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## Chemical Kinetics (CHB-201) Notes

## Rate of Reaction

## Rate Constant

## Order of a Reaction

### Examples:

## Unit of Rate Constant

## Molecularity of a Reaction

### Example:

## Differential and Integrated Rate Laws

### Key Points:

### Differential vs. Integrated Rate Laws

### Half-Life ( t1/2t_{1/2}t1/2 )

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Chemical kinetics is the branch of physical chemistry that studies the speed of chemical reactions. This includes understanding the mechanisms by which reactions occur.

The rate of a reaction is the amount of chemical change occurring per unit time. It is generally expressed as the decrease in concentration of the reactant or the increase in concentration of a product per unit time.

For a reaction A→PA \rightarrow PA→P:

rate=−dCAdT=dCPdT\text{rate} = -\frac{dC_A}{dT} = \frac{dC_P}{dT}rate=−dTdCA=dTdCP

For a reaction aA+bB→cC+dDaA + bB \rightarrow cC + dDaA+bB→cC+dD:

rate=−1adCAdt=−1bdCBdt=1cdCCdt=1ddCDdt\text{rate} = -\frac{1}{a}\frac{dC_A}{dt} = -\frac{1}{b}\frac{dC_B}{dt} = \frac{1}{c}\frac{dC_C}{dt} = \frac{1}{d}\frac{dC_D}{dt}rate=−a1dtdCA=−b1dtdCB=c1dtdCC=d1dtdCD

The rate constant kkk for a reaction A→ProductA \rightarrow \text{Product}A→Product is given by r=kCAr = kC_Ar=kCA. For a general reaction aA+bB→ProductaA + bB \rightarrow \text{Product}aA+bB→Product:

r=k[A]x[B]yr = k[A]^x[B]^yr=k[A]x[B]y

The order of a reaction nnn is the sum of the exponents of the concentration terms in the rate equation. It indicates the quantitative dependence of the reaction rate on the concentration of the reacting substances.

For a reaction A+B+C→ProductA + B + C \rightarrow \text{Product}A+B+C→Product:

rate=k[A]α[B]β[C]γ\text{rate} = k[A]^\alpha[B]^\beta[C]^\gammarate=k[A]α[B]β[C]γ

Order of the reaction,n=α+β+γ\text{Order of the reaction}, n = \alpha + \beta + \gammaOrder of the reaction,n=α+β+γ

- 2HI→H2+I22HI \rightarrow H_2 + I_22HI→H2+I2 with rate=k[HI]2\text{rate} = k[HI]^2rate=k[HI]2, here n=2n = 2n=2
- If n=1n = 1n=1, it is a first-order reaction
- If n=2n = 2n=2, it is a second-order reaction
- If n=0n = 0n=0, it is a zero-order reaction

**Zero-order reaction:** rate=−d[A]dt=k\text{rate} = -\frac{d[A]}{dt} = krate=−dtd[A]=k

Unit of k=mol L−1 s−1\text{Unit of } k = \text{mol} \, L^{-1} \, s^{-1}Unit of k=molL−1s−1

**First-order reaction:** rate=−d[A]dt=k[A]\text{rate} = -\frac{d[A]}{dt} = k[A]rate=−dtd[A]=k[A]

Unit of k=s−1\text{Unit of } k = \text{s}^{-1}Unit of k=s−1

**Second-order reaction:** A+B→ProductA + B \rightarrow \text{Product}A+B→Product

rate=−dxdt=k[A][B]\text{rate} = -\frac{dx}{dt} = k[A][B]rate=−dtdx=k[A][B]

Unit of k=L mol−1 s−1\text{Unit of } k = L \, \text{mol}^{-1} \, \text{s}^{-1}Unit of k=Lmol−1s−1

Molecularity refers to the number of molecules or atoms involved in the process of a chemical change. Reactions can be unimolecular, bimolecular, or trimolecular depending on whether one, two, or three molecules are involved.

- A reaction 2HI→H2+I22HI \rightarrow H_2 + I_22HI→H2+I2 is a bimolecular reaction.

The molecularity must be an integer (1, 2, 3, etc.), but the order can be fractional. The order of a reaction is an experimental concept, while molecularity is theoretical.

Rate laws describe the progress of the reaction. They are mathematical expressions that describe the relationship between reaction rates and reactant concentrations.

For a reaction aA+bB→cC+dDaA + bB \rightarrow cC + dDaA+bB→cC+dD:

rate=k[A]m[B]n\text{rate} = k[A]^m[B]^nrate=k[A]m[B]n

- kkk is the rate constant.
- mmm and nnn are the orders of reaction for AAA and BBB, respectively.

- The orders of reaction are not necessarily equal to the stoichiometric coefficients from the balanced equation.
- Each reactant has its own independent order of reaction.
- Orders of reaction can be positive, zero, fractional, or negative.
- The overall reaction order is the sum of the individual orders ( m+nm + nm+n ).

**Differential Rate Laws:** Express the rate of reaction as a function of the change in concentration of reactants over time. They are used to describe the molecular-level process of the reaction.

Example for n=1n = 1n=1:

Rate=−d[A]dt=k[A]\text{Rate} = -\frac{d[A]}{dt} = k[A]Rate=−dtd[A]=k[A]

**Integrated Rate Laws:** Express the reaction rate as a function of the initial concentration and the concentration after a specific time. They are used to determine the rate constant and reaction order from experimental data.

Example for n=1n = 1n=1:

ln[A]=−kt+ln[A]0\ln[A] = -kt + \ln[A]_0ln[A]=−kt+ln[A]0

For zeroth-order reactions (n=0n = 0n=0):

[A]=−kt+[A]0[A] = -kt + [A]_0[A]=−kt+[A]0

For second-order reactions (n=2n = 2n=2):

1[A]=kt+1[A]0\frac{1}{[A]} = kt + \frac{1}{[A]_0}[A]1=kt+[A]01

The half-life is the time it takes for half of the initial amount of reactant to disappear.

**For first-order reactions:**

t1/2=0.693kt_{1/2} = \frac{0.693}{k}t1/2=k0.693

**For second-order reactions:**

t1/2=1k[A]0t_{1/2} = \frac{1}{k[A]_0}t1/2=k[A]01

This indicates that the half-life for second-order reactions depends on the initial concentration of the reactant, unlike first-order reactions where it is a constant.

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