When do we use the equilibrium arrows in reactions?
Does electrolysis/galvanic cell reactions require them?
I wouldn't put them in for electrolysis because equilibrium is not a concern; we're forcing the reaction in a particular direction.
Also, for galvanic cells, it can be shown that the standard electrode potential is directly proportional to the natural log of the equilibrium constant. For reactions involving one electron transfer per mole reaction, the constant of proportionality is around 1/39, which means the equilibrium constant is pretty large. You can generally leave the double way arrows out there.
You DO use them in acid-base reactions (unless one of the acids is strong), in anything where there is a quoted equilibrium constant of less than around 10^4...and where they tell you to put them in
Anyone able to provide me with a brief brief summary of the differences between HPLC and GLC and which one is better for which compounds? 
EDIT: I have another question, just so that I know that I've got my head wrapped around this equilibrium stuff,
so only temperature can change the value of K but say for like an increase in pressure, the reaction is pushed to the left or right (depending on particles) but the K has not changed, but we may get more reactant or product? I dont even know if I'm making sense but does it?
HPLC=>more expensive due to pressures, but can be used for large organic substances
GC is more accurate, but it requires moderately high temperatures, which can cause some organic compounds to decompose
Equilibrium constants are ONLY ever changed by temperature. What you're describing is a change in the reaction quotient; by changing the pressure, you may change the denominator and the numerator of the reaction quotient (concentration fraction) to varying extents.
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