Homework #69

[Casey Collet 1I]

In homework #69, I understand that the fact that the equilibrium constant is so small allows the reaction to strongly favor the reactants, but when doing similar problems how do we know that we are able to adjust the initial conditions according to the equilibrium constant?

[K Honeychurch 1K]

Adjusting the initial condition does not relate to the value of K being so small. In other words, we could adjust the initial condition for any value of K.
In this problem (and other problems with small K values), the very small K value allows us to ignore the change in the reactant (HCl) because 2x is much smaller than 4.0. With rounding, the final concentration of HCl will be 4.0 so we ignore the 2x to make solving the equation much easier.