How do I fix a thermometer if the mercury has separated?
You’re not going to get it cold enough with ice/salt (only goes to about -10 deg C). You’re going to need some dry ice/solvent mix (isopropanol is easiest to find, but most common organic solvents would work). Dry ice is ridiculously cheap and if you asked a grad student nicely you could probably just use a little from an area biology or chemistry department. Just pour a little solvent over some dry ice in a container. Once the bubbling stops, as long as there’s solid dry ice still visible, the liquid is at about -78 deg C. Stick the thermometer in there, tap it a bit to help the bubble escape, and try to let it warm it up slowly (or you can make matters worse). Liquid nitrogen does work too, but also leads to more frequent shattering (a lesson I keep relearning the hard way). But in all honesty, you should be able to just exchange it. A new thermometer shouldn’t come that way.