The cylinder contains compressed oxygen at a temperature of 25 degrees Celsius and a pressure

The cylinder contains compressed oxygen at a temperature of 25 degrees Celsius and a pressure of 1.5 * 10 ^ 7 Pa. in the process of gas welding, half of the oxygen is consumed. Determine what pressure will be established in the cylinder if the gas temperature has dropped to 15 degrees Celsius.

Let’s convert the temperature from Celsius to Kelvin:

T1 = 25 ° C = 298 K;

T2 = 15 ° C = 288 K;

For the calculation, we will use the Mendeleev-Clapeyron equation:

PV = nRT, where

n is the amount of gas substance, mol;

R – universal gas constant, 8.314 J / mol;

T is temperature, K;

Р – pressure, Pa;

V – volume, m3;

P = nRT / V;

n2 = 0.5 n1;

V = const;

P2 / P1 = (n ^ 2 * R * T ^ 2 / V): (n1 * R * T1 / V) = (0.5 * n1 * T ^ 2) / (n1 * T ^ 2) = (0 .5 * 288) / 298 = 0.48

P2 = 1.5 * 10 ^ 7 * 0.48 = 7.2 * 10 ^ 6 Pa.

Answer: P2 = 7.2 * 10 ^ 6 Pa.