Arc-Length Continuation Applied to the Haber Process

temperature in K

580

option

extent of reaction

K

v

The Peng–Robinson equation of state is used to compute the correction factor due to gas-phase nonideality,

K

v

, in the high-pressure synthesis of ammonia (

3

H

2

+

N

2

⇋2

NH

3

), known as the Haber process. In addition, the extent of reaction is computed. This Demonstration plots these two quantities versus pressure for temperatures ranging from 580 K to 710 K.

The extent of reaction is high and approaches one at very high pressure and low temperature, as expected from Le Chatelier's principle.

K

v

is close to one at low pressure and is considerably smaller than one for high pressure, which indicates that this correction factor must be taken into account at high pressure.

Here, the method of arc-length continuation is applied to solve the ammonia synthesis problem.