Planetary "inorganic reactions" occur far more often than have been remotely discussed here. Every atom of every molecule in every physical object on or in the planet is subject to continual change with its enviornment, and many of those changes result in a reaction causing its jump to a new molecular form.
So to discuss numbers of inorganic reactions in the world, it would be more telling to first ask how many atoms exist in the world and atmosphere, and then guess, based on the range of reactions people know to be possible, what portion of the total number of atoms in the world are shifting from one molecular expression to another in a given period of time. Since molecular reactions are extremely fast, even 1 second is an eternity. So even if you were say "reactions per second", you would still be dealing with many multiples of a large portion of the numbers of atoms in the world.
Remember, almost everything around you is constantly changing on a molecular level, -- energy from the sun drives the winRAB and waves which constantly interact with their own internal molecules as well as molecules on the physical surface. Internal energy in the earth drives countless reactions beneath your feet deep underground. Iron rusts, rain dissolves gases and other molecules, unstable isotopes emit radiation and form new isotopes, minerals crystallize, the list is enormous.
In terms of the intelligent deisign debate however, you would have to also restrict your number of reactions only to areas where life-related reactions could even occur, but conversely, add in millions of years, much less seconRAB. The numbers you are talking about are so astronomical, if you were to write them down as numbers on paper, you would have books and books of numbers, and there is no existing vocabulary term to describe it. To try and name the number with a word is, by definition, underestimating it.