Water has a mass per mole of 18.0 g/mol, and each molecule (H2O) has 10 electrons a)How many electrons are there in 9.68 liters of water? What is the net charge of all these electrons
The correct answer and explanation is:
Let’s analyze the problem step-by-step.
Given data:
- Molar mass of water, M=18.0 g/molM = 18.0 \, g/mol
- Each water molecule (H₂O) has 10 electrons
- Volume of water = 9.68 liters
- We want to find:
- (a) Number of electrons in 9.68 liters of water
- Net charge of all these electrons
Step 1: Find the mass of water in 9.68 L
Water has a density close to 1.00 g/cm31.00 \, g/cm^3 or 1.00 g/mL1.00 \, g/mL.
- 1 L=1000 mL1 \, L = 1000 \, mL
- Therefore, Mass of water=9.68 L×1000 mL/L×1.00 g/mL=9680 g\text{Mass of water} = 9.68 \, L \times 1000 \, mL/L \times 1.00 \, g/mL = 9680 \, g
Step 2: Calculate moles of water
Using the molar mass: Moles of water=massmolar mass=9680 g18.0 g/mol≈538.89 mol\text{Moles of water} = \frac{\text{mass}}{\text{molar mass}} = \frac{9680 \, g}{18.0 \, g/mol} \approx 538.89 \, mol
Step 3: Calculate number of water molecules
Using Avogadro’s number: NA=6.022×1023 molecules/molN_A = 6.022 \times 10^{23} \text{ molecules/mol} Number of molecules=538.89 mol×6.022×1023 molecules/mol≈3.24×1026 molecules\text{Number of molecules} = 538.89 \, mol \times 6.022 \times 10^{23} \, molecules/mol \approx 3.24 \times 10^{26} \text{ molecules}
Step 4: Calculate number of electrons
Each water molecule has 10 electrons: Number of electrons=3.24×1026×10=3.24×1027 electrons\text{Number of electrons} = 3.24 \times 10^{26} \times 10 = 3.24 \times 10^{27} \text{ electrons}
Step 5: Calculate net charge of all electrons
Charge of one electron is approximately: e=−1.602×10−19 Ce = -1.602 \times 10^{-19} \, C
Therefore: Net charge=3.24×1027×(−1.602×10−19)=−5.19×108 C\text{Net charge} = 3.24 \times 10^{27} \times (-1.602 \times 10^{-19}) = -5.19 \times 10^{8} \, C
Final answers:
- Number of electrons in 9.68 L of water: 3.24×1027 electrons\boxed{3.24 \times 10^{27} \text{ electrons}}
- Net charge of all electrons: −5.19×108 coulombs (C)\boxed{-5.19 \times 10^{8} \, \text{coulombs (C)}}
Explanation:
Water molecules contain electrons that carry a negative electric charge. To find how many electrons are in a specific volume of water, we first calculate the total mass using water’s density, then convert that mass into moles by dividing by the molar mass of water. Using Avogadro’s number, which tells us how many molecules are in one mole, we find the total number of water molecules. Multiplying by the number of electrons per molecule gives the total electrons.
The net charge is then calculated by multiplying the number of electrons by the charge of one electron (which is negative). The result is a very large negative charge because the number of electrons in even a small volume of water is enormous. This illustrates how electrically neutral matter contains a huge number of charged particles, but their charges balance out to net zero overall (since protons have positive charge to balance the electrons in neutral water molecules).