A 12-liter cylinder contains nitrogen weighing 1.5 kg at a temperature of 37 C, what will the pressure

A 12-liter cylinder contains nitrogen weighing 1.5 kg at a temperature of 37 C, what will the pressure be if, during its heating to 50 C, 50% of the nitrogen leaves the cylinder? Find the starting nitrogen pressure.

In the ideal gas approximation, the pressure change is described by the Mendeleev-Clapeyron equation:

P = (n * R * T) / V, where

Р – pressure, Pa;

n is the amount of gas substance, mol;

R – universal gas constant, 3.14 J / (mol * K);

T is temperature, K;

V – volume, m3.

T1 = 37 ° C = 310 K;

T2 = 50 ° C = 323 K;

V = 12 l = 0.012 m3;

Let’s find the amount of nitrogen substance:

n1 (N2) = m (N2) / M (N2) = 1500/28 = 53.57 mol;

n2 (N2) = 0.5n1 (N2) = 26.785 mol;

Let’s find the initial and final pressure:

Р1 = (n1 * R * T1) / V = (53.57 * 8.314 * 310) / 0.012 = 11 505 675 Pa = 11.506 MPa;

P2 = (n2 * R * T2) / V = (26.785 * 8.314 * 323) / 0.012 = 5 994 246 Pa = 5.994 MPa.

Answer: Р1 = 11.506 MPa; P2 = 5.994 MPa.