A 45.0 g ball of copper has a net charge of 1.5 µC. What fraction of the copper's electrons have been removed? (Each copper atom has 29 protons, and copper has an atomic mass of 63.5.)
To determine the fraction of electrons that have been removed from the copper ball, we need to calculate the number of electrons in the ball and compare it to the number of electrons in an uncharged copper ball.
We can start by finding the number of moles of copper in the ball using its molar mass:
Molar mass of copper = 63.5 g/mol
Number of moles of copper = mass of copper ball / molar mass of copper
= 45.0 g / 63.5 g/mol
= 0.71 mol
Next, we need to find the number of copper atoms in the ball. Since 1 mole contains Avogadro's number (6.022 x 10^23) of particles, we can calculate the number of copper atoms:
Number of copper atoms = number of moles of copper x Avogadro's number
= 0.71 mol x 6.022 x 10^23 atoms/mol
= 4.27 x 10^23 atoms
Now, each copper atom has 29 protons, which means it has 29 electrons in a neutral state. Therefore, the number of electrons in an uncharged copper ball is:
Number of electrons in an uncharged copper ball = number of copper atoms x 29 electrons/atom
= 4.27 x 10^23 atoms x 29 electrons/atom
= 1.24 x 10^25 electrons
Since the copper ball has a net charge of 1.5 µC, we can use the charge of a single electron (1.6 x 10^-19 C) to find the number of electrons that have been removed:
Number of electrons removed = net charge of copper ball / charge of a single electron
= 1.5 x 10^-6 C / 1.6 x 10^-19 C
= 9.4 x 10^12 electrons
Finally, we can calculate the fraction of electrons that have been removed by dividing the number of electrons removed by the number of electrons in an uncharged copper ball:
Fraction of electrons removed = number of electrons removed / number of electrons in an uncharged copper ball
= 9.4 x 10^12 electrons / 1.24 x 10^25 electrons
= 7.6 x 10^-13
Therefore, approximately 7.6 x 10^-13 of the copper's electrons have been removed.