A vessel with a volume of 1 liter contains 0.28 g of nitrogen. Nitrogen is heated to a temperature of 1500 ° C.

A vessel with a volume of 1 liter contains 0.28 g of nitrogen. Nitrogen is heated to a temperature of 1500 ° C. At this temperature, 30% of nitrogen molecules dissociated into atoms. Determine the pressure in the vessel.

Given: V = 1 liter = 1 * 10-3 m3;

m = 0.0028 kilograms;

t = 1500 ° С – we will translate into SI system: T = 1500 + 273 = 1773 K;

Find: p -?

Decision:

Let N be the number of molecules before the start of dissociation.

Therefore, N = (Na * m) / M $;
Since about 30% of the molecules are dissociated into atoms, this means that the number of molecules in the vessel has changed. Thus, the vessel contains molecules 0.7 N – ((100 – 30) / 100 = 0.7) and atoms, their number will be 0.6 N. Partial pressure (p) of the gas p1 = (0.7 * k * T * N) / V, and the pressure of the atoms is p2 = (0.6 * k * T * N) / V.

The total pressure on the walls of the vessel will be the sum of these pressures, that is:
P = p1 + p2 = (1.3 * R * T * m) / (MV),

P = (1.3 * 8.31 * 1773 * 0.0028) / (0.00014 * 0.001) = 1.92 * 105 Pa,

Answer: 1.92 * 105 Pa.