What is the total charge of all the electrons in a 13 kg bar of silver? (Silver has 47 electrons per atom and an atomic mass of 108 u.)
6*10^23 silver atoms have a mass of 0.108 kg
n of atoms = 13 kg ( 6*10^23 atoms / 0.108 kg)
n of electrons =47*13*6*10^23/0.108
charge on each electron = 1.6*10^-19 Coulombs
so
charge = 1.6*10^-19*47*13*6*10^23/0.108
To find the total charge of all the electrons in a 13 kg bar of silver, we need to follow these steps:
1. Determine the number of silver atoms in the bar: To do this, we can use the atomic mass of silver (108 u) and the given mass of the bar (13 kg).
First, convert the mass of the silver bar from kg to grams:
13 kg = 13,000 grams
Next, find the molar mass of silver by multiplying the atomic mass (108 u) by the molar mass constant (1 g/mol):
Molar mass of silver = 108 g/mol
Now, divide the mass of the silver bar by the molar mass to find the number of moles:
Number of moles = mass / molar mass = 13,000 g / 108 g/mol
Finally, calculate the number of silver atoms using Avogadro's number (6.022 x 10^23 atoms/mol):
Number of silver atoms = number of moles x Avogadro's number
2. Calculate the total number of electrons: Since silver has 47 electrons per atom, we can multiply the number of silver atoms by 47 to find the total number of electrons.
3. Calculate the total charge of the electrons: Each electron has a charge of -1.6 x 10^-19 coulombs. Multiply the total number of electrons by the charge of each electron to find the total charge of all the electrons.
By following these steps, we can determine the total charge of all the electrons in the 13 kg bar of silver.