The total number of electrons in 2.0 g of `D_(2)O` to that in 1.8 g of `H_(2)O`

Options

A. Double
B. Same
C. Triple
D. One fourth

Answer

To solve the problem of finding the total number of electrons in 2.0 g of D₂O compared to that in 1.8 g of H₂O, we can follow these steps:

### Step 1: Determine the molar mass of D₂O
- The molar mass of D₂O can be calculated as follows:
- Molar mass of Deuterium (D) = 2 g/mol (since there are 2 deuterium atoms)
- Molar mass of Oxygen (O) = 16 g/mol
- Therefore, Molar mass of D₂O = (2 × 2) + 16 = 20 g/mol

### Step 2: Calculate the number of moles of D₂O in 2.0 g
- Use the formula:
\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} \]
- For D₂O:
\[ \text{Number of moles of D₂O} = \frac{2.0 \text{ g}}{20 \text{ g/mol}} = 0.1 \text{ moles} \]

### Step 3: Determine the total number of electrons in D₂O
- Each molecule of D₂O contains:
- 2 electrons from 2 deuterium atoms (1 electron each)
- 8 electrons from 1 oxygen atom
- Total electrons in one molecule of D₂O = 2 + 8 = 10 electrons
- Therefore, for 0.1 moles of D₂O:
\[ \text{Total electrons in D₂O} = 0.1 \text{ moles} \times 10 \text{ electrons/molecule} = 1 \text{ mole of electrons} \]

### Step 4: Determine the molar mass of H₂O
- The molar mass of H₂O can be calculated as follows:
- Molar mass of Hydrogen (H) = 1 g/mol (since there are 2 hydrogen atoms)
- Molar mass of Oxygen (O) = 16 g/mol
- Therefore, Molar mass of H₂O = (2 × 1) + 16 = 18 g/mol

### Step 5: Calculate the number of moles of H₂O in 1.8 g
- For H₂O:
\[ \text{Number of moles of H₂O} = \frac{1.8 \text{ g}}{18 \text{ g/mol}} = 0.1 \text{ moles} \]

### Step 6: Determine the total number of electrons in H₂O
- Each molecule of H₂O contains:
- 2 electrons from 2 hydrogen atoms (1 electron each)
- 8 electrons from 1 oxygen atom
- Total electrons in one molecule of H₂O = 2 + 8 = 10 electrons
- Therefore, for 0.1 moles of H₂O:
\[ \text{Total electrons in H₂O} = 0.1 \text{ moles} \times 10 \text{ electrons/molecule} = 1 \text{ mole of electrons} \]

### Step 7: Compare the total number of electrons
- Total number of electrons in 2.0 g of D₂O = 1 mole of electrons
- Total number of electrons in 1.8 g of H₂O = 1 mole of electrons

### Conclusion
The total number of electrons in 2.0 g of D₂O is equal to that in 1.8 g of H₂O, both being 1 mole of electrons.

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