The current required to diplace 0.1 g of `H_(2)` in 10 seconds will be

Options

A. 9.65 amp
B. 1.988 amp
C. 198 amp
D. 965 amp

Answer

To find the current required to displace 0.1 g of hydrogen in 10 seconds, we can use Faraday's laws of electrolysis. Here’s a step-by-step solution:

### Step 1: Determine the equivalent weight of hydrogen.
The equivalent weight (E) of hydrogen can be calculated using the formula:
\[ E = \frac{\text{Molar mass}}{n} \]
where the molar mass of hydrogen (H₂) is 2 g/mol and n (the number of electrons transferred) is 2. Thus,
\[ E = \frac{2 \, \text{g/mol}}{2} = 1 \, \text{g/equiv} \]

### Step 2: Use the formula for weight deposited.
According to Faraday's first law of electrolysis, the weight (W) of the substance deposited is given by:
\[ W = Z \times I \times t \]
where:
- \(W\) = weight of the substance deposited (in grams)
- \(Z\) = equivalent weight (in grams per equivalent)
- \(I\) = current (in amperes)
- \(t\) = time (in seconds)

### Step 3: Substitute the known values into the equation.
We know:
- \(W = 0.1 \, \text{g}\)
- \(Z = 1 \, \text{g/equiv}\)
- \(t = 10 \, \text{s}\)

Substituting these values into the equation gives:
\[ 0.1 = 1 \times I \times 10 \]

### Step 4: Solve for current (I).
Rearranging the equation to solve for \(I\):
\[ I = \frac{0.1}{10} = 0.01 \, \text{A} \]

### Step 5: Conclusion.
The current required to displace 0.1 g of hydrogen in 10 seconds is \(0.01 \, \text{A}\).

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