B.F. Goodrich Co. reported yesterday a 23 percent drop in first-quarter income because of slumping tire sales but, pinning hopes on its robust chemical business, said it still looks to post a fourth year of record profits.

Net income was $20.3 million ($1.20 a share on sales of $767.5 million in the first quarter. That compared with $26.4 million ($1.57) on sales of $716.8 million a year earlier, which was a record for the company.

Chemicals posted a 45 percent increase in operating profits, and Goodrich said chemical revenues this year could surpass those from the tire operations for the first time.

W.R. Grace & Co., the chemically oriented conglomerate, earned $65.08 million ($1.37 a share) in the first quarter, up from $57.06 million ($1.20) a year ago, on a rise in sales to $1.362 billion from $1.166 billion.

The company said the turnaround in the fertilizer chemical business that started last year is continuing.

Profit from Grace's petroleum operations more than doubled from a year earlier, but Grace's retailing and restaurant operations had a small loss.

Burlington Northern Inc. said yesterday its profits jumped 88 percent in the first quarter to $76.4 million ($4.70 a share) from $40.7 million ($3.13) in the same period last year.

The company, which has interests in railroads, natural resources, and real estate, said revenues climbed 38 percent to $912 million from $660 million in the first quarter in 1979.

Norman M. Lorentzen, president and chief executive officer, said the improvement resulted primarily from "better operating conditions for our railroad" and a mild winter that enabled BN to keep running with few interruptions.

American Home Products Corp. reported its net income rose to $115.74 million (72 cents a share) in the 1980 first quarter from $103.62 million (64 cents) a year earlier. Sales rose to $1.02 billion from $916.85 million from a year ago, the company said.

Alcan Aluminum reported 1980 first-quarter net earnings of $148.4 million ($1.83 a share), compared to $96.7 million ($1.19) a year ago. Revenue rose to $1.31 billion from $1.08 billion.

The company said it anticipates uncertainties in the second half, largely from a downturn in segments of the U.S. market but that demand for aluminum in world markets continues to exceed supply.

Bausch & Lomb said it had first-quarter net income of $11.09 million (93 cents a share), up from $8.06 million (68 cents) a year ago. Revenue was $133.84 million compared to $116.55 million the year before.

AMAX Inc. the large American metallurgical and mining company, earned $2.45 a share in the first quarter, up from $1.39 a year ago on 5.2 million fewer shares. Chairman Pierre Gousseland told Japanese security analysts yesterday.

Net income rose to $140.26 million on sales of $879.02 million, from $76.98 million a year ago on sales of $634.42 million.