2.49g of ammonia at STP occupies a volume of 5.48 `dm^3` calculate the molar mass of ammonia.

Options

A. 13g/mol
B. 10g/mol
C. 19g/mol
D. 14g/mol

Explanation

To calculate the molar mass of ammonia (NH₃) from 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 = 5.48 dm³

### Step 2: Convert volume from dm³ to liters
Since 1 dm³ is equivalent to 1 liter, we can say:
- Volume of ammonia = 5.48 L

### Step 3: Use the molar volume of gas at STP
At Standard Temperature and Pressure (STP), 1 mole of any ideal gas occupies 22.4 L.

### Step 4: Calculate the number of moles of ammonia
Using the formula:
\[ \text{Number of moles} = \frac{\text{Volume}}{\text{Molar Volume}} \]
Substituting the values:
\[ \text{Number of moles} = \frac{5.48 \, \text{L}}{22.4 \, \text{L/mol}} \approx 0.24464 \, \text{moles} \]

### Step 5: Calculate the molar mass of ammonia
The molar mass can be calculated using the formula:
\[ \text{Molar Mass} = \frac{\text{Mass}}{\text{Number of Moles}} \]
Substituting the values:
\[ \text{Molar Mass} = \frac{2.49 \, \text{g}}{0.24464 \, \text{moles}} \approx 10.17 \, \text{g/mol} \]

### Step 6: Round to appropriate significant figures
The molar mass of ammonia is approximately 10 g/mol when rounded to two significant figures.

### Final Answer
The molar mass of ammonia (NH₃) is approximately **10 g/mol**.

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