Number of neutrons in 5.5gm `T_(2)O` (T is `._1H^(3))` are.

Options

A. `0.25 N_(A)`
B. `2.5N_(A)`
C. `3N_(A)`
D. None of these

Explanation

To solve the problem of finding the number of neutrons in 5.5 g of \( T_2O \) (where \( T \) is the isotope \( _1H^{3} \)), we will follow these steps:

### Step 1: Calculate the Molar Mass of \( T_2O \)
- The molar mass of \( T_2O \) consists of 2 atoms of tritium (T) and 1 atom of oxygen (O).
- The molar mass of tritium (T) is approximately 3 g/mol (since it is \( _1H^{3} \)).
- The molar mass of oxygen (O) is 16 g/mol.

Thus, the molar mass of \( T_2O \) is:
\[ \text{Molar mass of } T_2O = (2 \times 3) + 16 = 6 + 16 = 22 \text{ g/mol} \]

### Step 2: Calculate the Number of Moles of \( T_2O \)
- We can find the number of moles of \( T_2O \) in 5.5 g using the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
Substituting the values:
\[ \text{Number of moles} = \frac{5.5 \text{ g}}{22 \text{ g/mol}} = 0.25 \text{ moles} \]

### Step 3: Determine the Number of Neutrons in One Mole of \( T_2O \)
- The molar mass of \( T_2O \) is 22 g/mol, which corresponds to the total number of protons and neutrons in the molecule.
- The atomic number of tritium (T) is 1 (1 proton), and since there are 2 tritium atoms, the total number of protons in \( T_2O \) is:
\[ \text{Total protons} = 2 \times 1 = 2 \]
- Therefore, the number of neutrons in one molecule of \( T_2O \) is:
\[ \text{Number of neutrons} = \text{Molar mass} - \text{Total protons} = 22 - 2 = 20 \]

### Step 4: Calculate the Total Number of Neutrons in 5.5 g of \( T_2O \)
- To find the total number of neutrons in 5.5 g of \( T_2O \), we multiply the number of moles by the number of neutrons per molecule and Avogadro's number (\( N_A \)):
\[ \text{Total number of neutrons} = \text{Number of moles} \times \text{Number of neutrons per molecule} \times N_A \]
Substituting the values:
\[ \text{Total number of neutrons} = 0.25 \text{ moles} \times 20 \text{ neutrons/molecule} \times N_A \]
\[ \text{Total number of neutrons} = 5N_A \]

### Final Answer
The total number of neutrons in 5.5 g of \( T_2O \) is \( 5N_A \).

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