How to add a css class to sidebar first render
Create a template file with name region--sidebar-first.tpl.php in side the your theme template folder. Copy below code to inside the newly created template file 

&lt;?php if ($content): ?&gt;
     &lt;div class="my_class &lt;?php print $classes; ?&gt;"&gt;
       &lt;?php print $content; ?&gt;
     &lt;/div&gt;
  &lt;?php endif; ?&gt;


replace my_class with you desire class name, clear the drupal cache. It will wrap a new class on the sidebar first region. Good luck