Answer :
To determine the mass in grams of 1 mole of electrons, we need to know the mass of a single electron and Avogadro's number. Let's proceed step-by-step.
1. Mass of a Single Electron:
The mass of a single electron is approximately [tex]\(9.10938356 \times 10^{-31}\)[/tex] kilograms.
2. Avogadro's Number:
Avogadro's number, which is the number of particles in one mole, is approximately [tex]\(6.02214076 \times 10^{23}\)[/tex] particles/mole.
3. Convert the Mass of an Electron from Kilograms to Grams:
Since 1 kilogram is equal to 1000 grams, the mass of one electron in grams is:
[tex]\[ 9.10938356 \times 10^{-31} \text{ kg} \times 1000 \frac{\text{g}}{\text{kg}} = 9.10938356 \times 10^{-28} \text{ g} \][/tex]
4. Calculate the Mass of 1 Mole of Electrons:
To find the mass of one mole of electrons, multiply the mass of a single electron by Avogadro's number:
[tex]\[ (9.10938356 \times 10^{-28} \text{ g}) \times (6.02214076 \times 10^{23} \text{ electrons/mole}) \][/tex]
5. Perform the Multiplication:
[tex]\[ 9.10938356 \times 10^{-28} \times 6.02214076 \times 10^{23} = (9.10938356 \times 6.02214076) \times 10^{-28 + 23} \][/tex]
[tex]\[ = 54.948242573 \times 10^{-5} \][/tex]
[tex]\[ = 5.4948242573 \times 10^{-4} \text{ g/mol} \][/tex]
6. Round to the Appropriate Significant Figures:
Since the given values (mass of electron and Avogadro's number) have been provided to an 8 significant figure accuracy, it is appropriate to keep that level of precision:
[tex]\[ = 5.4948 \times 10^{-4} \text{ g/mol} \][/tex]
Therefore, the mass of 1 mole of electrons is [tex]\(5.4948 \times 10^{-4}\)[/tex] grams per mole.
1. Mass of a Single Electron:
The mass of a single electron is approximately [tex]\(9.10938356 \times 10^{-31}\)[/tex] kilograms.
2. Avogadro's Number:
Avogadro's number, which is the number of particles in one mole, is approximately [tex]\(6.02214076 \times 10^{23}\)[/tex] particles/mole.
3. Convert the Mass of an Electron from Kilograms to Grams:
Since 1 kilogram is equal to 1000 grams, the mass of one electron in grams is:
[tex]\[ 9.10938356 \times 10^{-31} \text{ kg} \times 1000 \frac{\text{g}}{\text{kg}} = 9.10938356 \times 10^{-28} \text{ g} \][/tex]
4. Calculate the Mass of 1 Mole of Electrons:
To find the mass of one mole of electrons, multiply the mass of a single electron by Avogadro's number:
[tex]\[ (9.10938356 \times 10^{-28} \text{ g}) \times (6.02214076 \times 10^{23} \text{ electrons/mole}) \][/tex]
5. Perform the Multiplication:
[tex]\[ 9.10938356 \times 10^{-28} \times 6.02214076 \times 10^{23} = (9.10938356 \times 6.02214076) \times 10^{-28 + 23} \][/tex]
[tex]\[ = 54.948242573 \times 10^{-5} \][/tex]
[tex]\[ = 5.4948242573 \times 10^{-4} \text{ g/mol} \][/tex]
6. Round to the Appropriate Significant Figures:
Since the given values (mass of electron and Avogadro's number) have been provided to an 8 significant figure accuracy, it is appropriate to keep that level of precision:
[tex]\[ = 5.4948 \times 10^{-4} \text{ g/mol} \][/tex]
Therefore, the mass of 1 mole of electrons is [tex]\(5.4948 \times 10^{-4}\)[/tex] grams per mole.
