Two kinds of space: 空 (kōng) and 空 (kòng)

The character 空 can be pronounced either (kōng) or (kòng). How do you know when to use which tone?

空 (kōng) emphasizes the ongoing presence of space. It has volume and consequence. It is "nothing" as opposed to "something," an emptiness that exists in its own right:

空間 space
太空 outer space
天空 the sky
空氣 air
真空 a vacuum
中空 hollow
空想 fantasy, daydreams
憑空 an argument is baseless (lit: relies on nothing)
空心菜 cooking greens with hollow stems (lit: empty center greens)
目空一切 condescending (lit: the eye sees everything as mere empty space)

空 (kòng), on the other hand, emphasizes a vacancy that is immanently fill-able:

空格 a check box; a blank to fill in
空位 an empty seat
空房 an available room for rent
有空 to have free time; to be available
一片空白 a blank slate; to draw a blank
An interesting one is 空地 ，translated in dictionaries as "open space" as in 孩子喜歡在空地玩 , "kids like to play in open spaces." At first this sounds like it could mean parks or fields or the great outdoors, but a quick search on Google Images reveals that in fact 空地 refers to empty lots in cities.