To determine the net charge on a 100 g piece of sulfur when an extra electron is placed on 1 in $10^{12}$ of its atoms, we can follow these steps:

1. Calculate the number of moles of sulfur:

Given:

• Mass of sulfur: 100 g
• Molar mass of sulfur ($M$): 32.1 g/mol

The number of moles of sulfur ($n$) is calculated by: $n = \frac{\text{mass}}{\text{molar mass}} = \frac{100 \, \text{g}}{32.1 \, \text{g/mol}} \approx 3.115 \, \text{mol}$

2. Determine the number of sulfur atoms:

Using Avogadro's number ($N_A = 6.022 \times 10^{23} \, \text{atoms/mol}$): $\text{Number of sulfur atoms} = n \times N_A = 3.115 \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol} \approx 1.876 \times 10^{24} \, \text{atoms}$

3. Calculate the number of sulfur atoms with an extra electron:

Given that an extra electron is placed on 1 in $10^{12}$ atoms: $\text{Number of atoms with an extra electron} = \frac{1.876 \times 10^{24} \, \text{atoms}}{10^{12}} \approx 1.876 \times 10^{12} \, \text{atoms}$

4. Calculate the net charge:

Each extra electron has a charge of $-1.6 \times 10^{-19} \, \text{C}$. The total net charge ($Q$) is: $Q = \text{Number of extra electrons} \times \text{Charge of one electron}$ $Q = 1.876 \times 10^{12} \times (-1.6 \times 10^{-19} \, \text{C}) \approx -3.002 \times 10^{-7} \, \text{C}$

Answer:

The net charge on the 100 g piece of sulfur is approximately $-3.002 \times 10^{-7} \, \text{C}$.

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Would you like any more details or have any questions? Here are five related questions you might find interesting:

1. How would the net charge change if the mass of sulfur was doubled?
2. What would happen to the net charge if you placed two extra electrons on each affected sulfur atom?
3. How does the atomic structure of sulfur affect its ability to gain or lose electrons?
4. What would be the net charge if the atomic mass of sulfur was different?
5. How does the concept of quantization of charge relate to this problem?

Tip: Remember that when working with charges, the sign is important! Positive for protons, negative for electrons.