2 Answers

PV = nRT
n = mass / mw
PV = (mass / mw) RT
(mass / V) = mw x P / (RT)
density = mw x P / (RT)
density = (17.0 g/mole) x (837/760 atm) / [(0.0821 Latm/moleK) x (328K)]
density = 0.717 g/L
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just for the record…ammonia’s not really the best example to use for this type of problem. Because it has a high degree of hydrogen bonding and tends to deviate from ideality.
If I were to do the same type of analysis via Van Der Waals equation, which includes a term for intermolecular forces, I’d find this…
(P + an² / V²) x (V – nb) = nRT
where
P = 837 /760 = 1.101 atm
a = 4.170 L² atm / mole²
b = 0.03707 L/mole
R = 0.08206 Latm/moleK
T = 273.15 + 45 = 328 K
and if I let V = 1 L…
(1.101 atm + 4.170 L² atm / mole² n² / (1L)²) x (1L – 0.03707 L/mole n) = 0.08206 Latm/moleK x 328 K x n
factoring out atm, L, canceling L², simpilfying the right side…
(1.101 + 4.170 / mole² n² / ) x (1 – 0.03707 /mole x n) = 26.92 /mole x n
so the units will end up wth n in moles.. so I’ll cancel the units for simplicity…
(1.101 + 4.170 n² ) x (1 – 0.03707 n) = 26.92 x n
1.101 – 0.0408 n + 4.170 n² – 0.1546 n³ = 26.92 n
0.1546 n³ – 4.170 n² + 26.96 n – 1.101 = 0
the solution to that cubic is n = 0.04086
so that mass NH3 = 0.04086 moles x (17.0 g / mole) = 0.695 g per the 1 L that I assumed…
so density = 0.695 g/L… difference is about 3%…

Convert pressure to atm, and T to Kelvin:
P = 837/760 = 1.10 atm
T= 45+273 = 318 K
PV = nRT
Rearrange ideal gas law to give:
n/V = P/RT = 1.10 atm/(.0821 Latm/molK) 318K = 0.0421 mol/L
multiply mol/L X g/mol to get g/L
0.0421 mol/L X 17 g/mol = 0.716 g/L