This is the 2075th most frequent Russian word.
китаю
The word "китаю" is the dative form of "Китай," meaning "to China" in English.
"Китаю" is used here to refer directly to the country China as an indirect object of the verb.
Я написала письмо китаю.
I wrote a letter to China.
"Китаю" is used in this context to indicate a motion toward or direction to the country China.
Он часто ездит в китаю.
He often travels to China.
"Китаю" in this sentence denotes location, specifying that the action took place within China and involves a prepositional structure.