The total number of neutrons present in `10g D_(2)O (D "is" 2 H are .

Options

A. `2.5`
B. `5.0`
C. `10.0`
D. none of these

Answer

To find the total number of neutrons present in 10 grams of D₂O (Deuterium Oxide), we can follow these steps:

### Step 1: Determine the Molar Mass of D₂O
- Deuterium (D) has an atomic mass of approximately 2 g/mol.
- Therefore, two deuterium atoms contribute:
\[ 2 \times 2 \, \text{g/mol} = 4 \, \text{g/mol} \]
- Oxygen (O) has an atomic mass of approximately 16 g/mol.
- Thus, the molar mass of D₂O is:
\[ 4 \, \text{g/mol} + 16 \, \text{g/mol} = 20 \, \text{g/mol} \]

### Step 2: Calculate the Number of Moles of D₂O
- The number of moles (n) can be calculated using the formula:
\[ n = \frac{\text{mass}}{\text{molar mass}} \]
- Given that the mass of D₂O is 10 g:
\[ n = \frac{10 \, \text{g}}{20 \, \text{g/mol}} = 0.5 \, \text{mol} \]

### Step 3: Determine the Number of Neutrons in D₂O
- The molar mass of D₂O is 20 g/mol, which corresponds to the total number of nucleons (protons + neutrons).
- The atomic number of D₂O (which is the number of protons) is 10 (2 from deuterium and 8 from oxygen).
- The number of neutrons can be calculated as:
\[ \text{Number of neutrons} = \text{Molar mass} - \text{Atomic number} = 20 - 10 = 10 \]

### Step 4: Calculate the Total Number of Neutrons in 10 g of D₂O
- The total number of neutrons in the sample can be found by multiplying the number of neutrons per molecule by Avogadro's number:
\[ \text{Total neutrons} = \text{Number of neutrons per molecule} \times n \times N_A \]
- Where \( N_A \) (Avogadro's number) is approximately \( 6.02 \times 10^{23} \).
- Thus:
\[ \text{Total neutrons} = 10 \times 0.5 \times 6.02 \times 10^{23} = 3.01 \times 10^{24} \]

### Final Answer
The total number of neutrons present in 10 g of D₂O is \( 3.01 \times 10^{24} \).

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