What are the total number of action potentials in the human brain?
If firing rate is from 1 Hz to 200 Hz, 100 trillion to 20 quadrillion synaptic firings. Neuronal (say, measured from soma) firings  will add up to 86 billion to 17.2 trillion action potentials per second.

It important to remember, that synaptic firings "sum up" in soma or interfere between each other, so the are more of those.
Read more: http://neuroblog.stanford.edu/?p=4541