So, under the Fighter's fighting styles, Dueling says
"When you are wielding a melee weapon in one hand and no other
weapons, you gain a +2 bonus to damage rolls with that weapon."
I was wondering if that fighter could wield Alchemist's Fire in their offhand and still gain the benefits of Dueling for their main weapon- although AF does damage, it is classified under "Adventuring Gear". It says that when you make the attack, you treat it as an improvised weapon-
"Make a ranged attack against a creature or object, treating the
alchemist's fire as an improvised weapon."
Would it always count as an improvised weapon, or just for the duration of the attack?
Best Answer
Yes
You gain the benefit of the Dueling Fighting Style with your weapon when you hold an improvised weapon in your other hand.
Any object that is not a weapon could be an improvised weapon, including a shield, a spell component pouch, or a flask of alchemist's fire.
You can wield a shield or hold a spell component pouch and benefit from the Dueling Fighting Style, so the logic should follow for a flask of alchemist's fire.
While you can use the alchemist's fire as an improvised weapon, you could use anything as an improvised weapon; that doesn't make it a weapon.
If the Dueling Fighting Style required your other hand to be empty, it would say so.