Question

Which of the following carbonate salt is soluble due to high entropy change?
A. ${{K}_{2}}C{{O}_{3}}$
B. $L{{i}_{2}}C{{O}_{3}}$
C. ${{(N{{H}_{4}})}_{2}}C{{O}_{3}}$
D. $N{{a}_{2}}C{{O}_{3}}$

Answer 1

Generally entropy is defined as a measurement of randomness or disorder of a system. Entropy can also describe the behavior of a system in terms of thermodynamic properties like temperature, pressure and heat capacity.

Complete step by step solution:
Entropy change is a process which is defined as the amount of heat emitted or absorbed isothermally and reversibly divided by the absolute temperature. Entropy formula is shown as:
$\Delta S=\dfrac{{{q}_{rev}}}{T}$
If at higher temperature and lower temperature we add the same quantity of heat then randomness will be maximum at a lower temperature. Hence we can easily say that temperature is inversely proportional to the entropy.
Total entropy change is given by:
$\Delta {{S}_{total}}=\Delta {{S}_{surroundings}}+\Delta {{S}_{solvent}}$
Total entropy change is equal to the sum of entropy change of system and surroundings.
If $\Delta {{S}_{total}}$is positive then the process is spontaneous, If it is negative then the process is nonspontaneous and If it is zero then the process is at equilibrium.
Out of all the above cases the$\Delta H$ is very large in case of ${{(N{{H}_{4}})}_{2}}C{{O}_{3}}$ due to it $\Delta G$ becomes negative and it is highly soluble in nature while all other carbonates solubility depend on lattice energy and hydration energy.

Thus we can say that option C is the right answer.

Note: In thermodynamics the Gibbs free energy is a thermodynamic potential which is used to calculate the maximum of reversible work that is performed by a thermodynamic system at a constant temperature and pressure.