In each city of the second class, the city council shall elect one of its own body who shall be styled the president of the city council and who shall preside at all meetings of the city council in the absence of the mayor. In the absence of the president, the city council shall elect one of its own body to occupy his or her place temporarily, who shall be styled acting president of the city council. The president, and acting president, when occupying the place of the mayor, shall have the same privileges as other members of the city council; and all acts of the president or acting president, while so acting, shall be as binding upon the city council and upon the city as if done by the mayor.