Time required for complete decomposition of 4 mol of water using a current of 4 ampere is `yxx10^(5)` seconds. Value of y is ? (Use `F=96500"C mol"^(-1)`)

Explanation

To find the time required for the complete decomposition of 4 moles of water using a current of 4 amperes, we can follow these steps:

### Step 1: Understand the decomposition of water
The decomposition of water (H₂O) can be represented by the following reaction:
\[ 2H_2O \rightarrow 2H_2 + O_2 \]
From this reaction, we can see that for every 2 moles of water decomposed, 4 moles of electrons are required.

### Step 2: Calculate the number of moles of electrons needed
Since 2 moles of water require 4 moles of electrons, 4 moles of water will require:
\[ 4 \text{ moles of water} \rightarrow 8 \text{ moles of electrons} \]

### Step 3: Convert moles of electrons to charge
Using Faraday's constant (\( F = 96500 \, C \, mol^{-1} \)), we can calculate the total charge (\( Q \)) required for 8 moles of electrons:
\[ Q = \text{moles of electrons} \times F \]
\[ Q = 8 \, mol \times 96500 \, C/mol = 772000 \, C \]

### Step 4: Use the formula to find time
We know that the relationship between charge (\( Q \)), current (\( I \)), and time (\( T \)) is given by:
\[ Q = I \times T \]
Rearranging this formula to find time gives us:
\[ T = \frac{Q}{I} \]
Substituting the values we have:
\[ T = \frac{772000 \, C}{4 \, A} \]
\[ T = 193000 \, seconds \]

### Step 5: Express time in scientific notation
To express \( 193000 \) seconds in scientific notation:
\[ 193000 = 1.93 \times 10^5 \, seconds \]

### Step 6: Identify the value of \( y \)
From the expression \( 1.93 \times 10^5 \), we can see that \( y = 1.93 \).

### Final Answer
Thus, the value of \( y \) is:
\[ y = 1.93 \]

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