amazon ec2 - Approximately, how many writes can a EC2 large dedicated Mongo server handle?

Let's assume that it was only writes.
Each "document" inserted is less than 140 characters.

How many writes can this database handle?

Answer

EC2 is notorious for inconsistent throughput. There is no way to answer this question reliably, and even testing this in "production" is going to be problematic because of the varied nature of your platform.

If you want to load-test your application, you need a different platform, and really should be using a hosted (or better, leased) server environment.

With that said, to maximize throughput, use SSD drives, ensure that at least your indexes can remain in memory and that they're useful indexes (though keeping your indexes + db in memory is even more ideal), and shard. (Keep in mind that sharding increases complexity, especially on the backup/recovery front.