Calculating Equilibrium Concentrations
To find equilibrium concentrations, combine an ICE table with the known K: substitute the equilibrium row into the K expression and solve for the unknown change x. When K is small, the small-x approximation (ignoring x where it is added to a much larger number) simplifies the algebra — but its validity must be checked afterward.
The trap leaves the small-x approximation unchecked. It is valid only when x is small compared to the initial concentration (commonly, x is under ~5% of it); if not, you must solve the full equation. Approximate, then verify.
The work
3 ways in · any order
Lesson
Equilibrium Concentrations
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An ICE table plus K solves for equilibrium concentrations, with the small-x approximation used only when valid. The lesson solves and checks the approximation, then closes with a ten-scenario check.
Diagnostic
10-item topic check
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Ten items spanning the Topic 7.7 misconception: the small-x approximation left unchecked when it does not actually hold.
Targeted Practice
Drill a single misconception
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Pick one of the failure modes you missed and drill it on its own. The round is adaptive: two correct in a row clears the misconception and moves you to the next.