A compounds contains 69.5% oxygen and 30.5 % nitrogen and its molecular weight is 92. The formula of that compound is :-

Options

A. `N_(2)O`
B. `NO_(2)`
C. `N_(2)O_(4)`
D. `N_(2)O_(5)`

Answer

To solve the problem, we need to determine the molecular formula of a compound that contains 69.5% oxygen and 30.5% nitrogen, with a molecular weight of 92 g/mol. Here’s a step-by-step solution:

### Step 1: Calculate the moles of each element
We start by assuming we have 100 grams of the compound, which makes it easier to convert percentages to grams.

- Mass of Nitrogen (N) = 30.5 g
- Mass of Oxygen (O) = 69.5 g

Next, we calculate the number of moles of each element using their atomic masses:
- Atomic mass of Nitrogen (N) = 14 g/mol
- Atomic mass of Oxygen (O) = 16 g/mol

**Moles of Nitrogen:**
\[ \text{Moles of N} = \frac{30.5 \text{ g}}{14 \text{ g/mol}} \approx 2.18 \text{ moles} \]

**Moles of Oxygen:**
\[ \text{Moles of O} = \frac{69.5 \text{ g}}{16 \text{ g/mol}} \approx 4.34 \text{ moles} \]

### Step 2: Determine the simplest molar ratio
Now we need to find the simplest ratio of moles of nitrogen to moles of oxygen.

To do this, we divide the number of moles of each element by the smallest number of moles calculated:

- For Nitrogen:
\[ \frac{2.18}{2.18} = 1 \]

- For Oxygen:
\[ \frac{4.34}{2.18} = 2 \]

Thus, the simplest molar ratio is 1:2.

### Step 3: Write the empirical formula
From the simplest molar ratio, we can write the empirical formula:
\[ \text{Empirical formula} = \text{N}_1\text{O}_2 \Rightarrow \text{NO}_2 \]

### Step 4: Calculate the empirical formula weight
Next, we calculate the empirical formula weight:
\[ \text{Empirical formula weight} = \text{Atomic mass of N} + 2 \times \text{Atomic mass of O} = 14 + 2 \times 16 = 14 + 32 = 46 \text{ g/mol} \]

### Step 5: Determine the value of n
Now, we can find the value of \( n \) using the molecular weight of the compound:
\[ n = \frac{\text{Molecular weight}}{\text{Empirical formula weight}} = \frac{92 \text{ g/mol}}{46 \text{ g/mol}} = 2 \]

### Step 6: Write the molecular formula
Finally, we can write the molecular formula by multiplying the subscripts in the empirical formula by \( n \):
\[ \text{Molecular formula} = \text{(NO}_2)_2 = \text{N}_2\text{O}_4 \]

### Final Answer
The molecular formula of the compound is \( \text{N}_2\text{O}_4 \).

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