Question

What special power was given only to the House of Representatives?

Answer 1

Have the sole power of impeachment.
Originate all bills of raising revenue.
Elect a President of the U.S. in case the Presidential electors fail to elect one.

Answer 2

The power of impeachment (meaning the house can bring charges against the president), the power to elect the President (only in circumstances in which none of the candidates receives a majority of the electoral vote), and the power to initiate bills (meaning everything that involves taxes, spending and funding must first begin in the House.)