The density of Nitrogen is 1.25kg/m^3, at STP determine the density of nitrogen at 42 degres celcius and 730mmHg?

Method 1:

Consider 1 m³ of the nitrogen at STP, its mass is 1.25 kg.
Initial (STP): P₁ = 760 mmHg, V₁ = 1 m³, T₁ = 273 K
Final: P₂ = 730 mmHg, V₂ = ? m³, T₂ = (273 + 42) K = 315 K

For a fixed amount of gas: P₁V₁/T₁ = P₂V₂/T₂
Then, V₂ = V₁ × (P₁/P₂) × (T₂/T₁)
Final volume of 1.25 kg of nitrogen, V₂ = (1 m³) × (760/730) × (315/273) = 1.20 m³

Final density = m/V₂ = (1.25 kg) / (1.20 m³) = 1.04 kg/m³


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Method 2:

Gas law: PV = nRT and n = m/M, where M is the molar mass
Then: PV = (m/M)RT
PM = (m/V)RT
There PM = dRT, where d is the density

For a certain gas, M and R are constant.
Then, dT/P = R/M = costant
Hence, d₁T₁/P₁ = d₂T₂/P₂
Hence, d₂ = d₁ × (T₁/T₂) × (P₂/P₁) …… (*)

Initial (STP): d₁ = 1.25 kg/m³, T₁ = 273 K, P₁ = 760 mmHg
Finial: d₂ = ? kg/m³, T₂ = (273 + 42) K = 315 K, P₂ = 730 mmHg

Substitute the values into (*)
Final density, d₂ = (1.25 kg/m³) × (273/315) × (730/760) = 1.04 kg/m³

0 °C = 273 K; 42 °C = 315 K, so the temperature ratio is 315/273 = 1.15.
The pressure ratio is (730 mmHg)/(760 mmHg) = 0.960.

The volume varies directly with the temperature and inversely with the pressure, so the volume ratio is
(T₂/T₁)(P₂/P₁) = (1.15)(0.960) = 1.10.

The density varies inversely with the volume (for a given mass), so the new density ρ₂ = ρ₁/1.10
= (1.25 kg/m³)/1.10 = 1.14 kg/m³.

Should've asked me a few months ago. Schools out and I'm done with chem