Hougen-Watson formula

Section 9.2. Rate-controlling steps the Hougen-Watson formula... 

The Hougen-Watson formula is derived in terms of fractional surface coverage, and so does not explicitly contain the total of catalytic sites, qE. Otherwise it gives the same results as the long-hand derivation shown previously. 

The Hougen-Watson formula allows this to be done more quickly. 

Limitations. The Hougen-Watson formula is widely used, but has its limitations. Specifically, it assumes ... 

The Hougen-Watson formula presupposes the surface reaction to occur in a single step. This is rarely the case, and may often not even be an acceptable approximation. To reduce the mathematical complexity introduced by a multistep surface reaction, the practical engineer will then look for other simplifications that do not entail undue loss of accuracy. Here, the concept of relative abundance of adsorbed species on the catalyst surface is a very useful tool. 

The reaction orders are the same as in eqn 9.9, obtained from the Hougen-Watson formula, only the physical interpretation of the coefficient k is different. 

Although the Hougen-Watson formula presumes the surface reaction to occur in a single step, it may provide a good approximation in more complex cases. This helps to explain its popularity and success rate. 

Self-acceleration requires the denominator of the rate equation to decrease more steeply with decreasing reactant concentration than does the numerator. In the general Hougen-Watson formula... 

This work was exploratory research, not process development, and predated the Hougen-Watson formula. Despite its shortcomings, it serves admirably to demonstrate that a model meeting all other criteria may nevertheless have to be rejected if its predictions fail. However, its flaws also show that older work, even if reproduced in respected texts, cannot be accepted uncritically. 

As in homogeneous catalysis, the existence of a most abundant catalyst-surface species (macs) or one or several low-abundance catalyst-surface species (lacs) can greatly simplify the mathematics of multistep surface reactions. In some cases, mathematics reduces to that of a single reaction step, so that the Hougen-Watson formula becomes applicable. 

Langmuir-Hishelwood-Hougen-Watson (LHHW) formulation, 21 341 Langmuir isotherm, 1 592-593, 626 11 169 Langmuir monolayer formation, 17 56 Lanham Act, 25 259, 261, 265 Lanicor, molecular formula and structure, 5 98t... 

For a reaction of such complexity as methanation (or FTS) an exact kinetic theory is actually out of the question. One has to introduce one or more approximations. The usual assumption made is that one reaction step is rate determining (r.d.s.) and other steps are in equilibrium or steady state. Adsorption equilibria are described by Langmuir formulas (Langmuir-Hinshelwood, Hougen-Watson... 

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