Kinetics – graphical work

After teaching for more than 5 years, I always feel that kinetics is one of the easiest chapters to score, provided one does not make careless mistakes!

Remember fundamentals are important!!

The basics of Kinetics: remember…
1) Rate = change of concentration / time
2) Rate = k[A]^n (where A is reactants, n is order of reaction)
3) units of rate = concentration units /time (eg, moldm-3s-1 , molm-3min-1 etc)
4) orders of reaction is an integer with values 0,1 and 2 only

Graph work:

ZERO ORDER REACTIONS
- Concentration vs time graph = downwards straight line. Gradient gives you rate. (from the equation Rate = change of concentration / time)
- Rate vs Concentration = flat straight line. Gradient gives you k. (from the equation, Rate = k[A]^n)
- Essentially, rate is INDEPENDENT of concentration, rate = k

FIRST ORDER REACTIONS
- Concentration vs time graph = downwards parabolic curve. Gradient gives you rate. (from the equation Rate = change of concentration / time)
- Rate vs Concentration = increasing constant straight line. Gradient gives you k. (from the equation, Rate = k[A]^n)
- Essentially, rate is DIRECTLY PROPORTIONAL to concentration
- Rate constant, k, is INDEPENDENT of concentration
- Concentration/time graph has a half-life that is constant, hence, we have the equation, t 1/2 = ln2 /k

SECOND ORDER REACTIONS
- Concentration vs time graph = downwards curve. Gradient gives you rate. (from the equation Rate = change of concentration / time)
- Rate vs Concentration = upwards curve. Gradient gives you k. (from the equation, Rate = k[A]^n)
- Essentially, rate is NOT PROPORTIONAL to concentration
- Rate constant, k, is DEPENDENT of concentration
- Concentration/time graph has a half-life that is NOT constant, dependent on initial [A]
- Half life t 1/2 = 1/k[A]

TIP:
When finding half-life, note the y-axis.

If it is concentration of REACTANTS against time,
determine half-life at 1/2 [A], 1/4[A] and 1/8[A], where [A] refers to the INITIAL concentration of reactant.

If it is the concentration of PRODUCTS against time,
determine half-life at 7/8 [B], 3/4 [B] and 1/2[B], where [B] refers to the MAXIMUM concentration of products formed (if it can be possibly found from the question)