What mass of electrons would be required to just neutralize the charge of 3.9 grams of protons?

To determine the mass of electrons required to neutralize the charge of protons, we need to use the concept of charge neutrality. The total charge of protons is equal to the total charge of electrons for a system to be neutral.

The charge of a single proton is +1.6 x 10^(-19) coulombs (C), and we assume that the protons are fully ionized.

First, we need to find the total charge of the protons, which could be calculated using the formula:

Total charge = Charge per proton x Number of protons

The mass of protons is given as 3.9 grams. To convert this mass to the number of protons, we need to use the atomic mass of protons.

The atomic mass of protons is approximately 1.67 x 10^(-27) kilograms (kg).

The number of protons can be calculated using the formula:

Number of protons = Mass of protons / atomic mass of protons

Let's now calculate the total charge and the number of electrons required to neutralize it:

Mass of protons = 3.9 grams = 0.0039 kg
Atomic mass of protons = 1.67 x 10^(-27) kg
Number of protons = (0.0039 kg) / (1.67 x 10^(-27) kg) = 2.34 x 10^23 protons

Total charge = (Charge per proton) x (Number of protons)
= (1.6 x 10^(-19) C) x (2.34 x 10^23 protons)
= 3.74 x 10^4 C

Since the system is neutral, the total charge of electrons required to neutralize the protons is equal in magnitude but opposite in sign to the total charge of protons.

Number of electrons = Total charge / Charge per electron
= (3.74 x 10^4 C) / (1.6 x 10^(-19) C)
≈ 2.34 x 10^23 electrons

Finally, to calculate the mass of electrons, we use the mass of an electron, which is approximately 9.11 x 10^(-31) kg.

Mass of electrons = Number of electrons x Mass of electron
= (2.34 x 10^23 electrons) x (9.11 x 10^(-31) kg)
≈ 2.13 x 10^(-7) kg

So, the mass of electrons required to neutralize the charge of 3.9 grams of protons is approximately 2.13 x 10^(-7) kilograms.

To solve this problem, we need to find the number of protons in 3.9 grams of protons and then determine the mass of electrons required to neutralize their charge.

Step 1: Find the number of protons
The molar mass of protons is approximately 1 g/mol. Therefore, the number of moles of protons in 3.9 grams can be calculated as:

Number of moles = Mass / Molar mass
Number of moles = 3.9 g / 1 g/mol
Number of moles = 3.9 mol

Since 1 mol contains Avogadro's number (6.022 x 10^23) of particles, we can determine the number of protons in 3.9 grams:

Number of protons = Number of moles x Avogadro's number
Number of protons = 3.9 mol x 6.022 x 10^23
Number of protons ≈ 2.395 x 10^24 protons

Step 2: Find the mass of electrons
The charge of a proton is +1 elementary charge (e), and the charge of an electron is -1 elementary charge. Therefore, to neutralize the charge of one proton, we need one electron.

Since the masses of protons and electrons are negligible compared to each other, we assume their masses are the same. The molar mass of electrons is approximately 1 g/mol.

To find the mass of electrons required to neutralize the charge of 3.9 grams of protons, we can use the following steps:

Number of electrons = Number of protons = 2.395 x 10^24 protons
Mass of electrons = Number of electrons x Molar mass
Mass of electrons = 2.395 x 10^24 x 1 g/mol
Mass of electrons ≈ 2.395 x 10^24 g
Mass of electrons ≈ 2.4 x 10^24 g

Therefore, approximately 2.4 x 10^24 grams of electrons would be required to neutralize the charge of 3.9 grams of protons.

The mass of one proton is 1.67 x 10^-24 grams. So 1.67 x 10^-24 g/proton x # protons = 3.9 grams.

Solve for # protons.
# electrons will be the same since the charges are the same (but opposite).
One electron has a mass of 9.11 x 10^-28 g; therefore,
9.11 x 10^-28 g x # electrons = mass of electrons.