By taking the easier classes, you're likely shortchanging your future self.
Yes, most web development does not require much mathematics (and probably no physics or chemistry), but you may find after a few years of doing it you long to work on more challenging problems. Most of the most interesting problems in software require math.
Most programming does not require chemistry or physics knowledge (with game development being a huge exception), but study in these fields is valuable in that they give you practice in applying match to real-world situations. For example, knowledge in physics is extremely valuable in finance.
By studying the hard stuff, you'll get better at learning complex topics. Given the rapid rate of change in software, that's probably the most valuable skill you can have. In fact, all things being equal, I usually prefer to hire physics majors over computer science majors because a demonstrated capability in physics implies an ability to pick up programming topics more quickly than just a comp. sci. degree.
Economics is a useful subject, but honestly, you cannot do anything significant in that without good knowledge of mathematics. In fact, although I was a Comp. Sci. major, I had an easier time in upperclass-level economics than most economics majors because of the calculus I had studied.
Finally, it's a lot easier to pick up knowledge of fields like civics and philosophy outside of the classroom than fields like physics and chemistry. You're likely paying a lot for your education (in time, if not money), so get the most of it! With discipline, you should still have plenty of free time, and you don't want to find yourself stuck in a field you hate if you get sick of basic web programming in a few years. Studying the hard stuff will give you lots of flexibility.