Concept 05 / 08Equilibrium
Reaction Quotient and Equilibrium Calculations
The reaction quotient Q and predicting the direction of reaction, setting up ICE tables, solving for equilibrium concentrations, degree of dissociation, and finding the extent of dissociation from vapour density measurements.
Reaction quotient. For any mixture (not necessarily at equilibrium), is written exactly like but with the actual concentrations at that moment.
: too few products; the reaction proceeds forward.
: too many products; the reaction proceeds backward.
: the system is at equilibrium (see figure).
Equilibrium calculations (ICE table). Write the Initial amounts, the Change in terms of a single unknown using stoichiometry, and the Equilibrium amounts; substitute into and solve. Convert moles to concentrations by dividing by volume (if the volume cancels). If is very small, is often negligible compared with initial concentrations, which simplifies the algebra; check afterwards that is less than about of the quantity it is subtracted from.
Degree of dissociation (). The fraction of a reactant that dissociates. For starting with : at equilibrium , , ; total moles . With total pressure , each partial pressure is its mole fraction times :
.
If , : raising pressure suppresses dissociation.
Vapour density method. Dissociation increases the number of moles, so the observed density (and apparent molar mass) of the equilibrium mixture falls. If one molecule gives particles,
,
where is the theoretical vapour density (no dissociation) and the observed one. (For association, such as dimerisation, the same idea gives .)
Key Takeaways:
- : forward; : backward; : equilibrium.
- ICE tables in one unknown; approximate only when is small, then verify.
- : .
- from vapour densities.
- Pitfall: in problems, partial pressure uses the total moles including products, so the denominator must appear.
Brain-Teaser 1: For , at about . each of and are heated in a flask. Find the equilibrium amount of HI.
Solution: At equilibrium: , , . , so , giving . HI ; and are each.
Brain-Teaser 2: The vapour density of at a certain temperature is observed to be . Find its degree of dissociation.
Solution: , so . One molecule gives particles: . About has dissociated.
Brain-Teaser 3: For , at some temperature. A mixture has , and . In which direction will it react?
Solution: . There is excess product, so ammonia decomposes (backward reaction) until falls to .
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