# How do you calculate rate of reaction?

Dec 27, 2013

CHEMICAL REACTION RATES
The reaction rate of a chemical reaction is the amount of a reactant reacted or the amount of a product formed per unit time. Often, the amount can be expressed in terms of concentrations or some property that is proportional to concentration.

For a reaction such as A → 2B, we could measure either the rate at which [B] increases or the rate at which [A] decreases.
Rate of formation of B = increase in concentration/time interval = Δ[B]/Δt
Rate of reaction of A = increase in concentration/time interval = -Δ[A]/Δt

Note that the rate is always expressed as a positive number (that’s the reason for the negative sign in front of the Δ[A]).

Also, the two rates are different. If [A] is decreasing at the rate of 0.1 mol•L⁻¹min⁻¹, [B] is increasing at the rate of 0.2 mol•L⁻¹min⁻¹. The rate of a reaction should be the same, no matter how we measure it. We must account for the stoichiometry of the reaction. So we divide the rate with respect to a component by its coefficient in the balanced equation. Thus, whether we are measuring [A] or [B], the rate of reaction is 0.1 mol•L⁻¹min⁻¹.

For a reaction such as aA + bB → cC + dD, our new definition becomes
Rate of reaction = -(1/a)Δ[A]/Δt = -(1/b)Δ[B]/Δt = (1/c)Δ[C]/Δt = (1/d)Δ[D]/Δt

Depending on the time interval between measurements, the rates are called
initial rate: instantaneous rate at the beginning of an experiment
average rate: rate measured between long time interval
instantaneous rate: rate measured between very short interval

MEASURING REACTION RATES
To measure a reaction rate, we usually monitor either a product or a reactant for its change. We can monitor any physical characteristic related to the quantity or concentration of a product or reactant.

EXAMPLE
N₂O₃(g) decomposes to NO₂(g) and NO(g) according to the reaction
N₂O₃(g) → NO₂(g) + NO(g)
The reaction is followed by measuring [NO₂] at different times. The following data are obtained.
t/s [NO₂]/mol•/L⁻¹
0,,,,,,,,,,,0
884,,,,,,0.193

What is the average rate of formation of NO₂ over this time interval? What is the average rate of reaction over this time interval?

Δ[NO₂]/Δt = (0.193 – 0) mol•L⁻¹/(884 – 0) s = 0.193/884 mol•L⁻¹s⁻¹ =
2.18 × 10⁻⁴ mol•L⁻¹s⁻¹

Since the coefficient of NO₂ in the balanced equation is 1,
Rate of reaction = (1/1)Δ[NO₂]/Δt = 2.18 × 10⁻⁴ mol•L⁻¹s⁻¹