Estimate the number of free electrons in `1g` of water and negative charge possessed by them. Given that Avogadro number `=6.02xx10^(23)` and molecular weight of water `= 18`

Options

A. `6.25xx10^(4)C`
B. `5.35xx10^(4)C`
C. `1.76xx10^(4)C`
D. `1.25xx10^(4)C`

Explanation

To estimate the number of free electrons in 1 gram of water and the negative charge possessed by them, we can follow these steps:

### Step 1: Calculate the number of moles of water in 1 gram
The molecular weight of water (H₂O) is given as 18 g/mol. To find the number of moles in 1 gram of water, we use the formula:

\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molecular weight (g/mol)}} \]

Substituting the values:

\[ \text{Number of moles} = \frac{1 \, \text{g}}{18 \, \text{g/mol}} = \frac{1}{18} \, \text{mol} \]

### Step 2: Determine the number of molecules in 1 gram of water
Using Avogadro's number, which is \(6.02 \times 10^{23}\) molecules/mol, we can find the number of molecules in \(\frac{1}{18}\) moles of water:

\[ \text{Number of molecules} = \text{Number of moles} \times \text{Avogadro's number} \]
\[ \text{Number of molecules} = \frac{1}{18} \times 6.02 \times 10^{23} \approx 3.34 \times 10^{22} \, \text{molecules} \]

### Step 3: Calculate the number of free electrons in one molecule of water
In one molecule of water (H₂O), there are:
- 2 hydrogen atoms, each contributing 1 free electron (total 2 electrons)
- 1 oxygen atom, which has 8 electrons, but we consider only the 6 that are not involved in bonding (since 2 are used for bonding with hydrogen).

Thus, the total number of free electrons in one molecule of water is:

\[ \text{Total free electrons in H₂O} = 2 + 6 = 8 \, \text{electrons} \]

### Step 4: Calculate the total number of free electrons in 1 gram of water
Now, we can find the total number of free electrons in 1 gram of water:

\[ \text{Total free electrons} = \text{Number of molecules} \times \text{Free electrons per molecule} \]
\[ \text{Total free electrons} = 3.34 \times 10^{22} \times 8 \approx 2.67 \times 10^{23} \, \text{electrons} \]

### Step 5: Calculate the total negative charge possessed by the free electrons
The charge of a single electron is approximately \(1.6 \times 10^{-19}\) coulombs. Therefore, the total negative charge can be calculated as:

\[ \text{Total charge} = \text{Total free electrons} \times \text{Charge of one electron} \]
\[ \text{Total charge} = 2.67 \times 10^{23} \times 1.6 \times 10^{-19} \approx 4.27 \times 10^{4} \, \text{C} \]

### Final Answers
- The number of free electrons in 1 gram of water is approximately \(2.67 \times 10^{23}\).
- The total negative charge possessed by these electrons is approximately \(4.27 \times 10^{4}\) coulombs.