# 5.2.2 Deriving Rate Equations

### Deducing Orders

#### Order of reaction

• The order of reaction shows how the concentration of a reactant affects the rate of reaction

Rate = k [A]m [B]n

• When m or n is zero = the concentration of the reactants does not affect the rate
• When the order of reaction (m or n) of a reactant is 0, its concentration is ignored
• The overall order of reaction is the sum of the powers of the reactants in a rate equation
• For example, in the reaction below, the overall order of reaction is 2 (1 + 1)

Rate = k [NO2] [Cl2]

#### Order of reaction from concentration-time graphs

• In a zero-order the concentration of the reactant is inversely proportional to time
• This means that the concentration of the reactant decreases with increasing time
• The graph is a straight line going down
• In a first-order reaction the concentration of the reactant decreases with time
• The graph is a curve going downwards and eventually plateaus
• In a second-order reaction the concentration of the reactant decreases more steeply with time
• The concentration of reactant decreases more with increasing time compared to in a first-order reaction
• The graph is a steeper curve going downwards

#### Order of reaction from initial rate

• The progress of the reaction can be followed by measuring the initial rates of the reaction using various initial concentrations of each reactant
• These rates can then be plotted against time in a rate-time graph
• In a zero-order reaction the rate doesn’t depend on the concentration of the reactant
• The rate of the reaction therefore remains constant throughout the reaction
• The graph is a horizontal line
• The rate equation is rate = k
• In a first-order reaction the rate is directly proportional to the concentration of a reactant
• The rate of the reaction decreases as the concentration of the reactant decreases when it gets used up during the reaction
• The graph is a straight line
• The rate equation is rate = k [A]
• In a second-order reaction, the rate is directly proportional to the square of concentration of a reactant
• The rate of the reaction decreases more as the concentration of the reactant decreases when it gets used up during the reaction
• The graph is a curved line
• The rate equation is rate = k [A]2

#### Order of reaction from half-life

• The order of a reaction can also be deduced from its half-life (t1/2 )
• For a zero-order reaction the successive half-lives decrease with time
• This means that it would take less time for the concentration of reactant to halve as the reaction progresses
• The half-life of a first-order reaction remains constant throughout the reaction
• The amount of time required for the concentration of reactants to halve will be the same during the entire reaction
• For a second-order reaction, the half-life increases with time
• This means that as the reaction is taking place, it takes more time for the concentration of reactants to halve

#### Calculating the initial rate

• The initial rate can be calculated by using the initial concentrations of the reactants in the rate equation
• For example, in the reaction of bromomethane (CH3Br) with hydroxide (OH) ions to form methanol (CH3OH) the reaction equation and rate are as follows:

CH3Br + OH → CH3Br + Br (aq)

Rate = k [CH3Br] [OH]

Where k = 1.75 x 10-2 dm-2 mol-1 s-1

• If the initial concentrations of CH3Br and OH are 0.0200 and 0.0100 mol dm-3 respectively, the initial rate of reaction is:

Rate = k [CH3Br] [OH]

Initial rate = 1.75 x 10-2 x (0.0200) x (0.0100)

Initial rate = 3.50 x 10-6 mol dm-3 s-1

### Deriving Rate Equations

Deriving Rate Equations

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