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Rate

A measure of how some property varies with time.

Rate of a chemical reaction

The change in the amount of a reactant or product per unit time.

Rate expression

The mathematical representation of the change in species concentration over time (e.g., $-rac{ riangle[H_2O_2]}{ riangle t}$).

Negative sign in rate expression for reactants

Added because reactant concentration decreases over time, ensuring the reaction rate remains a positive quantity.

Average rate

The rate calculated using the concentrations at the beginning and end of a specific time period.

Instantaneous rate

The rate at which a reaction is proceeding at any specific moment in time.

Initial rate of a reaction

The instantaneous rate at 'time zero,' when the reaction commences.

Instantaneous rate from a graph

Equal to the slope of a straight line tangent to the curve at a specific time.

Rate expressions of different substances

Related by the stoichiometry of the balanced equation.

Average rate expression example

For the reaction $aA \rightarrow bB$ : $rate = -\frac{1}{a} \frac{\Delta [A]}{\Delta t} = \frac{1}{b} \frac{\Delta [B]}{\Delta t}$.

Five typical factors affecting reaction rate

1. Chemical nature of the reacting substances 2. State of subdivision 3. Temperature 4. Concentration 5. Presence of a catalyst.

Chemical nature affecting reaction speed

Reactions may occur at vastly different rates depending on the identity of the reactants.

Phase interface in reactions

Chemical reactions between different physical states occur at the surface of contact.

State of subdivision

Smaller particles increase the effective surface area, hence increasing the reaction rate.

Temperature's effect on reaction rates

Reactions typically occur faster at higher temperatures; the rate approximately doubles for every 10 °C increase.

Concentration and reaction rate

Rates usually increase when the concentration of reactants increases.

Catalyst definition

A substance that increases the rate of a chemical reaction without being consumed.

Rate Laws

Mathematical expressions that describe the relationship between the rate of a chemical reaction and the concentrations of its reactants.

Rate Constant ($k$)

A value specific to a reaction that varies with temperature but is independent of reactant concentrations.

Overall Reaction Order

The sum of the orders for each reactant in the rate law.

Method of Initial Rates

An experimental approach to determine reaction orders and the rate constant using varying initial concentrations.

Stoichiometry vs. Rate Laws

Rate laws cannot reliably be predicted from stoichiometry but must be determined experimentally.

Units of Rate Constant (k) for different orders

Zero order: M/s First order: s^-1 Second order: M^-1 s^-1

Integrated rate law function

It relates concentrations of reactants and time, used to determine the amount present after time has passed.

First-order reaction's integrated rate law

$\ln[A]_t = -kt + \ln[A]_0$.

First-order reaction plot characteristics

A plot of $\ln[A]_t$ vs. $t$ yields a straight line with a slope of $-k$.

First-order half-life ($t_{1/2}$) formula

$t_{1/2} = \frac{0.693}{k}$.

Differential rate law for second-order reactions

$rate = k[A]^2$.

Integrated rate law for second-order reactions

$\frac{1}{[A]_t} = kt + \frac{1}{[A]_0}$.

Second-order half-life ($t_{1/2}$) formula

$t_{1/2} = \frac{1}{k[A]_0}$.

Zero-order reaction differential rate law

$rate = k$.

Zero-order reaction integrated rate law

$[A]_t = -kt + [A]_0$.

Zero-order half-life ($t_{1/2}$) formula

$t_{1/2} = \frac{[A]_0}{2k}$.

Collision theory

The reaction rate is proportional to the rate of reactant collisions.

Collision requirements for reactions

1. Orientation - proper atomic contact; 2. Adequate Energy - sufficient energy to penetrate valence shells.

Activated complex

An unstable species formed when reactants collide properly with adequate energy.

Collision theory and concentration

Increasing concentration increases the number of molecules, raising the collision frequency.

Activation Energy ($E_a$)

The minimum energy needed to form a product during a collision.

Reaction diagram and $E_a$ representation

The energy difference between reactants and transition state.

Nuclear Chemistry definition

The study of reactions that involve changes in nuclear structure.

Atomic Number (Z) vs. Mass Number (A)

Atomic Number (Z): number of protons; Mass Number (A): sum of protons and neutrons.

Nuclide identification

A nuclide is identified by the notation $^A_Z X$ where $X$ is the element symbol.