The term of office of each member shall be five years; provided, however, that of the members first appointed, three shall be appointed for terms of one year, three for terms of two years, three for terms of three years, three for terms of four years and three for terms of five years. Other than the chairman, no member of the council who serves a full five-year term shall be eligible for reappointment during a one-year period following the expiration of his term. The governor shall designate a chairman and a vice chairman from the members of the council, to serve as such at the pleasure of the governor. The chairman shall be the chief executive officer of the council. All vacancies shall be filled for the balance of the unexpired term in the same manner as original appointments. The members of the council shall not receive any compensation for their services but shall be reimbursed for their actual and necessary expenses incurred in the performance of their duties as members of the council.