Question

Ammonia gas has a molar mass of approximately 17 grams per mole. At 290K and 1.2 atm, a sample of ammonia has a volume of 3.7 L.Use the GUESS Method to find the mass of the ammonia. Given  R = 0.0821L⋅atommol⋅K

Answer 1

To find the mass of the ammonia gas using the GUESS method (Given, Unknown, Equation, Solve, and Statement), we can follow these steps:

### Given
- Molar mass of ammonia (NH₃) = 17 g/mol
- Temperature (T) = 290 K
- Pressure (P) = 1.2 atm
- Volume (V) = 3.7 L
- Ideal gas constant (R) = 0.0821 L·atm/(mol·K)

### Unknown
- Mass of ammonia (m)

### Equation
We can use the Ideal Gas Law to find the number of moles of ammonia (n):
\[ PV = nRT \]

We can then find the mass using the relationship:
\[ m = n \times \text{molar mass} \]

### Solve
1. Rearranging the Ideal Gas Law to solve for n:
\[ n = \frac{PV}{RT} \]

2. Substitute the values:
\[
n = \frac{(1.2 \, \text{atm})(3.7 \, \text{L})}{(0.0821 \, \text{L} \cdot \text{atm} / (\text{mol} \cdot \text{K}))(290 \, \text{K})}
\]

3. Calculate the denominator:
\[
(0.0821)(290) \approx 23.829
\]

4. Now calculate n:
\[
n = \frac{(1.2)(3.7)}{23.829} \approx \frac{4.44}{23.829} \approx 0.186
\, \text{moles}
\]

5. Now we can calculate the mass of ammonia:
\[
m = n \times \text{molar mass} = 0.186 \, \text{mol} \times 17 \, \text{g/mol} \approx 3.162 \, \text{g}
\]

### Statement
The mass of the ammonia gas at 290 K and 1.2 atm in a volume of 3.7 L is approximately **3.16 grams**.