Write equilibrium Constant expressions (k) for the following reactions:

Ni(s)+ 4CO(g) <-> Ni(CO)₄
HF(aq) <-> H(aq) + F(aq)

Cl₂(g)+2Br(aq) <-> Br₂(l) + 2Cl(aq)

What do you not understand about how to write these expressions? It's just "follow the rules."

when the element have different states, ie. (aq) (s) (g) etc. doesn't that change the way you write the constant expressions?

Yes. As a general rule, solids and pure liquids don't show up in the expression.

Ni(s)+ 4CO(g) <-> Ni(CO)₄
HF(aq) <-> H(aq) + F(aq)

Cl₂(g)+2Br(aq) <-> Br₂(l) + 2Cl(aq)

So #2 is
K=(H^+)(F^-)/(HF) and the concn of each is determined by the molarity.
For #1, K = (CO)^4

To write the equilibrium constant expressions for these reactions, we use the concentration of products raised to their stoichiometric coefficients divided by the concentration of reactants raised to their respective stoichiometric coefficients. Here are the equilibrium constant expressions for the given reactions:

1. For the reaction: Ni(s) + 4CO(g) <-> Ni(CO)₄
The equilibrium constant expression is:
K₁ = [Ni(CO)₄] / [Ni] * [CO]⁴

2. For the reaction: HF(aq) <-> H(aq) + F(aq)
The equilibrium constant expression is:
K₂ = [H] * [F] / [HF]

3. For the reaction: Cl₂(g) + 2Br(aq) <-> Br₂(l) + 2Cl(aq)
The equilibrium constant expression is:
K₃ = [Br₂] * [Cl]² / [Cl₂] * [Br]²

Note: The concentrations of the species should be expressed in molarity (M) units when calculating the equilibrium constant.