3 mL of wa
ter to the cylinder and warm the mixture in a boiling water bath until the solid
has all dissolved. Record the new volume of the solution and allow it to cool to determine the
temperature at which crystals first appear. Repeat this cycle of adding water
and measuring the
volume and temperature of crystallization until a crystallization temperature near 0
o

C is reached.

(This should require about six determinations. Temperatures below room temperature can be
achieved using an ice
-
water bath.)


Calculation
s:

Calculate the solubility of KNO
3

(in grams per L of solution) at each
crystallization temperature and plot a graph of solubility vs. temperature. Use this graph to
predict:


a.

the percentage of KNO
3

that could be recovered (i.e. would crystallize) whe
n a saturated
solution of KNO
3

at 60
o
C is cooled to 0
o
C.

b.

the minimum volume of water needed to dissolve 101 grams (1 mole) of KNO
3

at 50
o
C.


For each temperature, calculate:


c.

the solubility, s, of KNO
3

in moles per liter.

d.

the equilibrium constant, K
sp

e.

the
value of
G



Prepare a graph of lnK
sp

vs. 1/T and use the slope to calculate a value of
H over the
temperature range studied. Calculate a value of
S at each temperature from
G at each
temperature and the value of
H found from the graph. Compare these
S values with that
obtained by extrapolating the graph. Offer an explanation for the variation of the
S values
with temperature.