Question

Using the Gibbs change, \[\Delta {G^o} = + 63.3kJ\] for the following reaction, the \[Ksp\] of \[Ag_2CO_3\] (s) in water at \[{25^o}C\] is :
A. \[3.2 \times {10^{ - 26}}\]
B. \[8.0 \times {10^{ - 12}}\]
C. \[2.9 \times {10^{ - 3}}\]
D. \[7.9 \times {10^{ - 2}}\]

Answer 1

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

Complete step by step answer:
Given:
\[R = 8.31\;{\text{J}}{{\text{K}}^{ - 1}}mo{l^{ - 1}}\]
\[\Delta {G^o} = + 63.3kJ\]
Temp=25oC
Formula used:
\[\Delta {G^o} = - 2.303RT\;log{\text{ }}Ksp\]
Calculation:
The relationship between the Gibbs free energy and the solubility product is
​\[\Delta {G^o} = - 2.303RT\;log{\text{ }}Ksp\]
Substitute values in the above expression.
\[63.3 \times {10^3} = - 2.303 \times 8.31 \times 298\;logKsp\]
\[ - 11.09 = \log Ksp\]​
\[8 \times {10^{ - 12}} = Ksp8 \times {10^{ - 12}} = KspV\]
Hence, the Ksp​ of \[Ag_2CO_3\](s) in water \[at\;{25^o}C\;is\;8.0 \times {10^{ - 12}}.\]

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:
\[\Delta G{\text{ }} = {\text{ }}\Delta H{\text{ }} - {\text{ }}T{\text{ }} \times {\text{ }}\Delta S\]