Calculate the time required for a current of 2 amp to decompose two moles of water.

Answer

To calculate the time required for a current of 2 amperes to decompose 2 moles of water, we can follow these steps:

### Step 1: Write the balanced chemical equation for the decomposition of water.
The decomposition of water can be represented as:
\[ 2H_2O \rightarrow 2H_2 + O_2 \]

### Step 2: Determine the number of moles of electrons exchanged.
From the balanced equation, we see that 2 moles of water produce 2 moles of hydrogen and 1 mole of oxygen. Each mole of water decomposes to produce 2 moles of electrons. Therefore, for 2 moles of water:
\[ \text{Number of moles of electrons} = 2 \text{ moles of water} \times 2 \text{ moles of electrons/mole of water} = 4 \text{ moles of electrons} \]

### Step 3: Use Faraday's law to calculate the total charge.
According to Faraday's law, the total charge (Q) can be calculated using the formula:
\[ Q = n \times F \]
where:
- \( n \) = number of moles of electrons (4 moles)
- \( F \) = Faraday's constant (approximately \( 96500 \, \text{C/mol} \))

Calculating the total charge:
\[ Q = 4 \, \text{moles} \times 96500 \, \text{C/mol} = 386000 \, \text{C} \]

### Step 4: Calculate the time required using the formula \( Q = I \times t \).
Rearranging the formula gives us:
\[ t = \frac{Q}{I} \]
where:
- \( I \) = current (2 A)

Substituting the values:
\[ t = \frac{386000 \, \text{C}}{2 \, \text{A}} = 193000 \, \text{s} \]

### Step 5: Convert seconds to hours.
To convert seconds to hours, we divide by the number of seconds in an hour (3600 s/h):
\[ t = \frac{193000 \, \text{s}}{3600 \, \text{s/h}} \approx 53.61 \, \text{hours} \]

### Final Answer:
The time required for a current of 2 amperes to decompose 2 moles of water is approximately **53.61 hours**.

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