1.49g of ammonia at STP occupies a volume of 2.48 `dm^3` calculate the molar mass of ammonia.

Options

A. 13.45g/mol
B. 17.45g/mol
C. 16.48g/mol
D. None of these

Explanation

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

### Step 1: Understand the Given Data
We have:
- Mass of ammonia (NH₃) = 1.49 g
- Volume occupied by ammonia at STP = 2.48 dm³ (which is equivalent to 2.48 L)

### Step 2: Use the Ideal Gas Law Concept
At Standard Temperature and Pressure (STP), one mole of any ideal gas occupies 22.4 L.

### Step 3: Calculate the Number of Moles of Ammonia
To find the number of moles (n) of ammonia, we can use the formula:
\[ n = \frac{\text{Volume}}{\text{Molar Volume at STP}} \]
Where the molar volume at STP is 22.4 L.

Substituting the values:
\[ n = \frac{2.48 \, \text{L}}{22.4 \, \text{L/mol}} \]

### Step 4: Perform the Calculation
Calculating the number of moles:
\[ n = \frac{2.48}{22.4} \approx 0.1107 \, \text{mol} \]

### Step 5: Calculate the Molar Mass of Ammonia
The molar mass (M) can be calculated using the formula:
\[ M = \frac{\text{Mass}}{\text{Number of Moles}} \]
Substituting the known values:
\[ M = \frac{1.49 \, \text{g}}{0.1107 \, \text{mol}} \]

### Step 6: Perform the Calculation
Calculating the molar mass:
\[ M \approx \frac{1.49}{0.1107} \approx 13.45 \, \text{g/mol} \]

### Final Answer
The molar mass of ammonia (NH₃) is approximately **13.45 g/mol**.

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