4.49g of ammonia at STP occupies a volume of 5.48 `dm^3` calculate the molar mass of ammonia.

Options

A. 18.35g/mol
B. 20g/mol
C. 16.48g/mol
D. 13.5g/mol

Explanation

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

### Step 1: Understand the given data
- Mass of ammonia (NH₃) = 4.49 g
- Volume of ammonia at STP = 5.48 dm³

### Step 2: Convert the volume from dm³ to liters
Since 1 dm³ is equivalent to 1 liter, we have:
- Volume = 5.48 L

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

### Step 4: Calculate the number of moles of ammonia
To find the number of moles of ammonia (n), we can use the formula:
\[ n = \frac{\text{Volume of gas (L)}}{\text{Molar volume at STP (L/mol)}} \]

Substituting the values:
\[ n = \frac{5.48 \, \text{L}}{22.4 \, \text{L/mol}} \]

Calculating this gives:
\[ n = 0.24464 \, \text{mol} \]

### Step 5: Calculate the molar mass of ammonia
The molar mass (M) can be calculated using the formula:
\[ M = \frac{\text{mass (g)}}{\text{number of moles (mol)}} \]

Substituting the values:
\[ M = \frac{4.49 \, \text{g}}{0.24464 \, \text{mol}} \]

Calculating this gives:
\[ M \approx 18.35 \, \text{g/mol} \]

### Final Answer
The molar mass of ammonia is approximately **18.35 g/mol**.

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