Brackets vs P For Equilibrium Constants

[Hai-Lin Yeh 1J]

In an equilibrium constant expression (to find the equilibrium constant), it's [products]/ [reactants] (the concentration of products over the concentration of reactants), but if something is aqueous, do we use the brackets and if something is a gas, then we use partial pressure?
For example, P4S10(s) + 16 H2O(l) -> 4 H3PO4(aq) + 10 H2S(aq)
H3PO4: [H3PO4]^4 and H2S: [H2S]^10
Whereas in 2 BCl3(g) + 2 Hg(l) -> B2Cl4(s) + Hg2Cl2(s),
BCl3: P_BCl3^2.
Is this correct? When do you use P (partial pressure) and when do you use the brackets?

[Saman Andalib 1H]

When you are given concentrations, you must use the brackets as the notation. When partial pressures are given, the brackets are not necessary for writing the equilibrium constant expression.

[Hai-Lin Yeh 1J]

Thank you! But as a follow up question, in the 6th edition, number 11.13 part a, it asks to write the reaction quotient for:
2 BCl3(g) + 2 Hg(l) -> B2Cl4(s) + Hg2Cl2(s)
and in the answer key, the answer is given as: 1/ P_BCl3^2.
There was no "partial pressure" or "concentration" specified so how do we determine that it's P, not the brackets. Would you be wrong in writing it with brackets instead? So is it different between aqueous solutions and gas?

[Camille Marangi 2E]

As far as I can tell, unless the question specifies which equilibrium constant it wants you're fine writing either. However it wouldn't hurt being prepared and knowing how to convert Kp to Kc and vice versa. Here's the conversion equation: Kp=Kc(RT)^n

[Heesu_Kim_1F]

Although I think we can write the answers either way, my TA mentioned today that if the given equation is all in gas form, use partial pressure for K, while if the given equation is all in aqueous form, use concentration for K. He also mentioned that for heterogeneous equilibrium, use concentration for K as well. Hope this helps!