Countable Noun:
* When referring to individual rivers with specific names, it is countable.
* Example: "The Mississippi River is the longest river in the United States."
* You can have one river, two rivers, etc.
Mass Noun:
* When referring to river water in general, it is a mass noun.
* Example: "We need to protect the quality of river water."
* You don't count individual units of river water.
Therefore, the grammatical category of "river" depends on how it is used in a sentence.