Standard Oil Co. of Ohio, dripping with cash from Alaskan oil, agreed yesterday to pay $1.8 billion for Kennecott Corp., the nation's largest copper company.

Kennecott shareholders, if they approve the deal, would receive an enormous windfall. Kennecott stock, which did not trade yesterday pending the announcement, closed Wednesday at $27 1/8. Sohio said it will pay $62 for each of the 28.5 million Kennecott shares. Even so, Sohio plainly looks on the deal as a good one, partly because of Kennecott's large undeveloped mineral reserves.

Sohio, the 13th largest U.S. refiner, had profits of $1.8 billion last year on sales of $11 billion. It is 53 percent owned by British Petroleum Co. Ltd., the largest industrial concern in the United Kingdom. BP acquired control of Sohio in exchange for BP's 53 percent share of the Prudhoe Bay oil field that is now producing 1.6 million barrels of oil a day. The British government and the Bank of England together owned nearly half of BP but it remains privately controlled.

The purchase of Kennecott, technically by merging it into a wholly-owned Sohio subsidiary, is another in a string of oil company acquisitions primarily of other oil and natural resource companies. Last week, Standard Oil Co. of California bid even more money -- $3.9 billion -- to acquire AMAX, Inc., another minerals company. However, AMAX directors rejected the offer from Socal, which already owns 20 percent of AMAX.

Atlantic Richfield Corp. bought Anaconda Copper Co., second only to Kennecott in production in the United States, in 1977.

Sohio Chairman Alton W. Whitehouse and Kennecott Chairman Thomas D. Barrow, in a joint statement, said completion of the proposed merger would require approval by Kennecott shareholders and satisfaction of other unspecified conditions. They said Kennecott shareholders would be asked to consider the proposal at a meeting sometime in May.

"This merger is an opportunity for Kennecott to move ahead aggressively with its present plans to strengthen and expand its existing operations and to develop its extensive mineral resources," said Barrow, who is to remain the mining company's chief executive after the acquisition.

Whitehouse said energy will continue to be Sohio's main business but that Sohio plans to modernize Kennecott's facilities and proceed to develop the copper producer's mineral deposits. Such undeveloped resources have been the prime attraction in several of the oil company takeovers.

Sohio also bought three coal mines and some coal reserves from United States Steel Corp. last December for $750 million.

Kennecott, vulnerable to a takeover because of its reserves and a cash-poor position, only recently settled a disruptive attempt by Curtiss-Wright Corp., an aerospace conglomerate, to acquire it. That battle lasted three years.

The battle of Kennecott and Curtiss-Wright started in 1977, at one point had each company bidding for the other, and ended in a truce in January. Under this pact, Kennecott gave up its $112 million stake in Curtiss-Wright in return for Curtiss-Wright's Dorr-Oliver process equipment subsidiary. Kennecott also paid Curtiss-Wright $168 million in cash to retrieve the Kennecott shares held by the New Jersey company.

The battle reportedly left Kennecott with its debt up $115 million, to $800 million. While Sohio had $3.9 billion in debt at the end of 1980, largely incurred as a result of paying for its share of construction of the Trans-Alaskan oil pipeline, its holdings of cash and marketable securities stood at $3.8 billion.

Kennecott's U.S. mines -- mainly in Utah, Arizona and New Mexico -- produce 400,000 tons of copper a year, 25 percent of the nation's output.

The company also produces lead and silver, but its failure to diversify on a large scale out of the copper business, where prices are around a two-year low, has posed chronic problems for Kennecott and has left its shares trading near their lowest point in a year.

In 1980, Kennecott reported profits of $192.4 million on sales of $2.3 billion, while Sohio's earnings came to $1.8 billion on sales of $11 billion.

Although Sohio has diversified into coal, the company also has said it is interested in expanding into synthetic fuels, minerals, information processing, chemicals and other high-technology businesses.