Master AP Chemistry Topic 5.1 with this free practice quiz. Test your skills on rate of appearance, rate of disappearance, relative rates, and stoichiometry and rates to prepare for your AP exam.
What a Rate Is
The rate of a reaction is the change in concentration of a reactant or product per unit time. Its units are molarity per time, written M/s or M/min, since concentration itself is mol/L. A value in mol/s alone is a rate of change of amount, not a reaction rate, because it ignores the volume.
Rates are reported as positive numbers. Reactant concentrations fall, so Δ[reactant] is negative, and a minus sign is written in front of reactant terms to make the rate positive. Product concentrations rise, so product terms need no sign change.
A reaction does not keep one speed. As reactants are consumed, collisions become less frequent and the rate falls, so a concentration against time curve is steep at the start and flattens as the reaction proceeds.
One Reaction, One Rate: The Stoichiometric Factors
Each species in a reaction changes at its own rate, fixed by the balanced equation. For aA + bB → cC + dD, the single reaction rate is
rate = -(1/a) Δ[A]/Δt = -(1/b) Δ[B]/Δt = (1/c) Δ[C]/Δt = (1/d) Δ[D]/Δt
The coefficient of each species becomes a reciprocal factor in front of its concentration change. This makes every term give the same numerical value for the rate, even though the species themselves are disappearing and appearing at different speeds. A species with coefficient 3 changes three times as fast as the reaction rate; a species with coefficient 1 changes exactly at the reaction rate.
Multiplying every coefficient in the equation by the same factor does not change the calculated rate. The reciprocal factors shrink in exactly the proportion that the concentration changes grow, so the value is unchanged.
Average Rate and Instantaneous Rate
The average rate over a time interval is the total concentration change divided by the interval length, Δ[A]/Δt. It smooths over everything that happened inside the interval.
The instantaneous rate is the rate at one moment. On a concentration against time graph it is the slope of the tangent line drawn to the curve at that time. Draw the tangent, read two points on it, and divide the concentration difference by the time difference. For a reactant the slope is negative, and the rate of disappearance is its positive size.
As the interval used for an average rate shrinks toward zero, the average rate approaches the instantaneous rate, because a very short interval samples the curve at effectively one point.
Worked Examples
Example 1: average rate and the related rates
In N₂ + 3H₂ → 2NH₃, [H₂] falls from 0.90 M to 0.78 M over 5.0 min.
Average rate of disappearance of H₂: (0.90 – 0.78) / 5.0 = 0.024 M/min.
The reaction rate divides this by the coefficient 3: 0.024 / 3 = 0.0080 M/min. NH₃ appears at twice the reaction rate: 2 × 0.0080 = 0.016 M/min. N₂ disappears at the reaction rate itself, 0.0080 M/min, because its coefficient is 1.
Example 2: relating two species at one instant
In 4NH₃ + 5O₂ → 4NO + 6H₂O, at one instant Δ[NH₃]/Δt = -0.12 M/s.
The reaction rate is 0.12 / 4 = 0.030 M/s. O₂ disappears at 5 × 0.030 = 0.15 M/s, so Δ[O₂]/Δt = -0.15 M/s. H₂O appears at 6 × 0.030 = +0.18 M/s. The fastest-changing species is the one with the largest coefficient, not the one the question happens to name first.
Traps Specific to This Topic
The reciprocal factor is where marks are lost. The coefficient goes underneath: for 2NO + O₂ → 2NO₂ the NO term is -(1/2) Δ[NO]/Δt, never -2 Δ[NO]/Δt. Multiplying by the coefficient instead of dividing overstates the rate by the square of the coefficient.
A species’ own rate of change is not the reaction rate unless its coefficient is 1. If H₂ disappears at 0.024 M/min in the ammonia synthesis, the reaction rate is 0.0080 M/min, one third as large, and quoting 0.024 as the reaction rate is wrong.
Signs must be handled deliberately. Δ[H₂]/Δt is negative because H₂ is consumed; the rate of disappearance is the same number stated positively. Reporting a negative reaction rate is always an error.
A tangent slope read from a graph uses points on the tangent line, not points on the curve. Reading curve values at two times gives an average rate over that interval, which is a different quantity whenever the curve bends.