2.49g of ammonia at STP occupies a volume of 3.48 `dm^3` calculate the molar mass of ammonia.

Options

A. 14g/mol
B. 16g/mol
C. 17g/mol
D. 13g/mol

Explanation

To calculate the molar mass of ammonia (NH₃) using the given data, we can follow these steps:

### Step 1: Understand the given data
- Mass of ammonia (NH₃) = 2.49 g
- Volume of ammonia at STP = 3.48 dm³ (which is equivalent to 3.48 L)

### Step 2: Use the molar volume of a gas at STP
At Standard Temperature and Pressure (STP), 1 mole of any ideal gas occupies 22.4 L.

### Step 3: Calculate the number of moles of ammonia
To find the number of moles of ammonia in the given volume, we can use the formula:
\[ \text{Number of moles} = \frac{\text{Volume of gas (L)}}{\text{Molar volume at STP (L/mol)}} \]
Substituting the values:
\[ \text{Number of moles} = \frac{3.48 \text{ L}}{22.4 \text{ L/mol}} \approx 0.1554 \text{ moles} \]

### Step 4: Calculate the molar mass of ammonia
The molar mass can be calculated using the formula:
\[ \text{Molar mass} = \frac{\text{Mass of gas (g)}}{\text{Number of moles (mol)}} \]
Substituting the values:
\[ \text{Molar mass} = \frac{2.49 \text{ g}}{0.1554 \text{ mol}} \approx 16.03 \text{ g/mol} \]

### Step 5: Conclusion
The molar mass of ammonia (NH₃) is approximately 16 g/mol.