To determine 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: Write the balanced equation for the decomposition of water
The balanced chemical equation for the electrolysis of water is:
\[ 2H_2O \rightarrow 2H_2 + O_2 \]
From this equation, we can see that 2 moles of water produce 2 moles of hydrogen gas and 1 mole of oxygen gas.
### Step 2: Determine the number of moles of electrons required
From the balanced equation, for every 2 moles of water decomposed, 4 moles of electrons are needed (since 2 moles of water produce 2 moles of hydrogen ions, which each require 1 electron). Therefore, for 4 moles of water:
- Moles of electrons required = \( 4 \text{ moles of water} \times \frac{4 \text{ moles of electrons}}{2 \text{ moles of water}} = 8 \text{ moles of electrons} \)
### Step 3: Convert moles of electrons to coulombs
Using Faraday's constant, which is approximately \( 96485 \, C/mol \), we can calculate the total charge (Q) required:
\[ Q = \text{moles of electrons} \times \text{Faraday's constant} \]
\[ Q = 8 \, \text{moles} \times 96485 \, C/mol = 773,880 \, C \]
### Step 4: Use the formula to calculate time
The relationship between charge (Q), current (I), and time (t) is given by:
\[ Q = I \times t \]
Rearranging this gives:
\[ t = \frac{Q}{I} \]
Substituting the values we have:
\[ t = \frac{773,880 \, C}{4 \, A} = 193,470 \, seconds \]
### Step 5: Convert time into hours
To convert seconds into hours:
\[ t = \frac{193,470 \, seconds}{3600 \, seconds/hour} \approx 53.7 \, hours \]
### Final Answer
The time required for the complete decomposition of 4 moles of water using a 4 ampere current is approximately **53.7 hours**.
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