Norfolk and Western Railway reported yesterday its largest first-quarter profit ever, thanks to record-shattering coal exports.

The Roanoke-based railroad, scheduled to merge with Southern Railway on June 1, posted a net income of more than $89 million ($2.70 a share) in the first three months of 1982. That represents an increase of 13 percent from last year's record first quarter of $78.6 million ($2.43).

Robert Claytor, N&W president, said the railway originated 10.1 million tons of coal for export in the first quarter, surpassing its previous record by one million tons.

First-quarter operating revenues were a record $486 million, the railroad said, up 8 percent from last year's $449 million. At the same time, operating expenses increased 9 percent, to nearly $359 million, from $329 million.

While demand for export coal was soaring, the amount of coal shipped to domestic steel makers and utilities was declining, railroad figures show. In the first quarter of 1982, steel markets took 4.1 million tons of coal and utilities bought 6.7 million tons. Last year, the figures were 5.5 million and 7.2 million, respectively.

The continuing recession also showed up in low levels of merchandise traffic, down 7 percent from last year's first quarter.

Claytor predicted that seasonal factors and weaker demand for export coal will mean that profits in the second quarter will not be as high as those in the first quarter.

Union Trust Bancorp, parent company of Union Trust Co. of Maryland, posted a 64 percent gain in first-quarter 1982 income, the Baltimore firm announced yesterday. Net income came to $3.8 million ($1.53), compared with $2.3 million (93 cents) for last year's first quarter.

For the period ending March 31, Union's asets were $1.5 billion, total deposits were $1.05 billion and loans were $890 million.

Union Trust will pay a quarterly dividend of 42 1/2 cents a share on May 14.