3.49g of ammonia at STP occupies a volume of 5.48 `dm^3` calculate the molar mass of ammonia.

Options

A. 16g/mol
B. 13.54g/mol
C. 14.26g/mol
D. 19g/mol

Explanation

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

### Step 1: Understand the relationship between volume and moles of gas at STP
At Standard Temperature and Pressure (STP), 1 mole of any ideal gas occupies 22.4 liters.

### Step 2: Convert the given volume from dm³ to liters
The volume of ammonia given is 5.48 dm³. Since 1 dm³ is equivalent to 1 liter, we can say:
\[ \text{Volume} = 5.48 \, \text{liters} \]

### Step 3: Calculate the number of moles of ammonia
Using the volume of ammonia, we can find the number of moles (n) using the formula:
\[ n = \frac{\text{Volume}}{22.4 \, \text{liters/mole}} \]
Substituting the values:
\[ n = \frac{5.48 \, \text{liters}}{22.4 \, \text{liters/mole}} \]
Calculating this gives:
\[ n \approx 0.24464 \, \text{moles} \]

### Step 4: Use the mass of ammonia to calculate the molar mass
The molar mass (M) can be calculated using the formula:
\[ M = \frac{\text{mass}}{\text{number of moles}} \]
Substituting the given mass of ammonia (3.49 g) and the calculated number of moles:
\[ M = \frac{3.49 \, \text{g}}{0.24464 \, \text{moles}} \]
Calculating this gives:
\[ M \approx 14.26 \, \text{g/mole} \]

### Step 5: Conclusion
The molar mass of ammonia is approximately 14.26 g/mole.