Recently I saw a professor advertising an open PhD position in his group. He asked students to submit CV and motivation letter. I sent an email but received no reply. Two weeks after that I sent a follow up email, but still no reply. How much time would be reasonable to wait? Should I give up already? I know the professor doesn't owe me a reply, but since the position was advertised I thought he would sent an acknowledgement that the application was received. Am I wrong? Is that the common thing to do?
Some people are spectacularly slow. I got a phone call inviting me to an interview for a PhD at one university four months after I'd given up, applied elsewhere, had the interview, received the offer, and accepted that offer. Wait as little or as much time as you feel like waiting, frankly. I'd certainly be looking for other PhD opportunities, regardless.
Professors will often ignore emails that are not important to them. Many professors get a flood of emails everyday, and are willing to spend only so much time replying to them. While a response indicating they received your CV would be nice, I wouldn't expect it. One tactic that occasionally works is to contact one of the professor's Ph.D students. Every now and then someone will be nice enough to let you know what's going on if they know, or ask around for you. I wouldn't hold my breath, though. Just do you what you have to do to advance your academic career, even if it means applying and accepting a position somewhere else. You can always say sorry to choice number 2 if choice number 1 gets back to you later with a positive response.