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You would put x because you don't know the change in concentration for each molecule. Since the initial concentrations of the products are 0, the system would shift to the right, i.e. make more products, in order to achieve equilibrium, thus you put +x. Conversely, you would know that the concentration of PCl5 would decrease, so you put -x.
Hope this helps!
Hope this helps!
The reason you put ...-2x, -x, +x, +2x... in the change box of your ice table is because we know that the change in concentration from initial state to final state (equilibrium) is consistent across molecules and proportional to the molar ratio of reactants and products (the coefficients), and we know this fact even before we know the concentration change's value. Then you plug in the equilibrium concentrations (with x's included) to the K (equilibrium constant) equation. With this equation, you can solve for the value of x and go back to the icebox to finally solve for the now numerical equilibrium concentration of molecules involved in the reaction. Hope this was helpful!
The +x is determined by the stoichiometric coefficients. For example if the product has a 2 in front of it, it would have to be +2x. We're adding the x because its the change in the reaction and since we are assuming this a forward reaction, we are using up the reactants (thus the minus reactant) and making products (thus adding the change).
Simply put, look at the molar coefficients on each of the molecules and using that number, it will be the value of X in the ICE table. If you are looking at the reactants, you will subtract X. However, if you are looking at products, then you are adding X.
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