In an-aqueous solution of volume 500 ml , when the reaction of `2Ag^(+)+Cu hArr Cu^(2+)+2Ag` reached equilibrium , the `[Cu^(2+)]` was x M. when 500 ml of water if further a added at the equilibrium `[Cu^(2+)]` will be

Options

A. `2 xx M`
B. `x M `
C. between x M and x/2 M
D. less than x/2 M

Answer

To solve the problem step by step, we need to analyze the chemical equilibrium and the effect of dilution on the concentration of the products.

### Step 1: Write the balanced chemical equation.
The reaction given is:
\[ 2 \text{Ag}^+ + \text{Cu} \rightleftharpoons \text{Cu}^{2+} + 2 \text{Ag} \]

### Step 2: Understand the initial conditions.
We are given that at equilibrium, the concentration of \(\text{Cu}^{2+}\) is \(x\) M in a 500 ml solution.

### Step 3: Calculate the initial moles of \(\text{Cu}^{2+}\).
To find the number of moles of \(\text{Cu}^{2+}\) at equilibrium:
\[ \text{Moles of } \text{Cu}^{2+} = \text{Concentration} \times \text{Volume} = x \, \text{M} \times 0.5 \, \text{L} = 0.5x \, \text{moles} \]

### Step 4: Determine the new volume after adding water.
When we add 500 ml of water to the solution, the total volume becomes:
\[ \text{Total Volume} = 500 \, \text{ml} + 500 \, \text{ml} = 1000 \, \text{ml} = 1 \, \text{L} \]

### Step 5: Calculate the new concentration of \(\text{Cu}^{2+}\).
The concentration of \(\text{Cu}^{2+}\) after dilution can be calculated using the formula:
\[ \text{New Concentration} = \frac{\text{Moles of } \text{Cu}^{2+}}{\text{Total Volume}} = \frac{0.5x}{1 \, \text{L}} = 0.5x \, \text{M} \]

### Step 6: Conclusion.
Thus, the new concentration of \(\text{Cu}^{2+}\) after adding 500 ml of water will be:
\[ \text{New } [\text{Cu}^{2+}] = 0.5x \, \text{M} \]

### Final Answer:
The concentration of \(\text{Cu}^{2+}\) after adding 500 ml of water will be \(0.5x\) M.

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