Using the is_page() condition in comment file

G’day all,

I am trying to use the code below in my comments.php file to output nothing on a page when comments are closed, and ‘Comments are closed’ on posts when comments are closed.

<?php if(is_page()) : ?>
      <!-- Is a page so show nothing -->
 <?php else : ?>
      <p class="nocomments">Comments are closed.</p>
 <?php  endif; ?>

Any help is much appreciated