[CrimpJiggler]

Heres the question:

don't know why the hell I can't solve a simple equilibrium problem like this but I can't. I need to find out the equilibrium concentration of HBr but how do I do that when I don't know the starting concentration or the equilibrium constant? Also, if 0.5M of HBr is consumed, how does it only produce 0.13M of each product?

[Borek]

Imagine you have 1 L of the mixture. If so, you started with 0.5 mole of HBr. If 0.13 mole of Br₂ were produced, how much HBr was left? This is a simple stoichiometry.

Also, if 0.5M of HBr is consumed, how does it only produce 0.13M of each product?

It wasn't all consumed. 0.5M is the initial concentration, it doesn't mean there is no HBr left at equilibrium.

[Nisarg Shah]

Heres the question:

I need to find out the equilibrium concentration of HBr but how do I do that when I don't know the starting concentration or the equilibrium constant? Also, if 0.5M of HBr is consumed, how does it only produce 0.13M of each product?

                                           2HBr <--> Br₂ + H₂
At t=0s                                 0.5M        0M    0M
At t=t_equilibrium                   (0.5-2x)M    xM    xM 

(Using stoichiometry, if 2x moles of Hbr are dissociated then x moles of Br₂ and H₂ will be formed at equilibrium. Assuming volume= 1 litre)

Since 0.13M of Br₂ is formed at equilibrium, there x=0.13M.

K = [Br₂] x [H₂]/[HBr]²

The question doesn't mean that all of the HBr is consumed. HBr, H2 and Br2 all are present in the container in which the reaction has occurred. That is why they are said to be in equilibrium.
The reaction shifts backward or forward depending on various factors such as pressure, temperature, concentration of reactants and products, volume, etc.