Final answer:
To calculate the percentage of electrons removed, we need to find the number of electrons in the cube and the number of electrons removed. By using the density and mass of the cube, we can calculate the number of moles of aluminum and then the number of aluminum atoms. Since each aluminum atom has 13 electrons, we can determine the total number of electrons in the cube. Dividing the net charge by the charge of one electron gives us the number of electrons removed. Finally, we can calculate the percentage of electrons removed by dividing the number of electrons removed by the total number of electrons and multiplying by 100.
Step-by-step explanation:
To calculate the percentage of electrons that have been removed from the cube of aluminum, we first need to find the number of electrons in the cube. We can start by calculating the number of moles of aluminum in the cube using its density and mass:
Mass of the cube = side length * side length * side length * density = (1.00 cm)(1.00 cm)(1.00 cm)(2.70 g/cm³) = 2.70 g
Number of moles of aluminum = mass of aluminum / atomic weight = 2.70 g / 26.98 g/mol = 0.100 mol
Next, we can calculate the number of aluminum atoms in the cube using Avogadro's number:
Number of aluminum atoms = number of moles of aluminum * Avogadro's number = 0.100 mol * 6.022×10^23 = 6.022×10^22 atoms
Since each aluminum atom has 13 electrons, the total number of electrons in the cube is:
Total number of electrons = number of aluminum atoms * number of electrons per atom = 6.022×10^22 atoms * 13 electrons = 7.827×10^23 electrons
Now, we can calculate the number of electrons that have been removed by dividing the net charge by the charge of one electron:
Number of electrons removed = net charge / charge of one electron = 3.00 pC / (−1.60×10^−19 C) = -1.875×10^13 electrons
Finally, to find the percentage of electrons removed, we can divide the number of electrons removed by the total number of electrons and multiply by 100:
Percentage of electrons removed = (number of electrons removed / total number of electrons) * 100 = (-1.875×10^13 electrons / 7.827×10^23 electrons) * 100 = -2.395%