I'm trying to find out why this experiment takes so long to run. I posted a similar question in the biology section but I think this question deals more with the chemistry aspect.
In most reactions, the activity is happening everywhere. Pick any volume of the reaction and you will find the reaction occurring at its particular rate. The Miller Urey experiment has this spark... it's the only place where reactants are being 'stimulated' to react. It isn't a particularly large volume relative to the whole.