(a) Calculate the number of electrons in a small, electrically neutral silver pin that has a mass of 8.0 g. Silver has 47 electrons per atom, and its molar mass is 107.87 g/mol.
(b) Imagine adding electrons to the pin until the negative charge has the very large value 2.00 mC. How many electrons are added for every 109 electrons already present?
thanks
How many moles of silver do you have? 8/147.87
for each mole of silver atoms, you have avagnumber*47 electrons.
number electrons: charge/chargeof one electgron
ratio=number added/109
(a) To calculate the number of electrons in the silver pin, we need to use the information provided. We know the mass of the pin is 8.0 g and the molar mass of silver is 107.87 g/mol. We also know that the silver atom has 47 electrons.
Step 1: Calculate the number of moles of silver in the pin.
We can use the formula:
moles = mass / molar mass
moles = 8.0 g / 107.87 g/mol
moles ≈ 0.0742 mol
Step 2: Calculate the number of atoms in the pin.
Since 1 mole of a substance contains Avogadro's number of entities (6.022 x 10^23), we can multiply the number of moles by Avogadro's number to get the number of atoms.
number of atoms = moles x Avogadro's number
number of atoms ≈ 0.0742 mol x 6.022 x 10^23/mol
number of atoms ≈ 4.47 x 10^22 atoms
Step 3: Calculate the number of electrons in the pin.
Since each silver atom has 47 electrons, we can multiply the number of atoms by 47 to get the total number of electrons in the pin.
number of electrons = number of atoms x 47
number of electrons ≈ 4.47 x 10^22 atoms x 47
number of electrons ≈ 2.1 x 10^24 electrons
Therefore, the silver pin has approximately 2.1 x 10^24 electrons.
(b) To find out how many electrons are added for every 10^9 electrons already present, we need to determine how many electrons it takes to achieve a negative charge of 2.00 mC.
Step 1: Find the charge of a single electron.
The elementary charge is the fundamental unit of electric charge and is equal to approximately 1.60 x 10^-19 coulombs (C).
Step 2: Calculate the number of electrons needed to achieve a charge of 2.00 mC.
To find the number of electrons, we divide the desired charge by the charge of a single electron:
number of electrons = desired charge / charge of a single electron
number of electrons = 2.00 mC / (1.60 x 10^-19 C/electron)
number of electrons ≈ 1.25 x 10^16 electrons
Step 3: Calculate the ratio of added electrons to the initial number of electrons.
To find the ratio, we divide the number of electrons needed by every 10^9 electrons already present:
ratio = number of electrons / (10^9 electrons)
ratio = (1.25 x 10^16 electrons) / (10^9 electrons)
ratio ≈ 1.25 x 10^7
Therefore, approximately 1.25 x 10^7 electrons need to be added for every 10^9 electrons already present to achieve a negative charge of 2.00 mC.