E. I. du Pont de Nemours, the nation's largest chemical company, yesterday reported gains of 28 per cent in fourth-quarter profits and 18.7 per cent in profits for all of 1977.

Du Pont said its fourth-quarter profits totalled $119 million ($2.42 a share), up from the 1976 quarter's $92.9 million ($1.87). Sales were $2.33 billion, up 13.6 per cent from $2.05 billion a year ago.

For all of 1977, profits were $545 million ($11.06), up from $459 million ($9.30). Sales were $9.44 billion, up 13 per cent from 1976's $8.36 billion.

Du Pont said the 1977 sales figure represented an 8 per cent rise in volume, with the rest of the increase reflecting higher prices.

Atlantic Richfield Co. yesterday reported a 22 percent increase in earnings to $5.76 a share in 1977 from $5.04 a year earlier.

The company also announced a dividend increase to 60 cents a share from 50 cents. The higher rate will be paid Feb. 3.

Arco had 1977 net income of $701.51 million on sales of $11.4 billion compared with $575.18 million on sales of $8.9 billion in 1976.

In the fourth quarter, Arco earned $171.13 million ($1.40 a share) on sales of $2.95 billion compared with $124.87 million ($1.09) a year earlier on sales of $1.4 billion.

Chairman Robert O. Anderson said the 1977 profit gain reflected the inclusion of its Anaconda Co. results, production from the Alaska North Slope and the high level of investment tax credits available to the company because of the completion of several large capital projects.

Three M Co. yesterday reported a 22.5 per cent gain in fourth-quarter profits to 94 cents a share from 77 cents a year earlier. Profits for the year were $3.57 a share against $2.94 in 1976.

Net income for the quarter was $108.9 million on sales of $1.008 billion against $88.9 million on sales of $875.4 million a year earlier. The year's profits were $412.9 million on sales of $3.98 billion against $338.5 million in 1976 on sales of $3.514 billion.

Chairman Raymond H. Herzog said 3 M sales grew faster both in the United States and abroad than the economies of the countries the company operate in. He said this speaks extremely well for the productivity of all the company's personnel.

Trans World Airlines yesterday reported a 75.9 per cent gain in earnings for 1977 to $64.8 million ($3.83 a share) on a 13.9 per cent rise in revenues to $3.33 billion.

Fourth-quarter profit was $11.4 million (52 cents) against a loss of 20 cents a share a year ago on a 16.4 per cent rise in revenues to $864 million.

In 1976, TWA earned $36.8 million ($2.51) on revenues of $2.82 billion.

Chairman Edwin Smart said the air-line's pretax profit was up only 1.2 percent, but the Hilton Hotel and Canteen Corp had excellent gains.

Burlington Northern, Inc., has reported net income of $20.3 million ($1.46 a share) in the fourth quarter of 1977 compared with $22.1 million ($1.72) in the same quarter of 1976.

The transportation and natural resources firm said net income for 1977 was $76.9 million ($5.74) compared with $73 million ($5.69) in 1976.

Operating revenue and sales for the fourth quarter of 1977 were $546.6 million compared with $497.8 million in the same 1976 quarter. For 1977, operating revenue and sales totaled $2.109 billion compared with $1.896 billion for 1976.

Continental Illinois Corp., parent of Continental Illinois National Bank and Trust Co. of Chicago, the nation's eighth largest commercial bank, yesterday reported record income before security transactions of $144.2 million in 1977, up 10.2 percent from $130.8 million the previous year. Income per share before security transactions was $4.05 compared with $3.72 in 1976.

Fourth-quarter income before security transactions was $41.6 million ($1.16 a share), up 18.1 percent from the previous record level of $35.2 million (99 cents) reported in the same period in 1976.