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### Reaction rates

Chapter 14

Factors That Affect Reaction Rates

- Physical state of reactants:
- Reactants must come in contact with one another in order for a reaction to occur.

- Concentration of reactants:
- Reactions tent to proceed faster if the reactants are present in higher concentrations.

- The temperature at which the reaction occurs.
- In general reactions happen faster at higher temperatures.

How fast do reactions happen?

- The speed of any even is defined as a change that occurs over a given period of time.
- The rate of a reaction is stated as the change in concentration of a reactant or product per unit of time.
- Example:
- A B
- If we start with 1.0 moles of A and 0.0 moles of B in one liter of solution what is the concentration of each?
- If after 40 seconds the concentration of A is 0.3 M and the concentration of B is 0.7 M we can calculate the average rate of the reaction.

Example

- In a reaction between butyl chloride (C4H9Cl) and water, the concentration of C4H9Cl is 0.220M at the beginning of the reaction. At 4.00s, the concentration of butyl chloride is 0.100M. Calculate the average reaction rate as moles of C4H9Cl consumed per second.

Instantaneous Rate

- Take the derivative of the rate.

Reaction rates and stoichiometry

- In the reaction between C4H9Cl and water the rate of disappearance of C4H9Cl is the same as the rate of formation of C4H9OH because the stoichiometry is a one to one ratio.
- 2HI H2 + I2

- In the following reaction if the rate at which O2 appears is 6.0 x 10-5 M/s what would be the rate of disappearance of O3?
- 2O3 3O2

Reaction Orders

- The rate law for most reactions have the general from:
- Rate = k[reactant 1]m[reactant 2]n
- m and n are called the reaction orders
- The sum of m and n is called the overall reaction order.
- The exponents in a rate law are sometimes the same as the coefficients in the balanced equation but must be determined experimentally.

Units of rate constants

- units of rate = (units of rate constant)(units of concentration)2
- 2N2O5 4NO2 + O2
- Rate = k[N2O5]
- CHCl3 + Cl2 CCl4 + HCl
- Rate = k[CHCl3][Cl2]1/2
- H2 + I2 2HI
- Rate = k[H2][I2]

The Change of Concentration With Time

- First order reactions:
- A first order reaction is on whose rate depends on the concentration of a single reactant raised to the first power.

- A Products
- Rate = -Δ[A]/Δt = k[A]
- Integrated rate law
- ln[A]t – ln[A]0 = -kt

- ln[A]t = -kt + ln[A]0

Reaction Half Life

- The half life of a reaction is the time required for the concentration of a reactant to drop to one half of its initial value (t1/2)
- [A]t1/2 = ½[A]0

Temperature and Rate

- Most reactions proceed faster at higher temperatures.
- One explanation of this is the collision model
- Orientation factor
- Activation energy:
- The minimum amount of energy required to initiate a chemical reaction.

Collision Theory Summary

- Reacting substances must collide
- Reacting substances must collide in the correct orientation.
- Reacting substances must collide with enough energy to form an activated complex.

The Arrhenius Equation

- k = Ae-Ea/RT
- k = rate constant
- Ea = activation energy
- R = 8.314 J/mol-k
- T = Temperature in Kelvin
- A = frequency factor

Reaction Mechanisms

- The process by which a reaction occurs is called the reaction mechanism.
- Elementary reactions
- Happen in a single step.

- The number of molecules that participate as reactants in an elementary reaction is called its molecularity.
- Unimolecular
- Bimolecular

Multistep Mechanisms

- Multistep reaction mechanisms consist of a sequence of elementary reactions.
- NO2 + CO NO + CO2
- The chemical equations for the elementary reactions in a multistep mechanism must always add to give the chemical equation of the overall process.

Rate Laws for Elementary Reactions

- If a reaction is an elementary reaction, then it’s rate law is based directly on its molecularity.

Rate Determining Step

- If a reaction occurs as a series of elementary steps one of the steps must proceed slower than the other (or others).
- This step limits the rate of the overall reaction and is called the rate limiting step.
- The slowest step in a multistep reaction is the rate limiting step.

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