You are given an aqueous solution of hydrofluoric acid. (Recall that hydrofluoric acid is a weak acid; When you are given an aqueous solution of a weak acid you always assume that the dissociation reaction of the acid in water has reached equilibrium)

Predict whether the reaction will shift left ("left"), shift right("right"), or remain unchanged ("no change") upon the following disturbances.
Add solid sodium fluoride (assume no chnage in total volume)
Add solid sodium hydroxide (assume no chnage in total volume)
Add a drop of concetrated hydrochloric acid (assume no chnage in total volume)
Add solid iron(III) hydroxide (assume no chnage in total volume)
Add solid sodium nitrate (assume no chnage in total volume)
Add solid Barium fluoride (assume no chnage in total volume)
Add water

HF + H2O ==> H3O^+ + F^-

This is a problem on LeChatelier's Principle. I like the way the books say it (the Principle); however, it's confusing to most students. Here is another way of saying it.
When a system at equilibrium is disturbed, the system will shift one way or the other, to UNDO what we've done to it. With that in mind, I will do the first few and leave the others for you.
Add solid NaF. So NaF is an ionic salt, it ionizes in soln as NaF ==> Na^+ +F^- which says we are increasing the F^-. So what will the reaction do? It will try to UNDO (decrease) the F^-. How can it do that? Remember it can shift to the right which gives MORE H3O^+ and MORE F^- OR it can shift to the left which will DECREASE H3O^+ and DECREASE F^-. Since adding F^- make more F^-, it will shift to the left since that's the only way to decrease it.

Add solid NaOH. That will increase OH^-, that will react with H3O^+, decreasing H3O^+ (to form H2O) so the reaction will shift to try to add H3O^+ back. How can it do that? By shifting to the right.

Adding a drop of concd HCl. That will increase H3O^+ so the reaction will shift to the left so as to UNDO (decrease H3O^+).

Some hints:
BaF2 is not very soluble.
NaNO3 is quite soluble.

but what about water?

I'll bite. What about it? Are you concerned that I wrote the ionization with water? If so the solution said it was an aqueous soln; therefore, I just added the water in to show all of the ionization. That's what happens anyway. Or is it something else?

so for BaF2 its going to shift to the left. The iron (3) nitrate is going to shift to the right. The sodium nitrate is not going to affect the reaction. And water will make it shift to the right. Is that right?

What is the density of water in units of mg/cm3

and mg/mL? (1=1000 mg)

To determine whether the reaction will shift left, right, or remain unchanged upon each disturbance, we need to analyze the effect of the disturbance on the equilibrium of the hydrofluoric acid dissociation reaction.

The dissociation reaction of hydrofluoric acid (HF) in water can be represented as:
HF(aq) ⇌ H+(aq) + F-(aq)

1. Add solid sodium fluoride:
By adding solid sodium fluoride (NaF), which is a salt consisting of Na+ and F- ions, we are increasing the concentration of F- ions in the solution. According to Le Chatelier's principle, an increase in the concentration of one of the products (F-) will cause the equilibrium to shift toward the reactants to counterbalance the change. Therefore, the reaction will shift left.

2. Add solid sodium hydroxide:
Adding solid sodium hydroxide (NaOH) introduces OH- ions into the solution. These hydroxide ions will react with the H+ ions from the dissociation of HF, forming water molecules. This reaction consumes H+ ions, causing the equilibrium to shift right to produce more H+ ions. Hence, the reaction will shift right.

3. Add a drop of concentrated hydrochloric acid:
Concentrated hydrochloric acid (HCl) is a strong acid that completely dissociates in water. Adding a drop of HCl will increase the concentration of H+ ions in the solution. This increase of H+ ions will cause the equilibrium to shift left to counterbalance the change. Thus, the reaction will shift left.

4. Add solid iron(III) hydroxide:
Solid iron(III) hydroxide (Fe(OH)3) is an ionic compound that does not contribute to the concentration of H+ or F- ions in solution. Therefore, the presence of solid iron(III) hydroxide will not affect the equilibrium of the reaction. The reaction will remain unchanged.

5. Add solid sodium nitrate:
Solid sodium nitrate (NaNO3) dissociates completely in water, forming Na+ and NO3- ions. Since neither Na+ nor NO3- ions have any effect on the concentration of H+ or F- ions, the equilibrium of the reaction will not be affected. The reaction will remain unchanged.

6. Add solid Barium fluoride:
Adding solid barium fluoride (BaF2), a salt consisting of Ba2+ and F- ions, does not affect the concentration of H+ or F- ions in solution. Therefore, the equilibrium of the reaction will remain unchanged.

7. Add water:
Adding water to the system will change the total volume but will not affect the concentration of the existing H+ or F- ions. Consequently, the equilibrium of the reaction will not be affected. The reaction will remain unchanged.

In summary:
- Add solid sodium fluoride: Shift left
- Add solid sodium hydroxide: Shift right
- Add a drop of concentrated hydrochloric acid: Shift left
- Add solid iron(III) hydroxide: No change
- Add solid sodium nitrate: No change
- Add solid barium fluoride: No change
- Add water: No change