What can I make with Alchemist's Supplies?

Question

The page on D&D Beyond for Alchemist's Supplies doesn't specify what if anything you can make. Other tool are more obvious in what they're for, like the Forgery Kit is for making forgeries:

This small box contains a variety of papers and parchments, pens and inks, seals and sealing wax, gold and silver leaf, and other supplies necessary to create convincing forgeries of physical documents. Proficiency with this kit lets you add your proficiency bonus to any ability checks you make to create a physical forgery of a document.

But the text for the Alchemist's Supplies is much more vague:

These special tools include the items needed to pursue a craft or trade. Proficiency with a set of artisan's tools lets you add your proficiency bonus to any ability checks you make using the tools in your craft. Each type of artisan's tools requires a separate proficiency.

Is this listed in a book, or is it left up to the DM and Player to decide?

Answer 1

Acid, alchemist’s fire, antitoxin, oil, perfume, or soap.

We see in Xanathar's Guide to Everything under "Alchemist's Supplies" in the Tool Descriptions section (p. 79):

Alchemical Crafting. You can use this tool proficiency to create alchemical items. A character can spend money to collect raw materials, which weigh 1 pound for every 50 gp spent. The DM can allow a character to make a check using the indicated skill with advantage. As part of a long rest, you can use alchemist’s supplies to make one dose of acid, alchemist’s fire, antitoxin, oil, perfume, or soap. Subtract half the value of the created item from the total gp worth of raw materials you are carrying.

The Tool Descriptions section of Xanathar's Guide adds quite a bit more detail to many of the artisan tools found in the Player's Handbook. Here is a helpful table:

Item	Value	PHB Page
Acid (vial)	25 gp	p. 148
Alchemist's Fire (flask)	50 gp	p. 148-151
Antitoxin	50 gp	p. 151
Oil (flask)	1 sp	p. 152
Perfume (vial)	5 gp	p. 150
Soap	2 cp	p. 150

Potion of Cold Resistance

Additionally, Icewind Dale: Rime of the Frostmaiden provides another use for alchemist's supplies. With the heart of an ice troll (Icewind Dale: Rime of the Frostmaiden, p. 295), a character proficient in alchemist's supplies can craft a potion of resistance (cold) (Dungeon Master's Guide, p. 188):

A creature proficient with alchemist's supplies can squeeze enough residual fluid out of the heart to mix with other alchemical ingredients, creating one potion of resistance (cold). It takes 1 hour to create this potion.