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
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Rearranging the Ideal Gas Law to solve for n: \[ n = \frac{PV}{RT} \]
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Substitute the values: \[ n = \frac{(1.2 , \text{atm})(3.7 , \text{L})}{(0.0821 , \text{L} \cdot \text{atm} / (\text{mol} \cdot \text{K}))(290 , \text{K})} \]
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Calculate the denominator: \[ (0.0821)(290) \approx 23.829 \]
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Now calculate n: \[ n = \frac{(1.2)(3.7)}{23.829} \approx \frac{4.44}{23.829} \approx 0.186 , \text{moles} \]
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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.