<u>Answer:</u>
<u>For A:</u> The expression for
is given below.
<u>For B:</u> The value of
at 25°C is 0.0185512
<u>For C:</u> The value of
at 65°C is 0.2887886
<u>For D:</u> The reaction is endothermic in nature.
<u>Explanation:</u>
Equilibrium constant is defined as the ratio of concentration of products to the concentration of reactants each raised to the power their stoichiometric ratios. It is expressed as 
For the given chemical reaction:
![[Co(H_2O)_6]^{2+}(aq.)+4Cl^-(aq.)\rightleftharpoons [CoCl_4]^{2-}(aq.)+6H_2O(l)](https://tex.z-dn.net/?f=%5BCo%28H_2O%29_6%5D%5E%7B2%2B%7D%28aq.%29%2B4Cl%5E-%28aq.%29%5Crightleftharpoons%20%5BCoCl_4%5D%5E%7B2-%7D%28aq.%29%2B6H_2O%28l%29)
The expression of
for above equation without the concentration of liquid water is:
......(1)
The expression is written above.
We are given:
![[CoCl_4]^{2-}=0.0334612M](https://tex.z-dn.net/?f=%5BCoCl_4%5D%5E%7B2-%7D%3D0.0334612M)
![[Co(H_2O)_6]^{2+}=0.966539M](https://tex.z-dn.net/?f=%5BCo%28H_2O%29_6%5D%5E%7B2%2B%7D%3D0.966539M)
![[Cl^-]=1.86616M](https://tex.z-dn.net/?f=%5BCl%5E-%5D%3D1.86616M)
Putting values in equation 1, we get:

Hence, the value of
at 25°C is 0.0185512
We are given:
![[CoCl_4]^{2-}=0.234625M](https://tex.z-dn.net/?f=%5BCoCl_4%5D%5E%7B2-%7D%3D0.234625M)
![[Co(H_2O)_6]^{2+}=0.765375M](https://tex.z-dn.net/?f=%5BCo%28H_2O%29_6%5D%5E%7B2%2B%7D%3D0.765375M)
![[Cl^-]=1.06150M](https://tex.z-dn.net/?f=%5BCl%5E-%5D%3D1.06150M)
Putting values in equation 1, we get:

Hence, the value of
at 65°C is 0.2887886
For Endothermic reactions,
, which is positive
For Exothermic reactions,
, which is negative
To calculate
of the reaction, we use Van't Hoff's equation, which is:
![\ln(\frac{K_{65^oC}}{K_{25^oC}})=\frac{\Delta H}{R}[\frac{1}{T_1}-\frac{1}{T_2}]](https://tex.z-dn.net/?f=%5Cln%28%5Cfrac%7BK_%7B65%5EoC%7D%7D%7BK_%7B25%5EoC%7D%7D%29%3D%5Cfrac%7B%5CDelta%20H%7D%7BR%7D%5B%5Cfrac%7B1%7D%7BT_1%7D-%5Cfrac%7B1%7D%7BT_2%7D%5D)
where,
= equilibrium constant at 65°C = 0.2887886
= equilibrium constant at 25°C = 0.0185512
= Enthalpy change of the reaction = ?
R = Gas constant = 8.314 J/mol K
= initial temperature = ![25^oC=[25+2730]K=298K](https://tex.z-dn.net/?f=25%5EoC%3D%5B25%2B2730%5DK%3D298K)
= final temperature = ![65^oC=[65+2730]K=338K](https://tex.z-dn.net/?f=65%5EoC%3D%5B65%2B2730%5DK%3D338K)
Putting values in above equation, we get:
![\ln(\frac{0.2887886}{0.0185512})=\frac{\Delta H}{8.314J/mol.K}[\frac{1}{298}-\frac{1}{338}]\\\\\Delta H=57471.26J/mol](https://tex.z-dn.net/?f=%5Cln%28%5Cfrac%7B0.2887886%7D%7B0.0185512%7D%29%3D%5Cfrac%7B%5CDelta%20H%7D%7B8.314J%2Fmol.K%7D%5B%5Cfrac%7B1%7D%7B298%7D-%5Cfrac%7B1%7D%7B338%7D%5D%5C%5C%5C%5C%5CDelta%20H%3D57471.26J%2Fmol)
As, the calculated value of
. Thus, the reaction is endothermic in nature.