How many moles of electrons weigh one kilogram?

Options

A. `6.022 xx 10^(23)`
B. `1/(9.108) xx 10^(31)`
C. `6.022/9.108 xx 10^(54)`
D. `1/(9.108 xx 6.022) xx 10^(8)`

Answer

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:
\[ m_e = 9.1 \times 10^{-31} \text{ kg} \]

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

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

### Step 4: Calculate the number of moles of electrons
To find the number of moles of electrons, we use Avogadro's number (\( N_A \)), which is approximately \( 6.022 \times 10^{23} \) mol\(^{-1}\):
\[ \text{Number of moles} = \frac{\text{Number of electrons}}{N_A} \]
Substituting the values:
\[ \text{Number of moles} = \frac{1.0989 \times 10^{30}}{6.022 \times 10^{23}} \]

### Step 5: Perform the calculation for moles
Calculating the above expression:
\[ \text{Number of moles} \approx 1.83 \times 10^{6} \text{ moles} \]

### Final Answer
Thus, the number of moles of electrons that weigh one kilogram is approximately:
\[ \text{Number of moles} \approx 1.83 \times 10^{6} \]

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