I need to remove some old, but very thin yellow adhesive from a concrete floor. The adhesive was used to glue a carpet to the floor. I have been using diluted muriatic acid and a metal hand-brush ("elbow grease"), but it it really difficult to take it off. It the acid is too strong, it etches the surface too much and this is not desired because the floor is decorative with a tiled border.

You would be better off using something like paint remover to attack the glue and not the concrete. Muratic acid is good for removing alkaline minerals or mortar splatters from concrete, but not organics like adhesive. Lye might work on older adhesives, but not on some of the newer synthetics.

If you use paint remover, be very careful with the fumes. They are both toxic and flammable. You might spread the remover, cover it with a plastic sheet, let it work, and then clean up the adhesive.

Has it come off yet?