To determine the number of missing electrons in the lead sphere, we need to calculate the number of excess electrons first. Given that the mass of the sphere is 8.0 g, we can assume that the entire mass comes from lead.
First, we need to calculate the number of moles of lead in the sphere. The molar mass of lead is given as 207 g/mol. Therefore, the number of moles (n) can be calculated using the formula:
n = mass / molar mass = 8.0 g / 207 g/mol
Now, let's calculate the number of excess electrons. Since lead has an atomic number of 82, it means that each lead atom has 82 electrons when it's neutral. Thus, the number of electrons in the sphere can be calculated using Avogadro's number (6.022 x 10^23 electrons/mol):
Number of electrons = n * Avogadro's number * 82 = (8.0 g / 207 g/mol) * (6.022 x 10^23 electrons/mol) * 82
Now we have the number of electrons in the sphere. To find the number of missing electrons, we need to compare it with the number of electrons in a neutral lead atom.
The number of electrons in a neutral lead atom is also equal to its atomic number, which is 82.
Therefore, the number of missing electrons can be calculated by subtracting the number of electrons in the sphere from the number of electrons in a neutral lead atom:
Number of missing electrons = 82 - Number of electrons in the sphere
By plugging in the values, we can find the result.