Adding a second css to sidebar

I am adding a text widget to my sidebar called News. I am using it to add a short text and a link to a page. The regular links on the sidebar uses a “>” before the text link. I don’t want to have this on my News text link. Can I add a second sidebar css? And how do I use it on an html?

I thought that if I created a #sidebar2 on my css and add <div id=”sidebar2″> it would work, but does not.

Thanks for your help.