The Smithsonian Institution has sold the historic Belmont estate and 287 acres of surrounding land for $2 million, Smithsonian officials announced last week.

The Belmont House, a 25-room house on 82 acres in Elkridge, Md., was sold to the American Chemical Society for $800,000. The Maryland Department of Natural Resources purchased the 287-acre parcel for $1.2 million.

The house has been operated as a conference center by the Smithsonian Institution for 15 years and includes a swimming pool, tennis courts, several tenant houses, and various outbuildings.

The American Chemical Society is a nonprofit scientific and educational organization with a membership of 123,000 chemists and chemical engineers.

ACS intends to operate the conference center for its own use as well as for organizations currently served by the Smithsonian.

The land acquired by the state of Maryland will be added to Patapsco State Park.

Belmont was acquired by the Smithsonian in the early 1960s from former U.S. ambassador to Britain David Bruce, who inherited it from his cousin Howard Bruce.

The main building's 25 rooms include 15 bedrooms with 11 baths on the second floor, as well as first-floor meeting rooms and a dining room that can accommodate 32.

Recent developments in commercial real estate in the Washington area:

* The National Tooling and Machining Association expects to occupy this month its expanded headquarters in Fort Washington. The group's offices have been expanded by 15,000 square feet.

* The International Telecommunications Satellite Organization, Intelsat, broke ground last week for its new $50 million headquarters building at Connecticut Avenue and Van Ness Street NW.

Intelsat, with 106 member countries, owns and operates the satellite system used to provide about two-thirds of the world's overseas telecommunications and almost all overseas television.

The new headquarters building, which will sit on a 12-acre site, is scheduled for completion in October, 1984. The land is owned by the U.S. government and will be leased by Intelsat.

* Allstate Leasing, Inc. has broken ground for a new automobile leasing facility at 16405 Shadygrove Rd. in Gaithersburg. Allstate's facility will house offices, a leasing showroom and service area and is set to be completed in September.

* San Diego Gas and Electric Co. has relocated its Washington office from 1150 Connecticut Ave. NW to the National Capital Bank of Washington Building at 316 Pennsylvania Ave. S.E. Total aggregate lease value of the more than 1,300 square feet is about $223,000.

* United Technologies Corp. has leased 33,000 square feet in International Square-Phase III at 1825 I St. NW.

* Construction is in progress on Tektronix Inc.'s new eastern regional sales and service headquarters in Gaithersburg. The 67,000-square-foot facility will be on a 14.3-acre site off Professional Drive. It will house equipment showrooms, sales classrooms, administrative offices and a service center.

Tektronix manufactures test and measurement and computer display hardware. Donohoe Construction Co. Inc. is the general contractor, and completion is projected for late spring, 1983.

* The Virginia Beach Medical Building in Virginia Beach, Va., has been sold to the H.G. Smith Co., a real estate firm based in the District.