The Virginia Senate tonight easily approved a controversial measure that would authorize a special sales tax in the Washington suburbs to finance Metro transit operations. The legislation now goes to the House, where it faces an uncertain future.

In another victory for Northern Virginia legislators today, the region's long quest for a law school for George Mason University apparently succeded, as the House approved the proposal, 84 to 7. The measure already has passed the Senate, and Gov. John N. Dalton is expected to sign it after any technical differences between the House and Senate bills are reconciled.

The Metro sales tax bill was approved by the Senate, 30 to 10. It would provide a 1-cent increase in the current 4-cent sales tax. To become effective, voters in the three cities and two counties served by Metro would have to approve imposition of the tax in their localities before it could become effective in any of them

Northern Virginia's Senate delegation had unanimously sought passage of the Metro tax, which would earmark up to two-thirds of the $40 million the tax would produce annually to cover Metro operating deficits.

Dalton has said repeatedly he is opposed to local sales taxes, but Northern Virginia's legislators are still hoping he will sign the bill if it passes in the House. It was the House last year that failed by one vote to approve similar legislation after it had passed in the Senate.

Despite today's easy passage of the Metro tax bill in the Senate, several legislators raised objections to making a special exception for Northern Virginia by allowing the use of a local sales tax increase to meet new revenue demands.

"We've already been good Samaritans in helping out their system up there," said Sen. Edward E. Willey (D-Richmond), who read aloud figures he said he got from Dalton's office that showed direct or indirect state aid to Northern Virginia's transportation needs totaling $208.9 million.

"All of our localities are hurting for some kind of tax relief," Willey said. He added that Northern Virginia's chance to hold down its property taxes by increasing the sales tax "should be extended to everyone in the state on an equal basis."

But Sen. Omer L. Hirst (D-Fairfax) the prime sponsor of the bill as leader of the Northern Virginia delegation to the General Assembly, said the measure was "critical" to completion and maintenance of the 100-mile Metro rail system.

"We have to have a vehicle to create a dedicated revenue source to operate the system," said Hirst, adding that the Metro is used by about 500,000 riders a day.

And Sen. Charles L. Waddell (D-Loudoun) said Northern Virginia had long ago "declared war on one-man, one-car" when it joined in a tripartite agreement with Maryland and the District of Columbia in 1958 to build Metro.

The bill's passage in the Senate brought a warning from its non-Northern Virginian supporters that any future money requests might not fare as well.

"I am convinced they have a problem," said Sen. Hunter B. Andrews (D-Hampton), who voted for the bill. "But when the bleeding hearts north of the Occoquan say they need more money, we will have every right to say in the future that we gave you something we wouldn't give ourselves."

The law school approved today for George Mason University has been a major goal of Northern Virginia legislators for years, but their proposal has foundered in the past on the skepticism of state officials, who questioned the need for creating a third state law school in Virginia.

Acquisition of the International School of Law last year by the George Mason University Foundation neutralized most of the opposition. The bills approved by both houses of the assembly permit a merger between the state university in Fairfax City and the law school under a plan that is expected to minimize costs to the state.

The law school owns a 45,000 square foot building in an 11-acre shopping center in Arlington and proponents of the merger contend that income from the commercial property will largely offset costs of operating the school.

Del. Dorothy S. McDiarmid (D-Fairfax) promised the House during debate on the bill yesterday that the school will require no state appropriations before the 1980-82 budget period. "This is not a lame gift horse," she said, "it young, healthy and growing."

Approval of the law school was a major victory for the Northern Virginia delegation, especially for Sen. Omer L. Hirst (D-Fairfax), who is retiring from the Senate this year as the senior legislator from the Washington suburbs.

The delegation managed to win General Assembly approval of the bill despite continued opposition from the state Council on Higher Education. The council again recommended rejection of the proposal in December. It said the state should spend its money on upgrading salaries and facilities at existing law schools at the University of Virginia in Charlottesville and the College of William and Mary in Williamsburg.

The well-orchestrated lobbying campaign for the school included several trips to Richmond by the 420 International School of Law students. Their personal appeals to skeptical legislators apparently changed some votes.

Of the 19 Norghern Virginia delegates, all but Del. Robert L. Thoburn (R-Fairfax), voted for the law school bill.