What weight of water will be decomposed by a current of 100 amp in 12 h ?

Answer

To solve the problem of how much water will be decomposed by a current of 100 amperes in 12 hours, we can follow these steps:

### Step 1: Convert Time from Hours to Seconds
First, we need to convert the time from hours to seconds since the current is given in amperes (A), which is in terms of coulombs per second.

\[ \text{Time in seconds} = 12 \text{ hours} \times 60 \text{ minutes/hour} \times 60 \text{ seconds/minute} = 43200 \text{ seconds} \]

### Step 2: Calculate Total Charge (Q)
Using the formula for charge, \( Q = I \times t \), where \( I \) is the current in amperes and \( t \) is the time in seconds, we can calculate the total charge.

\[ Q = 100 \text{ A} \times 43200 \text{ s} = 4320000 \text{ C} \]

### Step 3: Calculate the Number of Equivalents of Water Decomposed
Water (H₂O) decomposes into hydrogen and oxygen. The equivalent weight of water is calculated as follows:

\[ \text{Equivalent weight of water} = \frac{\text{Molar mass of water}}{n} = \frac{18 \text{ g/mol}}{2} = 9 \text{ g/equiv} \]

Now, we can find the number of equivalents of water decomposed using Faraday's law of electrolysis:

\[ \text{Number of equivalents} = \frac{Q}{F} \]

Where \( F \) (Faraday's constant) is approximately \( 96500 \text{ C/equiv} \).

\[ \text{Number of equivalents} = \frac{4320000 \text{ C}}{96500 \text{ C/equiv}} \approx 44.75 \text{ equiv} \]

### Step 4: Calculate the Weight of Water Decomposed
Now, we can calculate the weight of water decomposed using the number of equivalents and the equivalent weight of water:

\[ \text{Weight of water} = \text{Number of equivalents} \times \text{Equivalent weight} \]

\[ \text{Weight of water} = 44.75 \text{ equiv} \times 18 \text{ g/equiv} \approx 805.5 \text{ g} \]

### Final Answer
The weight of water decomposed by a current of 100 amperes in 12 hours is approximately **805.5 grams**.

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