Chemical Kinetics · Study notes

CHERate, Order & Molecularity

Definitions, Concepts & Rate Expressions

This foundational subtopic covers how reaction rate is defined and expressed in terms of any species, plus the meaning and properties of the rate constant. Writing the rate expression with correct stoichiometric coefficients is a frequent, easy-to-lose mark.

General rate expression

\text{rate} = -\dfrac{1}{a}\dfrac{d[A]}{dt} = -\dfrac{1}{b}\dfrac{d[B]}{dt} = +\dfrac{1}{c}\dfrac{d[C]}{dt} = +\dfrac{1}{d}\dfrac{d[D]}{dt}

for

aA + bB \rightarrow cC + dD

Average vs instantaneous rate

r_{avg} = -\dfrac{\Delta[A]}{\Delta t} \qquad r_{inst} = -\dfrac{d[A]}{dt}

instantaneous rate is the limit as

\Delta t \to 0

Rate law

\text{rate} = k[A]^x[B]^y

k

= rate when all concentrations are unity

Average rate is the change in concentration over a finite interval; instantaneous rate is the rate at a single instant, $-\dfrac{d[A]}{dt}$ — preferred because rate changes continuously as reactants deplete.
For $aA + bB \rightarrow cC + dD$ , rate $= -\dfrac{1}{a}\dfrac{d[A]}{dt} = -\dfrac{1}{b}\dfrac{d[B]}{dt} = +\dfrac{1}{c}\dfrac{d[C]}{dt} = +\dfrac{1}{d}\dfrac{d[D]}{dt}$ .
Example: for $2SO_2 + O_2 \rightarrow 2SO_3$ , $-\dfrac{1}{2}\dfrac{d[SO_2]}{dt} = -\dfrac{d[O_2]}{dt} = +\dfrac{1}{2}\dfrac{d[SO_3]}{dt}$ , so $-\dfrac{d[O_2]}{dt} = \dfrac{1}{2}\dfrac{d[SO_3]}{dt}$ .
Rate constant $k$ is the proportionality constant in the rate law and numerically equals the rate when all reactant concentrations are unity.
Properties of $k$ : it is independent of concentration but depends on temperature and the presence of a catalyst; its units depend on the order.
Reaction rate units are $mol\,L^{-1}s^{-1}$ ; rate is always taken as a positive quantity, hence the minus sign on reactant terms.
A powdered catalyst works better than a lump because finer subdivision gives a much larger surface area, exposing more active sites for the reaction.
Instantaneous rate is found graphically as the slope of the tangent to the concentration-vs-time curve at the chosen instant.
For gaseous reactions, rate may also be expressed in terms of partial pressures, since pressure is proportional to concentration at fixed temperature.
The minus sign on reactant terms ( $-d[A]/dt$ ) keeps the rate positive because reactant concentration decreases with time.
Dividing each rate of change by its stoichiometric coefficient gives a single unique reaction rate, independent of which species is monitored.
Reaction rate is an intensive quantity (per unit volume) describing how fast concentration changes; $k$ is an intrinsic constant of the reaction at a given temperature — do not confuse the two.

Where the marks go

Omitting the stoichiometric coefficient — writing $-d[SO_2]/dt = +d[SO_3]/dt$ instead of dividing each by $2$ .
Dropping the negative sign on reactant terms, giving a negative rate.
Saying $k$ depends on concentration — $k$ depends only on temperature and catalyst, not on concentration.
Confusing average rate (finite $\Delta t$ ) with instantaneous rate (slope of the tangent) when a graph is given.
Assigning the wrong units to rate vs rate constant — rate is always $mol\,L^{-1}s^{-1}$ , but $k$ units vary with order.

How the board asks it

Derive / provegeneral rate expression with stoichiometric coefficients
For the reaction $4NH_3 + 5O_2 \rightarrow 4NO + 6H_2O$ , write the rate of the reaction in terms of the rate of change of concentration of each reactant and product.
Numericalrelating rates of different species via coefficients
In the reaction $2N_2O_5 \rightarrow 4NO_2 + O_2$ , the rate of formation of $NO_2$ is $1.6 \times 10^{-3}\ mol\,L^{-1}\,s^{-1}$ . Calculate the rate of disappearance of $N_2O_5$ and the rate of formation of $O_2$ .
Give reasonsminus sign convention and properties of the rate constant
Account for the following: (a) the rate of a reaction with respect to a reactant is written with a negative sign, and (b) the rate constant $k$ is independent of concentration but changes with temperature.
Distinguishaverage vs instantaneous rate
Distinguish between average rate and instantaneous rate of a reaction, and state how the instantaneous rate is determined from a concentration-versus-time graph.
Define / statedefinition of rate constant and its units
Define the rate constant of a reaction and state how its units depend on the order of the reaction.

Practise this topic

NextEffect of Concentration on Rate; Rate Expressions

Written for Sublevo. Question text quoted anywhere in these notes is the Council’s and carries its year and paper; the board’s own diagrams are not reproduced.