cleaning up coal dust

Our house had an old coal furnace. We are remodeling the basement and when we took out the ceiling, it was full of coal dust. Got all over everything, including the new basement floor. We are having a problem getting the floor clean. Is there a product we could get that would do a good job of cleaning this up? And how should we go about doing it? Mopping it up?

Thank you in advance for your reply.

Do not use a mop, water will just make it into mud. Use a shopvac with a good (drywall type) air filter. For the record, this would be from bituminous coal, not anthracite.

Our contractor already tried a mop; not being familiar with coal dust. So now what? Lots of soap and water?