For the reaction
2 D(g) + E(g) → products
experimental studies have established the rate law
rate = k[D][E]³
Let the original concentrations be [D]₀ and [E]₀, producing an initial rate r₀.
The concentrations are then changed so that [D] = a·[D]₀ and [E] = b·[E]₀, where a and b are positive real numbers.
Answer the following in terms of the variables a and b, showing algebraic steps and justifying each manipulation.
(a) Derive a general expression for the ratio r0rnew in terms of a and b.
(b) Using your expression from part (a), determine the numerical value of r0rnew when a = 0.25 and b = 2.0.
(c) Express the change in rate found in part (b) as a percentage increase or decrease relative to r₀, and interpret the physical meaning of your result in one or two sentences.