Add a class to each tag in WordPress

tag-classes.php

<?php
    $tags = get_the_tags();
    $html = '<div class="post_tags">';
    foreach ($tags as $tag){
        $tag_link = get_tag_link($tag->term_id);

        $html .= "<a href='{$tag_link}' title='{$tag->name} Tag' class='{$tag->slug}'>";
        $html .= "{$tag->name}</a>";
    }
    $html .= '</div>';
    echo $html;
?>