How many moles of electrons weigh one kilogram? (mass of electron $=9.108\times {10}^{-31}kg$ , Avogadro number $=6.023\times {10}^{23}$)

To calculate how many moles of electrons weigh one kilogram, we will use the given data:

• Mass of electron in kg: 9.108 × 10^-31 kg
• Avogadro's number: 6.022 × 10²³ particles/mol

Step-by-Step Calculation:

1. The mass of one electron in kilograms is given as:

Mass of electron in kg: 9.108 × 10^-31 kg

2. To find the number of electrons in 1 kilogram, divide the total mass (1 kg) by the mass of a single electron:

Number of electrons = 1 kg / Mass of electron in kg = 1 / (9.108 × 10^-31)

Number of electrons = 10³¹ / 9.108 electrons

3. Using Avogadro's number, the number of moles of electrons can be calculated as:

Moles of electrons = (Total number of electrons) / (Avogadro's number)

Moles of electrons = (10³¹ / 9.108) ÷ (6.022 × 10²³)

4. Simplifying further:

Moles of electrons = (10³¹) / (9.108 × 6.022 × 10²³)

5. Breaking it down:

Moles of electrons = 10⁶ / (9.108 × 6.022)

Final Answer:

The number of moles of electrons that weigh one kilogram is approximately:

Moles of electrons = 10⁶ / (9.108 × 6.022)