How many moles of electrons weigh one kilogram?

Options

A. `6.023 xx 10^(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 out how many moles of electrons weigh one kilogram, we can follow these steps:

### Step 1: Determine the mass of one electron
The mass of one electron is given as:
\[ \text{Mass of one electron} = 9.1 \times 10^{-31} \text{ kg} \]

### Step 2: Calculate the number of electrons in one kilogram
To find out how many electrons make up one kilogram, we can use the formula:
\[ \text{Number of electrons} = \frac{1 \text{ kg}}{\text{mass of one electron}} \]
Substituting the mass of one electron:
\[ \text{Number of electrons} = \frac{1 \text{ kg}}{9.1 \times 10^{-31} \text{ kg}} \]

### Step 3: Calculate the number of electrons
Now, we perform the calculation:
\[ \text{Number of electrons} = \frac{1}{9.1 \times 10^{-31}} \approx 1.0989 \times 10^{30} \text{ electrons} \]

### Step 4: Use Avogadro's number to find moles of electrons
To find the number of moles of electrons, we use Avogadro's number, which is approximately \( 6.022 \times 10^{23} \) particles/mol. The formula for calculating moles is:
\[ \text{Number of moles of electrons} = \frac{\text{Number of electrons}}{\text{Avogadro's number}} \]
Substituting the values:
\[ \text{Number of moles of electrons} = \frac{1.0989 \times 10^{30}}{6.022 \times 10^{23}} \]

### Step 5: Perform the final calculation
Now, we perform the division:
\[ \text{Number of moles of electrons} \approx 1.826 \times 10^{6} \text{ moles} \]

### Conclusion
Thus, the number of moles of electrons that weigh one kilogram is approximately:
\[ \text{Number of moles of electrons} \approx 1.826 \times 10^{6} \]

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