Organic Chemistry Problem Set 4: Aqueous Solubility Solutions

This document provides detailed solutions to an organic chemistry problem set focused on aqueous solubility. The solutions cover the calculation of solubility coefficients for various compounds, including propane, ethylbenzene, and phenanthrene. It also explores the effect of temperature on the solubility and activity coefficient of Freon 12 (dichlorodifluoromethane) in freshwater and seawater, including calculations for different temperatures and the use of the Setchenow approach. Furthermore, the document includes solutions for estimating the solubility and activity coefficient of a solid compound (1,2,3,7 tetrachlorodibenzo-p-dioxin), along with enthalpy calculations and considerations for the assumptions made. The solutions presented are designed to help students understand and solve complex chemistry problems related to solubility and thermodynamics.

Organic Chemistry
Problem set 4: Aqueous Solubility
1. Calculate the aqueous solubility coefficients γw
sat of the three following compounds at
25 ° C;
a) Propane
For organic solutes that are liquids at25 °C;
Cw
sat ( L )= 1
γ w
sat V w
Therefore
γw
sat = 1
Cw
sat ( L ) V w
= 1
(3−6.57 mol/ L)(0.331l/mol) =4120
b) Ethylbenzene
For organic solutes that are liquids at25 °C;
Cw
sat ( L )= 1
γ w
sat V w
Therefore
γw
sat = 1
Cw
sat ( L ) V w
= 1
( 8−6.57 mol /L)(24.43 l/mol)=35100
c) Phenanthrene
For organic solutes that are liquids at25 °C;
Cw
sat ( L )= 1
γ w
sat V w
Therefore
γw
sat = 1
Cw
sat ( L ) V w
= 1
(14−6.57 mol /L)(18.32l /mol )=1 850 000
2. Evaluating the effect of temperature on the solubility and the activity coefficient of a
gaseous compound (Freon 12; dichlorodifluoromethane) in freshwater and seawater.
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a) Estimate the solubilities (M) of Freon 12 in freshwater and seawater at 1 bar
pressure at 5 and 25o C
The aqueous mole fraction solubility of an organic liquid is simply given by the inverse
aqueous activity coefficient:
Cw
sat ( L )= 1
γ w
sat V w
For liquids
Cw
sat ( L )= 1
γ w
sat V w
. e−∆fus Gi IRT
For solids
For freshwater at 5oC
Cw
sat ( L ) = 1
γ w
sat V w
=0.0071 M
For freshwater at 25oC
Cw
sat ( L )= 1
γ w
sat V w
=0. 003 1 M
For seawater at 5oC
Cw
sat ( L ) = 1
γ w
sat V w
=0.00 47 M
For seawater at 25oC
Cw
sat ( L ) = 1
γ w
sat V w
=0.00 21 M
Answers; Freshwater for 5 and 25oC s 0.0071M and 0.0031M, Seawater for 5 and 25oC
is 0.0047 and 0.0021M
b) Calculate the activity coefficient of Freon 12 in freshwater and seawater at these
temperatures using vapor pressure temperature data given in problem P 8.3.
For freshwater for 5oC
γw
sat = 1
Cw
sat ( L ) V w
= 1
0.0071 ×0.0649 =21 70
2

For freshwater for 25oC
γw
sat = 1
Cw
sat ( L ) V w
= 1
0.003 1× 0.1156 =279 0
For seawater for 5oC
γw
sat = 1
Cw
sat ( L ) V w
= 1
0.0047 ×0. 06486 =3280
For seawater for 25oC
γw
sat = 1
Cw
sat ( L ) V w
= 1
0.002 1× 0.1155 =4120
Answers; Freshwater for 5 and 25oC is 2170 and 2790 and Seawater for 5 and 25oC is
3280 and 4120
c) Determine the average excess enthalpy ( ∆w H E kJ mol−1) of Freon 12 in fresh and
seawater for the ambient temperature range (0-40o). Use p-T data from problem P
8.3 to get the enthalpy vapor of Freon 12.
For freshwater
H I
E=−R T 2 ∂∈γ i
∂T =−R× 3132 ∂∈×0.0018
∂ 313 =−8.5 kJ mol−1
For Seawater
H I
E=−R T 2 ∂∈γ i
∂T =−R× 3132 ∂∈×0. 0013
∂ 313 =−8.5 kJ mol−1
Answers; freshwater is−8.5 kJ mol−1, seawater is −7.6 kJ mol−1
d) Use the setchenow’s approach to estimate the solubility (M) of Freon 12 in seawater
at 25oC as best as possible using the data from tables 9.5 and 9.6. How does your
estimate compare with the solubility interpolated using the measured solubilities in
part (a).
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lg γi =−A z1
2
( √ I
1+ B ai √ 1 ) =¿
3. Problem P 9.4: Evaluating the effect of temperature on aqueous solubility and on the
aqueous activity coefficient of a solid compound
T (oC) 7.0 11.5 17.0 21.0 26.0
Ciw
sat × 1010 7.56 8.12 12.5 14.9 22.6
Solution
a) Estimate Cw
sat and γw
sat of 1,2,3,7 tetrachlorodibenzo-p-dioxin.
For organic solutes such as 1,2,3,7 tetrachlorodibenzo-p-dioxin the reference state is
assumed to be that of a pure liquid state and its activity coefficient in water is taken as a
measure of its activity in water in relation to its activity in pure liquid.
For organic solutes the formula is;
γw
sat = 1
Cw
sat ( L ) V w
Therefore for n-decane, the activity coefficient is;
γw
sat = 1
Cw
sat ( L ) V w
= 1
(10 ¿¿−6.57 mol /L)(0.018 L/mol)=2.06 ×108 ¿
For 1,2,3,7 tetrachlorodibenzo-p-dioxin, it solidifies at 25oC, therefore;
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Cw
sat ( s )=Cw
sat ( L ) P ° (s)
P ° (L) =Cw
sat ( L ) 1 atm
100.26 atm
But; Cw
sat ( s )=10−10.3M, P ° ( s ) =10−11.6 atm and P °(s)
P °(L) =e−6.8(T m
T −1)
P ° (s)
P °(L)=e−6.8 (T m
T −1)
=2.71828¿ ¿
Therefore;
Cw
sat ( L )=10−10.3 ×4.8 × 102 0 .3=4.8× 1010 M
γw
sat = 1
Cw
sat ( L ) V w
= 1
4.8 ×1010 ×5.4 × 10−20 =3.8 ×108
b) Estimate the average excess enthalpy of the compound in water for the temperature
range considered. Comment on assumption made.
The enthalpy of mixing (or heat of mixing or excess enthalpy) is the enthalpy liberated or
absorbed from a substance upon mixing
H I
E=−R T 2 ∂∈γ i
∂T =−R× 2922 ∂∈×3.8 ×108
∂ 292 7.4 kJ mol−1Answers: a) Cw
sat=4.8× 1010 M
and γw
sat =3.8× 108
, b) 7.4 kJ mol−1
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