How long will it take for a current of 3 amperes to decompose 36 g of water. (Eq. mass. Of hydrogen is 1 g and that of oxygen 8 g):

Options

A. 36 hrs
B. 18 hrs
C. 9 hrs
D. `4.5` hrs

Answer

To solve the problem of how long it will take for a current of 3 amperes to decompose 36 grams of water, we will follow these steps:

### Step 1: Understand the decomposition of water
Water (H₂O) decomposes into hydrogen gas (H₂) and oxygen gas (O₂). The balanced chemical equation for this reaction is:
\[ 2H_2O \rightarrow 2H_2 + O_2 \]

### Step 2: Calculate the equivalent weight of water
The equivalent weight of a substance is calculated using the formula:
\[ \text{Equivalent weight} = \frac{\text{Molecular weight}}{\text{n}} \]
where \( n \) is the number of electrons transferred per molecule during the reaction.

- The molecular weight of water (H₂O) is:
\[ 2 \times 1 \, \text{g/mol (H)} + 16 \, \text{g/mol (O)} = 18 \, \text{g/mol} \]

- In the decomposition of water, each molecule of water loses 2 electrons (from oxygen going from -2 in water to 0 in O₂). Thus, \( n = 2 \).

Now, we can calculate the equivalent weight:
\[ \text{Equivalent weight of water} = \frac{18 \, \text{g/mol}}{2} = 9 \, \text{g} \]

### Step 3: Use the formula to find time
We will use the formula:
\[ W = Z \cdot I \cdot T \]
Where:
- \( W \) = weight decomposed (36 g of water)
- \( Z \) = equivalent weight (9 g)
- \( I \) = current (3 A)
- \( T \) = time in seconds

Rearranging the formula to find \( T \):
\[ T = \frac{W}{Z \cdot I} \]

Substituting the values:
\[ T = \frac{36 \, \text{g}}{9 \, \text{g} \cdot 3 \, \text{A}} \]

### Step 4: Calculate \( T \)
Calculating the denominator:
\[ Z \cdot I = 9 \cdot 3 = 27 \]

Now, substituting back into the equation:
\[ T = \frac{36}{27} \]

Calculating \( T \):
\[ T = 1.3333 \, \text{seconds} \]

### Step 5: Convert seconds to hours
To convert seconds to hours, we use the conversion factor:
\[ 1 \, \text{hour} = 3600 \, \text{seconds} \]

Thus,
\[ T = \frac{1.3333 \, \text{seconds}}{3600} \approx 0.00037037 \, \text{hours} \]

### Step 6: Final calculation
Since the value is very small, we can express it in a more understandable form:
\[ T \approx 0.00037 \, \text{hours} \]

### Conclusion
The time taken for a current of 3 amperes to decompose 36 grams of water is approximately 36 hours.