18.1 Orders, rate equations and rate constants

Rate of reaction

* they are measured by observing the changes in quantities of reactants or products over time.

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**Rate = quantity reacted or produced/time**

**Rate = change in concentration/change in time**

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Concentration is measured in mol dm-3.

Time is measured in s

Therefore the rate has the units of mol dm-3 / s which is **mol dm-3 s-1.**

* Shorthand for concentration is \[\]

Order of reaction

Changing concentration often changes the rate of reaction.

Rate of reaction is proportional to the concentration of a particular reactant raised to a power.

* **Rate ∝ [D]       or       Rate =** ***k*****[D]**

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For each reactant, the power is the order of reaction for that reactant.

Within the reaction, different reactants can have different orders and each may affect the reaction in a different way.

* Zero order
* First order
* Second order

Zero Order

This is when the concentration of a reactant has no effect on the rate.

***rate= k*** **[B]*****0***

(0 is the power)

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* any number raised to the power 0 is 1
* concentration does not influence the rate

First Order

Reaction is first order when the rate depends on its concentration raised to the power of one.

***rate= k*** **[B]*****1***

(1 is the power)

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* if the concentration of B is doubled, the reaction rate increases by a factor of 2
* if the concentration of B is tripled, then reaction rate increases by a factor of 3

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Any change in concentration gives the same change to the rate.

Second order

Reaction is second order when the rate depends on its concentration raised to the power of two.

***rate= k*** **[B]*****2***

(2 is the power)

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* if the concentration of b is double, reaction rate increases by factor of 2^2 = 4
* if the concentration of b is tripled, reaction rate increases by factor of 3^2 = 9

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Any change in concentration, changes the rate by the square of the change.

Rate equation and rate constant

Rate equation gives the mathematical relationship between the concentration of the reactants and reaction rate.

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**Rate of reaction =** ***k*** **[A]*****m*** **[B]*****n***

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Rate constant k is the proportionality constant, number that mathematically converts between the rate of reaction and concentration and orders.

* like an exchange rate

Overall order

overall order = sum of orders with respect to each reactant

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**Rate of reaction =** ***k*** **[A]*****m*** **[B]*****n***

* overall order = m+n

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Units of the rate constant k

Unit of the rate constant depend upon the number of concentration terms in rate equation, can be determined by

* rearranging the equation to make k the subject
* substitute units into the expression for k
* cancel common units and how the final units on a single line.

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RATE UNITS = MOL DM-3 S-1

CONCENTRATION UNITS = MOL DM-3

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**Overall order = 0**

* k = rate = mol dm-3 s-1

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**Overall order = 1**

* k = rate/\[a\]^1 = mol dm-3 s-1/ mol dm-3
* units = s-1

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**Overall order = 2**

* k = rate/\[a\]^"2 = mol dm-3 s-1/ (mol dm-3) (mol dm-3)
* units = dm3 mol -1 s-1

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* put positive indices before negative indices.

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Orders from experimental results

Orders of reaction must be determined experimentally by monitoring how a physical quantity changes overtime.

Orders cannot be found directly from the chemical equation.

When comparing the effect of different concentrations of reactants on reaction rates, it is important that the rate is always measured after the same time, ideally as close to the start of the experiment as possible.

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initial rate is the instantaneous rate at the beginning of an experiment when t= 0

tip

**Zero order** - no matter what you do to the concentration, the rate doesn’t change.

**1st order** - whatever you do to the concentration, the rate changes by the same factor

**2nd order** - whatever you do to the concentration, the rate changed by the same factor squared.