In: Chemistry
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Q. Solubility equilibria
In the table below, Ksp is the equilibrium constant for dissolving a salt in water and ΔsolH° the corresponding enthalpy change under standard conditions. Taking the last digit of your student ID number as the key, select the corresponding salt from the table, and answer the following questions for that salt only. answer Ca(OH)2 just
ID Key | Salt |
Solubility at 25°C g /100 mL |
Ksp | ΔsolH° mL kJ mol-1 |
0,4,8 | Ca(OH)2 | 0.168 | 5.02×10-6 | -218.64 |
1,5,9 | Ba(NO3)2 | 10.5 | 0.00464 | 40.36 |
2,6 | CdF2 | 4.35 | 0.00644 | -40.76 |
3,7 | Li2CO3 | 1.29 | 0.000815 | -18.22 |
(a) Calculate the corresponding values of ΔsolG° and ΔsolS° for the dissolution reaction.
(b) From the cited solubility (g/100 mL), calculate the maximum molar concentration of the aqueous salt and hence the mean activity coefficient, γ±. Comment briefly on the γ± value you obtain.
(c) Do you expect the salt to be more or less soluble at higher temperature? Why?
(a) ΔsolG° = -RTln(Ksp); where R = 8.314*10-3 KJ mol-1 K-1 and T = 25 oC, i.e. 298 K
= -8.314*10-3 * 298 * ln(5.02×10-6)
= -8.314*10-3 * 298 * (-12.2)
= 30.23 KJ mol-1
Given that ΔsolH° = -218.64 mL KJ mol-1
Since te solubility is per 100 mL, ΔsolH° = -218.64/100, i.e. -2.1864 KJ mol-1
Therefore, ΔsolG° = ΔsolH° - TΔsolS°
30.23 = -2.19 - 298ΔsolS°
i.e. ΔsolS° = -0.1088 KJ mol-1 K-1, i.e. -108.8 J mol-1 K-1
(b) The maximum molar concentration of the aqueous salt = (mass/molecular mass) * 1000/volume (mL)
= (0.168/74.092) * 1000/100, i.e. 0.023 mol/L (= c, let's say)
And Logγ± = -0.509(I)1/2
Where, I = (n+Z+2 + n-Z-2)*c/2, n+ andn- are the no. of cations and anions, respectively; Z+ and Z- are the charge on the cation and anion, respectively. For Ca(OH)2, i.e. n+ = 1,n- = 2; Z+ = 2, Z- = -1
Therefore, = 2 and I = (1*22 + 2*12)*0.023/2, i.e. 0.069
i.e. Logγ± = -2 * 0.509 * (0.069)1/2
Therefore, γ± = 0.54
In general, the Debye-Huckel theory of activity coefficients of electrolyte solutions is based on the assumption that Coulombic interactions between ions are dominant, a key idea of the theory is that of an ionic atmosphere.
(c) The salt is expected to be more soluble at a higher temperature.
Reason: At high temperatures, the degree of ionization of salt increases and hence, as a result, its solubility increases.