It seems like you are confusing JPA with straight JDBC.
A good overview of JPA is here (see the putting it all together portion)
https://glassfish.java.net/javaee5/persistence/persistence-example.html
You are calling em.merge() with a String, when you should really be updating the object and then telling the entity manager to merge the changes (which saves them to the database).
The UPDATE statement you've crafted is sort of how you'd do it with JDBC, but you'd use a Connection/PreparedStatement with ? for parameters/etc... It seems though like your sample code is JPA based.