Given exothermic reaction
`CoCl_4^(2-)(aq)+6H_2O(l) hArr [Co(H_2O)_6]^(2+) +4Cl^-`
Which one of the following will decrease the equilibrium concentration of `CoCl_4^(2-)` ?

Options

A. Addition of HCI
B. Addition of `Co(NO_3)_2`
C. The solution is diluted with water
D. The temperature is increased

Answer

To solve the problem, we need to analyze the given exothermic reaction and determine which condition will decrease the equilibrium concentration of `CoCl_4^(2-)`.

### Step-by-Step Solution:

1. **Identify the Reaction**:
The given reaction is:
\[ CoCl_4^{2-}(aq) + 6H_2O(l) \rightleftharpoons [Co(H_2O)_6]^{2+} + 4Cl^{-} \]
This reaction is exothermic, meaning it releases heat.

2. **Understand Le Chatelier's Principle**:
According to Le Chatelier's Principle, if a system at equilibrium is subjected to a change in concentration, temperature, or pressure, the system will adjust to counteract that change and restore a new equilibrium.

3. **Analyze the Options**:
We need to consider how different changes will affect the concentration of `CoCl_4^{2-}`. The options provided (not listed in the question) would typically include:
- Adding `Cl^-`
- Diluting the solution
- Increasing temperature
- Adding `Co(NO3)2`

4. **Effect of Adding `Cl^-`**:
Adding `Cl^-` ions will shift the equilibrium to the left (backward direction) to reduce the concentration of `Cl^-`, thus increasing the concentration of `CoCl_4^{2-}`.

5. **Effect of Dilution**:
Diluting the solution with water increases the volume, which decreases the concentration of all species in the solution, including `CoCl_4^{2-}`. This will shift the equilibrium to the right (forward direction) to produce more `Co(H2O)6^{2+}` and `Cl^-`, but since the concentration of `CoCl_4^{2-}` decreases, this is a valid option.

6. **Effect of Increasing Temperature**:
Since the reaction is exothermic, increasing the temperature will shift the equilibrium to the left (backward direction), increasing the concentration of `CoCl_4^{2-}`.

7. **Effect of Adding `Co(NO3)2`**:
Adding `Co(NO3)2` introduces more cobalt ions into the solution, which will also shift the equilibrium to the left (backward direction), increasing the concentration of `CoCl_4^{2-}`.

8. **Conclusion**:
The only condition that will decrease the equilibrium concentration of `CoCl_4^{2-}` is dilution of the solution with water. Therefore, the correct answer is the option that corresponds to dilution.

### Final Answer:
The condition that will decrease the equilibrium concentration of `CoCl_4^{2-}` is **dilution of the solution with water**.