To find the total charge of all the electrons in 1.0 L (1000 mL) of liquid water, we will need to break down the problem step-by-step:
1. Understanding the structure of water (H₂O):
- A water molecule consists of 2 hydrogen atoms and 1 oxygen atom.
- Each hydrogen atom has 1 electron.
- The oxygen atom has 8 electrons.
- Therefore, each water molecule (H₂O) has [tex]\(2 \times 1 + 8 = 10 \)[/tex] electrons.
2. Molar mass of water:
- The molar mass of water (H₂O) is approximately 18 grams per mole.
3. Density of liquid water:
- The density of liquid water is approximately 1 gram per milliliter (g/mL).
4. Calculating the mass of 1.0 L of water:
- Since the density of water is 1 g/mL, 1.0 L (which is 1000 mL) of water weighs 1000 grams.
5. Number of moles of water:
- The number of moles is given by the mass of water divided by its molar mass:
[tex]\[ \text{Number of moles} = \frac{1000 \text{ g}}{18 \text{ g/mol}} \approx 55.56 \text{ moles} \][/tex]
6. Number of water molecules:
- To find the number of molecules, we use Avogadro's number ([tex]\(6.022 \times 10^{23}\)[/tex]), which gives the number of molecules per mole:
[tex]\[ \text{Number of molecules} = 55.56 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mole} \][/tex]
[tex]\[ \text{Number of molecules} \approx 3.34 \times 10^{25} \text{ molecules} \][/tex]
7. Total number of electrons:
- Since each water molecule has 10 electrons:
[tex]\[ \text{Total number of electrons} = 3.34 \times 10^{25} \text{ molecules} \times 10 \text{ electrons/molecule} \][/tex]
[tex]\[ \text{Total number of electrons} \approx 3.34 \times 10^{26} \text{ electrons} \][/tex]
8. Charge of a single electron:
- The charge of a single electron is [tex]\(-1.602176634 \times 10^{-19} \text{ Coulombs (C)}\)[/tex].
9. Total charge of all electrons:
- To find the total charge, multiply the total number of electrons by the charge of one electron:
[tex]\[ \text{Total charge} = 3.34 \times 10^{26} \text{ electrons} \times (-1.602176634 \times 10^{-19} \text{ C/electron}) \][/tex]
[tex]\[ \text{Total charge} \approx -5.35 \times 10^{7} \text{ Coulombs (C)} \][/tex]
Thus, the total charge of all the electrons in 1.0 L of liquid water is approximately [tex]\(-53.5 \text{ Megacoulombs (MC)}\)[/tex].
