The sixth session of the marathon U.N. Conference on the Law of the Sea opened yesterday in an atmosphere of optimism as delegates from 150 nations prepared to concentrate on the key issue of devising a system for the equitable exploitation of deep sea mineral resources.

U.N. Secretary General Kurt Waldheim said at a news conference that he is "confident that this session will produce the necessary breakthrough."

The most conservative estimate of the stake involved is $300 billion, most of it in golfball-size nodules containing minerals.

If this eight-week session fails to break the deadlock, chief American negotiator Elliot L. Richardson has warned, "We may not get this close for years to come." Richardson indicated that the only fallback position the administration could adopt in the event of a failure would be to endorse legislation that would guarantee financing for American companies pressing to move into the international zone on a unilateral basis.

If a compromise can be reached on the exploitation of deep-sea minerals, the expectation is that the other issues - such as fishery rights, freedom for ocean research, pollution control, disputed settlement, and the limits of national jurisdiction in coastal waters - can be quickly wrapped up.