The number of neutrons in `5 "g of "D_(2)"O (D is "_(1)^(2)H)`

Options

A. `0.25 N_(A)`
B. `2.5 N_(A)`
C. ` 1.1 N_(A)`
D. None of these

Answer

To find the number of neutrons in 5 g of D₂O (where D is the heavy hydrogen isotope, deuterium), we can follow these steps:

### Step 1: Calculate the molar mass of D₂O
- Deuterium (D) has a mass of approximately 2 g/mol.
- Oxygen (O) has a mass of approximately 16 g/mol.
- Therefore, the molar mass of D₂O = (2 × mass of D) + (1 × mass of O) = (2 × 2 g/mol) + (1 × 16 g/mol) = 4 g/mol + 16 g/mol = 20 g/mol.

### Step 2: Calculate the number of moles of D₂O in 5 g
- The number of moles (n) can be calculated using the formula:

\[ n = \frac{\text{mass}}{\text{molar mass}} \]

- Substituting the values:

\[ n = \frac{5 \text{ g}}{20 \text{ g/mol}} = 0.25 \text{ moles} \]

### Step 3: Determine the number of neutrons in D₂O
- The mass number (A) of deuterium (D) is 2, and the atomic number (Z) is 1. Therefore, the number of neutrons in deuterium is:

\[ \text{Neutrons in D} = A - Z = 2 - 1 = 1 \]

- The mass number (A) of oxygen (O) is 16, and the atomic number (Z) is 8. Therefore, the number of neutrons in oxygen is:

\[ \text{Neutrons in O} = A - Z = 16 - 8 = 8 \]

- In D₂O, there are 2 deuterium atoms and 1 oxygen atom, so the total number of neutrons is:

\[ \text{Total neutrons} = (2 \times \text{Neutrons in D}) + \text{Neutrons in O} = (2 \times 1) + 8 = 2 + 8 = 10 \]

### Step 4: Calculate the total number of neutrons in 0.25 moles of D₂O
- Since we have 0.25 moles of D₂O, the total number of neutrons is:

\[ \text{Total neutrons in 0.25 moles} = 10 \times 0.25 \times N_A \]

where \( N_A \) (Avogadro's number) is approximately \( 6.022 \times 10^{23} \).

- Therefore:

\[ \text{Total neutrons} = 10 \times 0.25 \times 6.022 \times 10^{23} = 2.5 \times 6.022 \times 10^{23} \]

### Final Answer:
The total number of neutrons in 5 g of D₂O is approximately \( 1.5055 \times 10^{24} \) neutrons.

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