How may moles of electrons weigh one kilogram?

Options

A. `6.023 xx ^(23)`
B. `(1)/(9.108) xx 10^(31)`
C. `(6.023)/(9.108) xx 10^(54)`
D. `(1)/(9.108 xx 6.023) xx 10^(8)`

Explanation

To find how many moles of electrons weigh one kilogram, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the mass of one electron**:
The mass of one electron is given as:
\[ \text{Mass of one electron} = 9.108 \times 10^{-31} \text{ kg} \]

2. **Determine the number of electrons in one mole**:
According to Avogadro's number, the number of particles (in this case, electrons) in one mole is:
\[ N_A = 6.022 \times 10^{23} \text{ electrons/mole} \]

3. **Calculate the mass of one mole of electrons**:
To find the mass of one mole of electrons, we multiply the mass of one electron by the number of electrons in one mole:
\[ \text{Mass of one mole of electrons} = \text{Mass of one electron} \times N_A \]
\[ \text{Mass of one mole of electrons} = (9.108 \times 10^{-31} \text{ kg}) \times (6.022 \times 10^{23} \text{ electrons/mole}) \]
\[ \text{Mass of one mole of electrons} \approx 5.4858 \times 10^{-7} \text{ kg} \]

4. **Calculate the number of moles of electrons in 1 kg**:
To find the number of moles of electrons in 1 kg, we divide 1 kg by the mass of one mole of electrons:
\[ \text{Number of moles of electrons} = \frac{1 \text{ kg}}{\text{Mass of one mole of electrons}} \]
\[ \text{Number of moles of electrons} = \frac{1 \text{ kg}}{5.4858 \times 10^{-7} \text{ kg/mole}} \approx 1.82 \times 10^{6} \text{ moles} \]

### Final Answer:
Approximately \( 1.82 \times 10^{6} \) moles of electrons weigh one kilogram.