What are the reaction rate expressions for each reaction?

Question

What are the reaction rate expressions for each reaction?

1. H2(g) + I2(g) —> 2HI(g)
2. 2H2(g)+ o2(g) —> 2H2o(g)

Answer 1

There is one rule behind both of these. For a general reaction

a A + b B -> c C + d D

the unique rate of reaction is

rate = -(1/a) d[A]/dt = -(1/b) d[B]/dt = +(1/c) d[C]/dt = +(1/d) d[D]/dt

Two pieces to it. The minus signs go on reactants because their concentrations fall, and the rate itself must come out positive. The 1/coefficient factors are there so that every species gives you the SAME number - without them, HI would appear to react twice as fast as H2, which is not a meaningful thing to say about one reaction.

Reaction 1: H2(g) + I2(g) -> 2 HI(g)

rate = -d[H2]/dt = -d[I2]/dt = +(1/2) d[HI]/dt

H2 and I2 each have an implied coefficient of 1, so they take no fraction. HI has a coefficient of 2, so it takes 1/2.

Reaction 2: 2 H2(g) + O2(g) -> 2 H2O(g)

rate = -(1/2) d[H2]/dt = -d[O2]/dt = +(1/2) d[H2O]/dt

If your course has not covered calculus notation yet, write the same thing with changes instead of derivatives - for example rate = -(1/2)(change in [H2])/(change in t). The structure is identical.

A quick way to check yourself: pick a number. If oxygen disappears at 0.10 M/s in reaction 2, then hydrogen disappears at 0.20 M/s and water appears at 0.20 M/s, and all three expressions evaluate to 0.10 M/s. If your three expressions do not agree on one number, a coefficient is in the wrong place.