Pseudoelementary reactions in the Briggs-Rauscher oscillatory reaction mechanism
What do they mean when they say the reactions are pseudoelementary?


Here is a portion of the first page:


So for the reaction (I added an H+ to the product to balance it)
$$\ce{IO3- + HIO2 + 2H+ &lt;=&gt; 2IO2 + H2O + H+},$$

they assume that the two protons attach in a fast reversible step (not sure to which of the reactants), and then there is a bimolecular reaction between the two iodine-containing intermediates X and Y:

$$\ce{IO3- + HIO2 + 2H+ &lt;=&gt;[fast] X + Y -&gt; 2IO2 + H2O + H+},$$

The rate law for this set of reactions taken together is the one given in the question.


  Are reactions involving the collision of four or three molecules more common than I thought?


No, they are rare (and slow). They could have written out the separate elementary reactions, but they probably also did not know where the protons attach and in what order, and they are not claiming to get the mechanism right. They just want to show a plausible set of reactions and rate constants that leads to the observed oscillations.


  When they write down the equations for these reactions they write them as if the stoichiometric coefficients were the order with respect to each reagent, which seems to imply that the reactions are somehow elementary, which further confuses me. 


It does not imply that. From a rate law alone you can't distinguish between mechanisms. Take these two mechanisms for example:

$$\ce{ A + H+ &lt;=&gt;[fast] AH+}$$
$$\ce{ AH+ -&gt;[slow] B + H+}$$

on the one hand and
$$\ce{ A + H+ -&gt; B}$$

on the other hand. Both will be first order in $A$ and in $\ce{H+}$.