Why economic rent does not exist in perfect competition
Suppose the competitive price is P. If you quote at a a higher price Ph2>P, then someone else, say firm 2, will quote at a slightly lower price than you, say Ph2, and Ph1>Ph2>P. Since competition is perfect, firm 2 will capture all the market and you will go bankrupt. But firm 3 may put price Ph3 such that Ph2>Ph3>P and capture all the market. This process can be repeated until the equilibrium price is reached. 

On the other hand, if you place a price that is below the competitive price, you will go bankrupt. 

Hence, there is no economic rent because all firms in the competitive equilibrium will choose the equilibrium price which gives them an economic profit(rent) of zero.