How long should a graduate school statement of intent be? I'm attempting to apply to a graduate program for medicinal chemistry and the prompt for the statement of intent doesn't explicitly state a page length. Should I assume about one page? And are paragraphs generally single spaced or double spaced?
It depends on the program, but if no requirement is set, I would go for about 500 words. That's about two pages double-spaced. You want to be to the point in these essays. Too much rambling may turn the reader off.

I never turn anything in single-space. Double-spaced documents help for readability. It's up to you, but I suggest double-spacing.