The rate of a chemical reaction defines the speed at which a chemical change occurs. It quantifies how rapidly reactants are consumed and products are formed over a specific duration of time.
Mathematical Expression
For a generic reversible reaction where reactants (A) convert into products (B):
- Square brackets [ ] denote molar concentration (moles per liter).
- The negative sign indicates that the concentration of the reactant decreases with time.
- The positive sign indicates that the concentration of the product increases with time.
Units of Reaction Rate
- For liquid/aqueous solutions: mol L-1 s-1 (moles per liter per second) or mol L-1 min-1.
- For gaseous reactions: atm s-1 or bar s-1 (expressed in terms of partial pressures).
Average vs. Instantaneous Rate of Reaction
Chemical kinetics differentiates between rates measured over a finite time interval and those measured at a specific moment.
Average Rate of Reaction
The average rate (ravg) is calculated over a distinct, measurable time interval (Δ t). It does not reflect the variations in speed that occur during that interval.
Instantaneous Rate of Reaction
The instantaneous rate (rinst) is the rate of reaction at a specific infinitely small instant of time (t). It is determined by calculating the limiting value of the average rate as Δ t approaches zero, which corresponds to the derivative:
- Graphical Determination: On a plot of reactant concentration versus time, the instantaneous rate at any time t is equal to the negative slope of the tangent drawn to the curve at that specific point.
Reaction Stoichiometry and Rate Expressions
When the stoichiometric coefficients of reactants and products are not identical, the rate of disappearance of reactants differs from the rate of appearance of products. To establish a uniform rate for the entire reaction, the rate of change of each component is divided by its respective stoichiometric coefficient. For the general reaction:
Real-World Examples of Stoichiometric Rate Relations
- Synthesis of Ammonia (Haber’s Process):N2(g) + 3H2(g) → 2NH3(g)Rate = -d[N2]/dt = -1/3d[H2]/dt = +1/2d[NH3]/dt
- Decomposition of Dinitrogen Pentoxide:2N2O5(g) → 4NO2(g) + O2(g)Rate = -1/2d[N2O5]/dt = +1/4d[NO2]/dt = +d[O2]/dt
Factors Influencing the Rate of Reaction
The velocity of a chemical system is highly sensitive to external conditions and the intrinsic nature of the components involved.
1. Concentration of Reactants
As a general rule, increasing the concentration of reactants increases the frequency of collisions between molecules, thereby raising the reaction rate. According to the Law of Mass Action and Rate Laws, the rate is proportional to the concentration raised to an experimentally determined power (order of reaction).
2. Temperature
A rise in temperature accelerates almost all chemical reactions. For most corporate and basic chemical systems, the reaction rate approximately doubles or triples for every 10°C rise in temperature. This is due to an increase in the fraction of molecules possessing energy greater than or equal to the activation energy (Ea), as described by the Arrhenius Equation.
3. Presence of a Catalyst
A catalyst increases the rate of reaction by introducing an alternative reaction mechanism that possesses a lower activation energy barrier. It alters the reaction kinetics without changing the overall thermodynamic equilibrium constant (Keq) or Gibbs free energy (Δ G).
4. Surface Area of Reactants
In heterogeneous reactions (where reactants exist in different phases, such as a solid reacting with a liquid), the reaction rate increases with an increase in the surface area of the solid reactant. Finely divided powders react much faster than large solid blocks because more reactive sites are exposed simultaneously.
5. Nature of Reactants
The rate depends heavily on the specific chemical bonds that must be broken and formed. Reactions involving ions in aqueous solutions occur almost instantaneously because they do not require bond cleavage, whereas covalent molecular reactions proceed at a slower pace.
6. Exposure to Light (Photochemical Reactions)
Certain reactions do not proceed in the dark but are initiated or accelerated upon exposure to specific wavelengths of light (photons).
- Example: The synthesis of hydrogen chloride from hydrogen and chlorine gas is extremely slow in the dark but proceeds rapidly under sunlight:H2(g) + Cl2(g) hν→ 2HCl(g)
Connection to Chemical Equilibrium
The concept of reaction rate forms the operational foundation of dynamic chemical equilibrium.
Dynamic Equilibrium State
A reversible reaction achieves chemical equilibrium when the rate of the forward reaction equals the rate of the reverse reaction.
Kinetic Derivation of Equilibrium Constant
For a simple reversible step where A + B ⇌ C + D:
- Forward Rate = kf [A][B]
- Reverse Rate = kb [C][D]
At equilibrium, where the two rates balance: