A cylinder with a capacity of 25.6 liters contains 1.04 kg of nitrogen at a pressure of 35.5 atm.

A cylinder with a capacity of 25.6 liters contains 1.04 kg of nitrogen at a pressure of 35.5 atm. Determine the gas temperature (MN2 = 28 · 10-3 kg / mol is the molar mass of nitrogen; R = 8.3 J / (mol · K) is the gas constant).

The state of the gas is described by the Clapeyron formula:
PV = mRT / M,
where P is the pressure,
V – volume,
m – gas mass,
M – molar mass,
R is the gas constant,
T is the temperature.
The molar mass of molecular nitrogen is M = 0.028 kg.
We translate the pressure in atmospheres into pascals:
1 atm = 101325 Pa.
35.5 atm = 101325 Pa * 35.5 = 3597038 Pa.
We express the temperature in terms of known parameters:
T = PVM / Rm = (3597038 Pa * 0.0256 m3 * 0.028 kg) / (8.3 J / mol * K * 1.04 kg) = 298.7 K.
Answer: 298.7 K.