The Exxon Corp. will become the second private firm to be awarded a contract with China in current bidding for exploration and drilling rights for offshore oil, according to oil industry sources.

The sources said Exxon, despite maintaining an unusually firm position with the hard-bargaining Chinese, will sign a contract Aug. 23 with the China National Offshore Oil Corp., the agency that oversees oil exploitation in China's coastal waters.

The first U.S. company to win offshore oil rights from China was Occidental Petroleum Corp., which signed a contract Aug. 6, and a consortium led by British Petroleum also has been awarded a contract in the first round of bidding, which began a year ago and involves 33 foreign companies. The round is expected to end shortly with additional agreements between China and Caltex Petroleum Corp., Texaco, Inc., and the Japanese National Oil Co.

Since British Petroleum is partly state-owned and Occidental Chairman Armand Hammer has long maintained close ties with the Chinese government, industry sources consider the Exxon contract the first purely commercial agreement with Peking. One banker called it the first "that hasn't gone through the hoopla of state-to-state relations or political friendship."

Thus the terms of the Exxon contract will be watched closely by the industry, which has accused China since talks began in 1979 of taking an unrealistically inflexible position in its bargaining, and holding that position, despite the drop in world oil prices this year.

As is the practice with agreements involving foreign oil companies, the terms will not be made public. But it is understood that Exxon may have driven a harder deal with China than did Occidental and British Petroleum.

For example, of the 43 parcels on which the companies have bid, 22 are in the promising shallow waters of the Pearl River basin. Seismic studies of others, such as those in the Yellow Sea, hold less promise. The Chinese are asking the first round of companies awarded contracts to take less popular areas for development along with their first or second choice.

Both British Petroleum and Occidental reportedly were persuaded to accept at least one less desirable parcel, but Exxon reportedly has refused to accept the third of three offered it. The two parcels it has accepted are next to sectors at the mouth of the Pearl River that were won by British Petroleum and their consortium partners in May.

Although the official size of the Exxon area will probably not be known until the official signing, it is understood that it will be the largest awarded to any foreign company so far.

Exxon also has resisted Chinese pressure to drill quickly, and instead it decided to work only one well at a time. China wants to boost offshore production as soon as possible since onshore production has stagnated at around 2 million barrels a day. The country's major oilfields are showing signs of depletion at the very stage in China's modernization when energy and transportation should be stepped up to match growth in industry.

"The Chinese are convinced that there are tons of oil down there just waiting to be brought up, while the foreign companies think that there are only seismic indications that there may be a lot of oil to be found," said a China watcher with a foreign firm here.

Western oil officials are not encouraged by the failure of two French companies and the Japanese National Oil Co. to find oil since they began exploration in the Gulf of Tonkin and the Bohai Gulf. Those drilling rights were awarded outside the general round of bidding in early 1980. So far the only foreign company to find oil is Atlantic Richfield, which was permitted in an agreement signed outside the bidding to work an area off Hainan island in the South China Sea.

In other respects China has stood firm.

For example, although most international development contracts split the oil for 20 years after production begins, China has negotiated only 15 years with foreign companies to date, including Exxon. Similarly, while contracts typically allow the foreign company 10 years for exploration, China has set five to seven years as the norm with its foreign contracts.

Occidental agreed to commit $120 million to exploration, and, according to a source, Exxon also has made a commitment to spend a similar amount. Development costs are split between the foreign companies and the Chinese at a ratio of 49-to-51.