3.49g of ammonia at STP occupies a volume of 4.48 `dm^3` calculate the molar mass of ammonia.

Options

A. 17.45 g/mol
B. 13.45 g/mol
C. 15.59 g/mol
D. None of these

Explanation

To calculate the molar mass of ammonia (NH₃) given that 3.49 g of ammonia occupies a volume of 4.48 dm³ at STP, we can follow these steps:

### Step 1: Understand the relationship between volume and molar mass at STP
At standard temperature and pressure (STP), 1 mole of any ideal gas occupies a volume of 22.4 liters (or 22.4 dm³).

### Step 2: Convert the given volume to liters
The volume of ammonia given is 4.48 dm³, which is equivalent to 4.48 liters.

### Step 3: Calculate the number of moles of ammonia
Using the volume of ammonia and the molar volume at STP, we can calculate the number of moles of ammonia (n) using the formula:
\[ n = \frac{\text{Volume of gas at STP}}{\text{Molar volume at STP}} \]
\[ n = \frac{4.48 \, \text{liters}}{22.4 \, \text{liters/mole}} \]

### Step 4: Perform the calculation
Calculating the number of moles:
\[ n = \frac{4.48}{22.4} = 0.2 \, \text{moles} \]

### Step 5: Calculate the molar mass of ammonia
The molar mass (M) can be calculated using the formula:
\[ M = \frac{\text{mass of gas}}{\text{number of moles}} \]
Given that the mass of ammonia is 3.49 g, we can substitute the values:
\[ M = \frac{3.49 \, \text{g}}{0.2 \, \text{moles}} \]

### Step 6: Perform the calculation
Calculating the molar mass:
\[ M = \frac{3.49}{0.2} = 17.45 \, \text{g/mol} \]

### Conclusion
The molar mass of ammonia (NH₃) is approximately 17.45 g/mol.

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