An oxide of nitrogen has a molecular weight 92. Find the total number of electrons in one gram mole of that oxide.

Options

A. 4.6 N
B. 46 N
C. 23 N
D. 2.3 N

Explanation

To solve the problem of finding the total number of electrons in one gram mole of an oxide of nitrogen with a molecular weight of 92, we can follow these steps:

### Step 1: Determine the possible oxide of nitrogen
Given the molecular weight of the oxide is 92 g/mol, we need to identify the possible formula for the oxide. The oxides of nitrogen can be represented as \( N_xO_y \).

### Step 2: Calculate the molecular weight of common nitrogen oxides
We know the atomic weights:
- Nitrogen (N) = 14 g/mol
- Oxygen (O) = 16 g/mol

Let's check the common oxides of nitrogen:
1. \( N_2O_4 \):
- Molecular weight = \( 2 \times 14 + 4 \times 16 = 28 + 64 = 92 \) g/mol

Thus, the oxide is \( N_2O_4 \).

### Step 3: Determine the number of atoms in \( N_2O_4 \)
The formula \( N_2O_4 \) indicates:
- 2 nitrogen atoms
- 4 oxygen atoms

### Step 4: Find the number of electrons in each atom
Next, we find the number of electrons based on the atomic numbers:
- Nitrogen (N) has an atomic number of 7, thus each nitrogen atom has 7 electrons.
- Oxygen (O) has an atomic number of 8, thus each oxygen atom has 8 electrons.

### Step 5: Calculate the total number of electrons in one molecule of \( N_2O_4 \)
Now, we calculate the total number of electrons in one molecule of \( N_2O_4 \):
- Electrons from nitrogen: \( 2 \times 7 = 14 \) electrons
- Electrons from oxygen: \( 4 \times 8 = 32 \) electrons

Total electrons in one molecule of \( N_2O_4 \):
\[ 14 + 32 = 46 \text{ electrons} \]

### Step 6: Calculate the total number of electrons in one mole
Since one mole of any substance contains Avogadro's number of molecules (\( 6.022 \times 10^{23} \)), the total number of electrons in one mole of \( N_2O_4 \) is:
\[ 46 \text{ electrons/molecule} \times 6.022 \times 10^{23} \text{ molecules/mole} \]

### Final Answer
Thus, the total number of electrons in one gram mole of the oxide \( N_2O_4 \) is:
\[ 46 \text{ electrons} \]