Earlier quoted context omitted.
Has anyone who's been hackernews'd done an analysis on the load numbers? Back in the day there was http://en.wikipedia.org/wiki/Slashdot_effect#Notes_and_refer...
I got about 12k people through to my blog post "Thanks Louis C.K now here's my dad" post the other day, and then about 4,000 of them clicked through to nickdooley.com (which is on the same server). I had already increased my MaxClients setting to 120 a few weeks previously when I got about the same number through to "Your templating engine sucks and everything you've ever written is spaghetti code" post but I forgot…
A conservative estimate of 20MB per PHP process would already put the requirements for 220 of them at over 4GB (twice what you have) and that's not allowing anything for the OS and anything else running on the machine. Its not an exact science figuring out the appropriate MaxClients, but you should find out how much the rest of the machine needs, look up the average Apache process size (ps), divide the available memory by that and then reduce it a little. Use this as you starting point for figuring out the MaxClients. Keep an eye on the available free memory for a while (vmstat) and gradually up that limit until you reach a comfortable working level for the setting.