No more exploding rats for the staff of the International Trade Commission. The new building they will occupy at 500 E St. SW has begun going up.

The old building, a graceful, mid-19th century structure at 701 E St. NW, received widespread attention in 1983 for problems that included exposed wiring, falling plaster, a leaky roof and exploding rats (poison that was put out would cause their stomachs to burst when they drank water). The building, approximately 80,000 square feet, was one of three where ITC employes were located.

The ITC will occupy seven of the nine floors in the new building, a total of about 175,000 square feet. The building's design has been modified to include hearing rooms and other special features. The 10-year lease has an aggregate value of $41 million.

The building has exterior walls of glass and granite with a reinforced concrete frame. A tower was designed on the roof to counterpoint a church steeple across 6th Street. A rooftop terrace will feature views of the Capitol and the Potomac River area.

The staff doesn't know whether to be sorry or glad about the move. "We wanted to stay in the building and have it renovated," said Lorin Goodrich, director of administration, "but Congress decided otherwise." The cost of renovating the building was estimated at $16 million in 1982. The Smithsonian will have the responsibility of repairing the facility, which is across the street from the National Portrait Gallery.

Another recent development in commercial realty in the Washington metropolitan area:Federal Home Loan Mortgage Association leased 29,144 square feet at 2 Crystal Park, Crystal City.