The function that checks if he has liked I do not know!
Library
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/css/bootstrap.min.css">
<script src="https://ajax.googleapis.com/ajax/libs/jquery/3.2.1/jquery.min.js"></script>
<script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/js/bootstrap.min.js"></script>
HTML Modal
<div id="myModal" class="modal fade">
<div class="modal-dialog">
<div class="modal-content">
<div class="modal-header">
<button type="button" class="close" data-dismiss="modal" aria-hidden="true">×</button>
<h4 class="modal-title">Modal</h4>
</div>
<div class="modal-body">
<div id="fb-root"></div>
<script>(function(d, s, id) {
var js, fjs = d.getElementsByTagName(s)[0];
if (d.getElementById(id)) return;
js = d.createElement(s); js.id = id;
js.src = "//connect.facebook.net/pt_BR/sdk.js#xfbml=1&version=v2.10";
fjs.parentNode.insertBefore(js, fjs);
}(document, 'script', 'facebook-jssdk'));</script>
<div class="fb-like" data-href="https://www.facebook.com/www.maroclub.net/" data-width="150" data-layout="standard" data-action="like" data-size="small" data-show-faces="true" data-share="true">
</div>
</div>
<div class="modal-footer">
<button type="button" class="btn btn-default" data-dismiss="modal">Fechar</button>
</div>
</div>
</div>
</div>
SCRIPT - comments in the code
//verifica se o cookie não existe ou se já está expirado
if (document.cookie.indexOf("visita=") < 0) {
//abre o modal em 10 segundos
setTimeout(function() {
$('#myModal').modal();
}, 10000);
//grava cookie
var date = new Date();
//expira em 7 dias
date.setTime(date.getTime()+(7*24*60*60*1000));
var expires = "; expires="+date.toGMTString();
document.cookie = "visita=realizada"+expires+"; path=/";
}