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Le Chatelier's principle becomes quantitative once Q is compared with K. When Q is below K there is a shortage of products and the reaction runs forward; above K it reverses. The size of the drive is RT ln(Q/K), so a Q ten times below K at room temperature corresponds to about -5.7 kJ/mol pushing the reaction forward.
Comparison test
Q < K forward, Q > K reverse, Q = K at equilibrium
Free energy drive
dG = RT ln(Q/K)
No. A catalyst speeds both directions equally, so it changes how fast equilibrium is reached but not where it lies.
Because the free energy drive scales with RT. The direction depends only on Q versus K, but the energy behind the shift grows with temperature.