Ok, if country_id is unique then you don't need the limit statement. Use mysql_fetch_row() instead of mysql_fetch_array(), but you really should not use these function anymore, these are deprecated and will be removed. With PDO you can do:
$row = $pdo->query('SELECT name FROM countries WHERE country_id = 15', PDO::FETCH_OBJ)->fetch();
If you're in one of those predicaments where cls.__private attributes just aren't enough since they can easily be accessed through inst._cls__private, and you need something a little more secure, here's ...