Assertion : If `beta_(4)" for "[Cu(NH_3)_(4)]^(2+)" is "2.1 xx 10^(13)` its instability constant is `4.76 xx 10^(-14).`
Reason :Overall dissociation equilibrium constant varies inversely with formation constant.

Options

A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
C. Assertion is true but Reason is false
D. Both Assertion and Reason are false

Explanation

To solve the question regarding the assertion and reason provided, we will follow these steps:

### Step 1: Understand the Assertion
The assertion states that for the complex ion \([Cu(NH_3)_4]^{2+}\), the overall formation constant (\(\beta_4\)) is given as \(2.1 \times 10^{13}\). It also claims that the instability constant is \(4.76 \times 10^{-14}\).

### Step 2: Define the Formation Constant and Instability Constant
The formation constant (\(\beta\)) is a measure of the stability of a complex ion in solution. The instability constant (\(K_{instability}\)) is the reciprocal of the formation constant:
\[ K_{instability} = \frac{1}{\beta} \]

### Step 3: Calculate the Instability Constant
Using the value of \(\beta_4\):
\[ K_{instability} = \frac{1}{\beta_4} = \frac{1}{2.1 \times 10^{13}} \]
Calculating this gives:
\[ K_{instability} \approx 4.76 \times 10^{-14} \]
This confirms the assertion.

### Step 4: Understand the Reason
The reason states that the overall dissociation equilibrium constant varies inversely with the formation constant. This means:
\[ K_{dissociation} \propto \frac{1}{\beta} \]
This is indeed true, as the dissociation constant is the inverse of the formation constant.

### Step 5: Conclusion
Both the assertion and the reason are correct. The reason provided correctly explains the assertion regarding the relationship between the formation constant and the instability constant.

### Final Answer
Both the assertion and reason are true, and the reason is the correct explanation of the assertion.

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