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Question: Using the Gibbs change, \[\Delta {G^o} = + 63.3kJ\] for the following reaction, the \[Ksp\] of \[Ag_...

Using the Gibbs change, ΔGo=+63.3kJ\Delta {G^o} = + 63.3kJ for the following reaction, the KspKsp of Ag2CO3Ag_2CO_3 (s) in water at 25oC{25^o}C is :
A. 3.2×10−263.2 \times {10^{ - 26}}
B. 8.0×10−128.0 \times {10^{ - 12}}
C. 2.9×10−32.9 \times {10^{ - 3}}
D. 7.9×10−27.9 \times {10^{ - 2}}

Explanation

Solution

Initially you must be aware of the term KspKsp and gibbs free energy. Then putting the values in the relation of gibbs free energy and Ksp you can easily find the Value if KspKsp.

Complete step by step answer:
Given:
R=8.31  JK−1mol−1R = 8.31\;{\text{J}}{{\text{K}}^{ - 1}}mo{l^{ - 1}}
ΔGo=+63.3kJ\Delta {G^o} = + 63.3kJ
Temp=25oC
Formula used:
ΔGo=−2.303RT  log Ksp\Delta {G^o} = - 2.303RT\;log{\text{ }}Ksp
Calculation:
The relationship between the Gibbs free energy and the solubility product is
​ΔGo=−2.303RT  log Ksp\Delta {G^o} = - 2.303RT\;log{\text{ }}Ksp
Substitute values in the above expression.
63.3×103=−2.303×8.31×298  logKsp63.3 \times {10^3} = - 2.303 \times 8.31 \times 298\;logKsp
−11.09=log⁡Ksp- 11.09 = \log Ksp​
8×10−12=Ksp8×10−12=KspV8 \times {10^{ - 12}} = Ksp8 \times {10^{ - 12}} = KspV
Hence, the Ksp​ of Ag2CO3Ag_2CO_3(s) in water at  25oC  is  8.0×10−12.at\;{25^o}C\;is\;8.0 \times {10^{ - 12}}.

So, the correct answer is Option B.

Note: Gibbs free energy, also known as the Gibbs function, Gibbs energy, or free enthalpy, is a quantity that is used to measure the maximum amount of work done in a thermodynamic system when the temperature and pressure are kept constant. Gibbs free energy is denoted by the symbol ‘G’. Its value is usually expressed in Joules or Kilojoules. Gibbs free energy can be defined as the maximum amount of work that can be extracted from a closed system.
This property was determined by American scientist Josiah Willard Gibbs in the year 1876 when he was conducting experiments to predict the behaviour of systems when combined together or whether a process could occur simultaneously and spontaneously. Gibbs free energy was also previously known as “available energy.” It can be visualized as the amount of useful energy present in a thermodynamic system that can be utilized to perform some work.
Gibbs free energy can be calculated by:
ΔG = ΔH − T × ΔS\Delta G{\text{ }} = {\text{ }}\Delta H{\text{ }} - {\text{ }}T{\text{ }} \times {\text{ }}\Delta S