STATEMENT 1 : For the concentration cell `Zn(s)|Zn_(C_(2))^(+2)(aq)|Zn` for spontaneous cell reaction `C_(1)ltC_(2)` and
STATEMENT 2 For concentration cell `E_(cell)=(RT)/(nF)log_(e)(C_(2))/(C_(1))` for spontaneous rection `E_(cell)=+verarrc_(2)gtc_(1)`

Options

A. Statement 1 is ture , Statement 2 is true Statement 2 is correct explanation for Statement 1
B. Statement 1 is true Statement 2 is ture Statement 2 is NOT a correct explantion for Statement 1
C. Statement 1 is true statement 2 is false
D. Statement 1 is false Statement 2 is true

Answer

To solve the question, we need to analyze both statements regarding the concentration cell and determine their validity and relationship.

### Step 1: Analyze Statement 1
**Statement 1:** For the concentration cell `Zn(s)|Zn_(C_(2))^(+2)(aq)|Zn`, for a spontaneous cell reaction, `C_(1) < C_(2)`.

In a concentration cell, the electrode with the higher concentration of ions acts as the cathode, while the electrode with the lower concentration acts as the anode. For a spontaneous reaction to occur, the concentration at the anode (C1) must be less than the concentration at the cathode (C2). Therefore, this statement is **true**.

### Step 2: Analyze Statement 2
**Statement 2:** For the concentration cell, `E_(cell) = (RT)/(nF) log_e(C_(2)/C_(1))`. For spontaneous reaction, `E_(cell) = +ve` implies `C_(2) > C_(1)`.

The equation for the cell potential (E_cell) indicates that the potential will be positive when C2 (the concentration at the cathode) is greater than C1 (the concentration at the anode). This is necessary for the reaction to be spontaneous. Therefore, this statement is also **true**.

### Step 3: Determine the Relationship Between the Statements
Now we need to see if Statement 2 correctly explains Statement 1. Since both statements are true and Statement 2 provides the reasoning behind why C1 must be less than C2 for spontaneity (due to the condition that E_cell must be positive), we conclude that Statement 2 is indeed a correct explanation for Statement 1.

### Conclusion
Both statements are true, and Statement 2 correctly explains Statement 1. Therefore, the correct option is:
**Option 1: Both statements are true and Statement 2 is the correct explanation for Statement 1.**

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