We need to determine the net charge that would result from placing an extra electron on $1$ in $10^{12}$ sulfur atoms in a 100 g piece of sulfur. Here's the plan:

Step 1: Find the number of atoms in 100 g of sulfur

The atomic mass of sulfur is 32.1 g/mol, so we can find the number of moles of sulfur in 100 g using:

$\text{Number of moles} = \frac{\text{Mass}}{\text{Atomic Mass}}$

Then, we use Avogadro's number ($6.022 \times 10^{23}$ atoms/mol) to find the total number of sulfur atoms.

Step 2: Calculate the number of sulfur atoms with extra electrons

Once we have the total number of sulfur atoms, we calculate how many of them receive an extra electron by dividing the total number by $10^{12}$.

Step 3: Calculate the net charge

Since each extra electron contributes a charge of $1.60 \times 10^{-19}$ C, multiplying the number of atoms with extra electrons by the charge of an electron will give us the net charge.

Let’s proceed with the calculations.The net charge on the 100 g piece of sulfur, after placing an extra electron on $1$ in $10^{12}$ of its atoms, is approximately $-3.00 \times 10^{-7}$ C (Coulombs).

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Would you like any further explanation or details?

Here are 5 related questions to explore further:

1. How many sulfur atoms would receive extra electrons in a 50 g piece of sulfur?
2. How would the net charge change if you placed two extra electrons on $1$ in $10^{12}$ sulfur atoms?
3. What would be the net charge if the sulfur atoms lost electrons instead?
4. How many extra electrons would be needed to generate a net charge of $-1 \times 10^{-6}$ C on sulfur?
5. How does the atomic mass affect the calculation of the total number of atoms in a sample?

Tip: Remember that when dealing with atomic-scale charges, even small changes in the number of electrons can result in significant net charges.