A 45.0 g ball of copper has a net charge of 2.3 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 find the fraction of electrons that have been removed from the copper ball, we need to calculate the number of electrons in the ball and then determine how many of them have been removed.
First, let's calculate the number of copper atoms in the ball. To do this, we'll use the molar mass of copper, which is 63.5 g/mol.
Number of copper atoms = (Mass of the copper ball) / (Atomic mass of copper)
Number of copper atoms = (45.0 g) / (63.5 g/mol)
Using this calculation, we find that there are approximately 0.71 moles of copper atoms in the ball.
Next, let's calculate the number of electrons in the ball. Each copper atom has 29 protons, and since copper is electrically neutral, it also has 29 electrons.
Number of electrons = (Number of copper atoms) * (Number of electrons per copper atom)
Number of electrons = (0.71 mol) * (6.022 x 10^23/mol) * (29 electrons)
Using Avogadro's number (6.022 x 10^23), we can find that there are approximately 1.32 x 10^23 electrons in the copper ball.
Now, let's determine the number of electrons that have been removed. We know that the net charge on the ball is 2.3 µC, which is equivalent to 2.3 x 10^-6 C.
Number of electrons removed = (Net charge on the ball) / (Charge of an electron)
Number of electrons removed = (2.3 x 10^-6 C) / (1.6 x 10^-19 C)
Using the elementary charge of an electron (1.6 x 10^-19 C), we can find that approximately 1.44 x 10^13 electrons have been removed from the copper ball.
Finally, let's calculate the fraction of electrons that have been removed.
Fraction of electrons removed = (Number of electrons removed) / (Total number of electrons)
Fraction of electrons removed = (1.44 x 10^13 electrons) / (1.32 x 10^23 electrons)
Using this calculation, we find that approximately 1.09 x 10^-10, or 0.000000000109, of the copper's electrons have been removed.
Therefore, the fraction of copper's electrons that have been removed is approximately 1.09 x 10^-10.