`7.5` grams of a gas occupy `5.8` litres of volume at STP the gas is

Options

A. (a)`NO`
B. (b)`N_(2)O`
C. (c )`CO`
D. (d)`CO_(2)`

Explanation

To identify the gas based on the given data, we will follow these steps:

### Step 1: Calculate the number of moles of gas
At Standard Temperature and Pressure (STP), one mole of any gas occupies 22.4 liters. We can calculate the number of moles of the gas using the formula:

\[ \text{Number of moles} = \frac{\text{Volume of gas}}{\text{Volume of one mole at STP}} = \frac{5.8 \text{ L}}{22.4 \text{ L/mol}} \]

### Step 2: Perform the calculation
Now, we will perform the calculation:

\[ \text{Number of moles} = \frac{5.8}{22.4} \approx 0.2589 \text{ moles} \]

### Step 3: Calculate the molecular mass of the gas
Using the mass of the gas and the number of moles calculated, we can find the molecular mass using the formula:

\[ \text{Molecular mass} = \frac{\text{Mass of gas}}{\text{Number of moles}} = \frac{7.5 \text{ g}}{0.2589 \text{ moles}} \]

### Step 4: Perform the calculation
Now, we will perform the calculation:

\[ \text{Molecular mass} \approx \frac{7.5}{0.2589} \approx 29.0 \text{ g/mol} \]

### Step 5: Identify the gas based on molecular mass
Now we need to compare the calculated molecular mass (approximately 30 g/mol) with the molecular masses of the options provided.

1. **NO (Nitric Oxide)**:
- Nitrogen (N) = 14 g/mol
- Oxygen (O) = 16 g/mol
- Molecular mass = 14 + 16 = 30 g/mol (matches)

2. **N2O (Dinitrogen Monoxide)**:
- Nitrogen (N) = 14 g/mol × 2 = 28 g/mol
- Oxygen (O) = 16 g/mol
- Molecular mass = 28 + 16 = 44 g/mol (does not match)

3. **CO (Carbon Monoxide)**:
- Carbon (C) = 12 g/mol
- Oxygen (O) = 16 g/mol
- Molecular mass = 12 + 16 = 28 g/mol (does not match)

4. **CO2 (Carbon Dioxide)**:
- Carbon (C) = 12 g/mol
- Oxygen (O) = 16 g/mol × 2 = 32 g/mol
- Molecular mass = 12 + 32 = 44 g/mol (does not match)

### Conclusion
The only gas that matches the calculated molecular mass of approximately 30 g/mol is **NO (Nitric Oxide)**.

### Final Answer
The gas is **NO (Nitric Oxide)**.

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