5.1.1 How fast

Definitions

Term	Definition
Order	The power to which the concentration of a reactant is raised in the rate equation
Overall order	The sum of the individual orders of reactants in the rate equation
Rate constant	The constant that links the rate of reaction with the concentrations of the reactants raised to the powers of their orders in the rate equation
Initial rate of reaction	The change in the concentration of a reactant or product per unit time at the start of the reaction (\(t=0\))
Rate-determining step (RDS)	The slowest step in the reaction mechanism of a multi-step reaction
Molecularity	The number of molecules in the slow rate determining step

\(rate = k [A]^m [B]^n\)
\(overall \ order = m + n\)
\(k = rate \ constant\)
Unit of \(k = mol^{(1-\text{overall order})} \cdot dm^{3 \times (\text{overall order}-1)} \cdot s^{-1}\)

One change only
- Using experiments X and Y:
- \([A]\) changes from ... to ...: doubled / tripled / etc.
- \([B]\) constant
- Rate doubled / quadrupled / etc.
- Hence the order wrt A is ... order
Multiple changes - choose 2 experiments where all the concentrations are multiplied by the same amount
- Using experiments X and Y:
- \([A]\) changes from ... to ...: multiplied by \(x\)
- \([B]\) changes from ... to ...: multiplied by \(y\)
- Rate multiplied by \(z\)
- \(z = x^m \times y^n\) (where \(n\) is known from previous step)
- Hence the order wrt B is ...

Scenario	Method
Coloured compounds present	Colorimeter
Acidic / alkaline compound present	Monitor pH Use pH meter / titration to determine pH if reaction is slow
Gas produced	Measure volume of gas produced / mass loss if gas escapes
Aqueous reactions	Measure conductivity

Zero order
- Rate does not change with concentration
- Straight line with negative gradient
First order
- Downward curve with decreasing gradient over time
- Constant half-life (\(t_{1/2}\))
- \(k = \frac{\ln 2}{t_{1/2}}\) (\(k\) can also be worked out by finding the gradient of the rate-concentration graph)
Second order
- Rate is directly proportional to the square of concentration
- Downward curve steeper at start + tailing off more slowly

Several experiments with different concentrations of one reactant, all other reactant concentrations are kept constant
Time (\(t\)) measured from the start of reaction to when a visual change is observed (colour change / precipitate)
Initial rate is directly proportional to \(\frac{1}{t}\)
Iodine clocks
- Measure time taken for iodine colour (orange-brown) to appear
- Colour change is delayed by adding a small amount another chemical that removes iodine as it forms
- Starch can be added to form a blue-black colour
Plot a graph of \(\frac{1}{t}\) against concentration
- Deduce order of reaction from shape of graph (same as rate-concentration graphs)
Shorter time = higher accuracy

Reactants only include the species involved in the rate equation
Stoichiometry in the rate equation should match the stoichiometry in the overall reaction

Increase temperature = increase \(k\)
Higher temperature shifts the Boltzmann distribution to the right \(\rightarrow\) higher proportion of particles has a higher energy than \(E_a\)
Particles move faster + collide more frequently