Question

Which of the following statement is correct? (a) 1 mole of electrons weighs \(5.4 \mathrm{mg}\) (b) 1 mole of electrons weighs \(5.4 \mathrm{~kg}\) (c) 1 mole of electrons weighs \(0.54 \mathrm{mg}\) (d) 1 mole of electrons has \(1.6 \times 10^{-19} \mathrm{C}\) of charge

Short answer

None of the options are exactly correct, but (c) is closest.

Step-by-step solution

Understanding the Basics

A mole is a unit that measures an amount of substance. Avogadro's number, which is approximately \(6.022 \times 10^{23}\) entities per mole, is used to relate moles to individual particles. We will calculate the mass of 1 mole of electrons and their total charge.

Calculating Mass of 1 Mole of Electrons

The mass of an electron is approximately \(9.109 \times 10^{-31}\) kilograms. To find the mass of a mole of electrons, multiply the mass of one electron by Avogadro's number: \[\text{Mass of 1 mole of electrons} = 9.109 \times 10^{-31}\, \text{kg} \times 6.022 \times 10^{23} = 5.48 \times 10^{-7}\, \text{kg}\] Converting this to milligrams, we get \(5.48 \times 10^{-4} \mathrm{mg}\), which matches none of the options perfectly.

Calculating Charge of 1 Mole of Electrons

The charge of one electron is \(-1.6 \times 10^{-19}\) coulombs. The charge of a mole of electrons is: \[\text{Charge of 1 mole of electrons} = -1.6 \times 10^{-19}\, \text{C} \times 6.022 \times 10^{23} = -9.65 \times 10^{4}\, \text{C}\]Clearly, option (d), saying 1 mole of electrons has \(1.6 \times 10^{-19}\, \text{C}\), is incorrect.

Analyzing Options with Results

From Step 2, the calculated mass \(5.48 \times 10^{-4}\, \text{mg}\) is closest to option (c), which states 1 mole of electrons weighs \(0.54 \mathrm{mg}\). Check calculations again if necessary, but since option (a) and option (b) are clearly wrong due to their magnitude, and (d) is incorrect too, (c) seems closest.

Key concepts

Mass of Electrons

When considering the mass of electrons, it's crucial to understand that electrons are incredibly tiny particles with a very small mass. Each electron has a mass of approximately \(9.109 \times 10^{-31}\) kilograms. This value is so small that it is often difficult to imagine. However, when we accumulate a vast number of electrons, as we do when considering a mole, the total mass becomes more manageable for calculation.

• To find the mass of a mole of electrons, we simply take the mass of a single electron and multiply it by Avogadro's number. This gives us the collective mass of these particles.
• Through the calculation, the mass of one mole of electrons results in \(5.48 \times 10^{-7}\) kilograms.

This value, when converted into milligrams, becomes \(5.48 \times 10^{-4}\) mg, which helps us understand how option (c) fits—albeit not perfectly—in terms of magnitude.

Avogadro's Number

Avogadro's number is a cornerstone in the field of chemistry. This constant, approximately equal to \(6.022 \times 10^{23}\), allows scientists to bridge the gap between the microscopic scale of atoms and electrons and the macroscopic scale of laboratory measurements.

• This number represents the amount of substance in one mole, enabling conversions between individual atomic-scale entities and macroscopic quantities.
• Using Avogadro's number, you can calculate collective properties—like mass or charge—of a substance based on its fundamental components, such as electrons.

It plays a pivotal role in understanding the mole concept by visualizing how much a mole truly contains in terms of particles, which is subtly enormous and incredibly useful for quantitative chemistry.

Charge of Electrons

Electrons carry a fundamental property known as electric charge. Each individual electron has a charge of approximately \(-1.6 \times 10^{-19}\) coulombs. This tiny but significant charge is essential in the formation of electrical currents and is a cornerstone in explaining chemical bonding and reactions.

• When we discuss the charge of a mole of electrons, we're aggregating this minuscule charge over Avogadro's number of electrons – leading to a total charge.
• By multiplying the charge of a single electron by Avogadro's number, we determine the charge of a mole of electrons to be \(-9.65 \times 10^{4}\) coulombs.

This calculation is key in electrical studies, helping us to understand and predict the behavior of electric currents and the role electrons play in chemical processes.