What motivated United States interest in China and Japan in the 1840s and 1850s?
In a word, it was trade that motivated the United States's interest in China and Japan during this time period.
By this time, the US had gained a major foothold on the Pacific Coast since it had California and what is now Oregon and Washington. This made trade with Asia much more feasible. Therefore, the US started to push for greater contact with those two countries. This led to the "opening" of Japan in 1854 by Commodore Matthew Perry. When Perry went to Japan, he demanded no territory, just the right to trade. This shows that the main motive for this interest was the desire to trade and, thereby, make money.