To find the mass of the ammonia gas, we can use the Ideal Gas Law, which is represented by the equation \( PV = nRT \). Here, \( n \) represents the number of moles of the gas, which can be calculated using the rearranged equation \( n = \frac{PV}{RT} \). Once we find the number of moles, we can multiply it by the molar mass of ammonia (17 g/mol) to get the mass.
Now, substituting the given values into the equation:
- \( P = 1.2 , \text{atm} \)
- \( V = 3.7 , \text{L} \)
- \( R = 0.08211 , \text{atm·L/(mol·K)} \)
- \( T = 290 , \text{K} \)
We calculate \( n \): \[ n = \frac{PV}{RT} = \frac{(1.2 , \text{atm})(3.7 , \text{L})}{(0.08211 , \text{atm·L/(mol·K)})(290 , \text{K})} \]
Calculating the denominator: \[ RT = (0.08211)(290) \approx 23.9 , \text{atm·L/mol} \]
Now we can calculate \( n \): \[ n = \frac{(1.2)(3.7)}{23.9} \approx \frac{4.44}{23.9} \approx 0.185 , \text{mol} \]
Next, we find the mass of the ammonia: \[ \text{mass} = n \times \text{molar mass} = 0.185 , \text{mol} \times 17 , \text{g/mol} \approx 3.145 , \text{g} \]
Thus, the mass of the ammonia is approximately 3.15 grams.
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