In order to determine the number of moles of electrons in one kilogram, you need to first determine the number of electrons in one kilogram, and then convert the number of electrons to moles.
Known:
One electron (#"e"^-#) has a mass of #9.10938291xx10^(-31) "kg"#.
One mole of #"e"^-"# is #6.022xx10^23" e"^-#.
Solution:
Determine the number of #"e"# in one kilogram
Divide #"kg e"^(-)"# by the mass of one electron. Do this by multiplying by #("1 e"^(-1))/(9.10938291xx10^(-31) "kg")#
.
#1color(red)cancel(color(black)("kg e"^(-)))xx(1"e"^(-))/(9.10938291xx10^(-31)color(red)cancel(color(black)(" kg e"^(-))))=1.09776920xx10^30" e"^(-)"#
(Since 1 kg is an exact number and has an infinite number of significant figures, the number of significant figures in the answer is determined by the number of significant figures in the mass of an electron.)
Determine the number of moles of electrons in one kilogram.
#1.09776920xx10^30color(red)cancel(color(black)(" e"^(-)))xx(1"mol e"^(-))/(6.022xx10^23color(red)cancel(color(black)(" e"^(-1))))=1.823xx10^6" mol e"^(-)"#
(Since #6.022xx10^23# has only four significant figures, the answer has four significant figures.)
You can combine the two steps as follows:
#1color(red)cancel(color(black)"kg e"^(-))xx(1color(red)cancel(color(black)("e"^(-))))/(9.10938291xx10^(-31) color(red)cancel(color(black)("kg e"^(-))))xx(1"mol e"^(-))/(6.022xx10^23color(red)cancel(color(black)(" e"^(-1))))=1.823xx10^6" mol e"^(-)"#
Answer:
There are #1.823xx10^6" moles e"^-# in one kilogram of electrons.
