I have a MacBook Pro Early 2011 (Model A1278) and would like to know if Corsair CMSO8GX3M1C1600C11 memory will work on it. Before making the investment in memories, can someone help me?
The memory you specified, will not work. It is PC3-12800 while the memory you need is PC3-10600.
According to Everymac.com, your particular model can support up to 16GB of memory.
Apple officially supports a maximum of 8GB of RAM, but as first confirmed by site sponsor OWC, this model actually is capable of using up to 16 GB of RAM with two 8 GB memory modules.
Personally, I always recommend upgrading to the maximum amount of memory that you can get (I believe in the mantra it's better to have and not need, than need and not have). The memory that you need for your particular MBP is the Crucial 16GB Kit (8GBx2) 2CT2K8G3S1339M