Comprehensive Guide to Rates of Reaction and Collision Theory

Definition and Scope of Reaction Rates

The rate of a reaction is defined as the speed at which the reaction occurs. It is a measure of how quickly reactants are converted into products.
Rates of reaction differ significantly across different types of chemical processes:
- Very fast reactions include fireworks.
- Relatively slow reactions include the browning of an apple.
A reaction does not proceed at a steady rate for its entire duration; the speed at which chemical reactions occur changes as the reaction progresses.
In industrial chemistry and chemical engineering, reaction rates are critical for profitability. For the manufacture of products to be commercially viable, reactions must occur rapidly to maximize production efficiency.

Progression and Graphical Representation of Reactions

Reactions start at their fastest point and gradually get slower. This occurs because the concentration of reactants decreases over time, reducing the frequency of successful collisions.
Graphs of reaction rates track either the increasing amount of product or the decreasing amount of reactant over time:
- Steep Gradient: Indicates a fast reaction rate.
- Shallow Gradient: Indicates a slow reaction rate.
Over time, the gradient of the graph decreases as reactant concentration falls. The graph eventually flattens out completely when all reactant particles have reacted and the maximum amount of product has been formed.
In a typical reaction curve:
- The start represents all reactants.
- The middle section represents a mix of reactants and products.
- The flat end of the curve represents 100% product completion.

Measurement of Reaction Rates

Quantitative data for reaction rates is obtained by observing the rate of product production or the disappearance of reactants. Methods include:

Gas Production:
- Qualitative: Visually comparing the rate of effervescence.
- Quantitative: Measuring the volume of gas produced over a period of time using a gas syringe.
- Example: Acid reacting with a reactive metal to produce hydrogen ( $H_2$ ) gas.
Change of Mass:
- Quantitative: Measuring the loss of mass from a reaction that produces a gas using a balance. Typically involves cotton wool to prevent acid spray from escaping while allowing gas to vent.
- Example: Acid reacting with carbonate to produce carbon dioxide ( $CO_2$ ) gas; metal reacting with oxygen to produce metal oxide (corrosion).
Change of Appearance (Precipitation):
- Qualitative: Visually comparing the amount of solid being produced or dissolving.
- Quantitative: Measuring the time taken for a certain amount of solid to be produced. Often involves the "disappearing cross" experiment where the observer looks through the reaction at a cross until it is obscured by precipitate.
- Example: Precipitation reactions.
Change of Color:
- Qualitative: Visually comparing color changes between reactants and products.
- Quantitative: Using a colorimeter to measure color intensity change over time.
- Example: Displacement reactions producing colored metal solutions.
Change of pH:
- Qualitative: Visually comparing color changes using universal indicator.
- Quantitative: Using a pH meter to record the change in acidity or alkalinity over time.
- Example: Neutralization reactions.

Collision Theory

Chemical reactions occur only when reactant particles successfully collide with each other with enough energy to form products.
For a reaction to take place, the following conditions must be met:
- Reactants must physically collide.
- Reactants must have the correct orientation for bond breaking/forming to occur.
- Reactants must possess sufficient energy to overcome the energy barrier.
Activation Energy: This is the minimum energy required for a successful collision to occur.
Total product formation is directly proportional to the number of successful collisions.

Factors Affecting the Rate of Reaction (SCAT, Cat!)

The acronym SCAT, Cat! can be used to remember the factors that increase reaction rates: Surface area, Concentration, Agitation, Temperature, and Catalysts.

Surface Area

Successful collisions only occur at the surface of solid reactants.
Breaking a solid into smaller pieces increases the available surface area.
Increasing surface area increases the frequency of successful collisions, thereby increasing the reaction rate.
Example: Powdered zinc ( $Zn$ ) reacts much more rapidly with hydrochloric acid ( $HCl$ ) than zinc granules because the powder has a higher surface area.
Graphing Surface Area: A graph for a powder (high surface area) will be much steeper than a graph for lumps (low surface area), though both will reach the same final volume of product if the amount of reactant is equal.

Concentration

Concentration refers to the amount of solute in a particular volume of solvent. A dilute solution has few particles; a concentrated solution has many particles close together.
Increasing the concentration of solutions (or pressure of gases) increases the number of particles in a given volume.
This leads to an increase in the frequency of collisions.
While the number of successful collisions increases, the percentage (%) of successful collisions remains the same because concentration does not change the energy or orientation requirements.
Metaphor: Like a lottery where every ticket has an equal chance of winning; if you sell more tickets (collisions), you get more winners (successful reactions), even though the probability per ticket is unchanged.

Agitation (Stirring)

Agitation ensures that reactants remain in contact by physically moving them.
It functions by removing the build-up of products that may surround and "shield" the remaining reactants, allowing fresh reactant particles to collide.

Temperature

Increasing temperature increases the kinetic energy and speed of particles in liquids and gases.
This affects the rate in two ways:
1. Increased Frequency: Particles move faster and collide more often.
2. Increased Energy: Particles hit each other harder. More collisions meet or exceed the activation energy threshold, increasing the likelihood of breaking chemical bonds.
Unlike concentration, increasing temperature increases the percentage (%) of successful collisions.

Catalysts

A catalyst speeds up a reaction by offering an alternative pathway with a lower activation energy.
Because the activation energy is lower, a greater proportion of collisions are successful at any given energy level.
Properties of Catalysts:
- They are not reactants.
- They do not take part in the reaction directly.
- They remain chemically unchanged at the end of the process.
Applications of Catalysts:
- Iron ( $Fe$ ) is used in the Haber Process to manufacture fertilizer.
- Catalysts are used to produce synthetic materials like polyester and plastics.
- Biological catalysts, known as enzymes, are used in biological soap powders and to tenderize meat (e.g., enzymes in pineapple helping ham).

Mathematical Calculations of Reaction Rates

Rates of reaction are always reported as absolute (positive) values: $| \text{Rate} |$ .

Average Rate of Reaction

The average rate is the slope of the line between any two time points on a reaction curve.
Calculated using the gradient formula: $\text{Rate} = \frac{\text{Change in Amount}}{\text{Change in Time}} = \frac{\nabla y}{\nabla x}$
Based on product appearance or reactant disappearance: $\text{Rate} = \frac{\text{Amount of Mass Lost } (g)}{\text{Change in Time } (s)}$ $\text{Rate} = \frac{\text{Amount of Gas Collected } (mL)}{\text{Change in Time } (s)}$
In terms of concentration for a reaction $A \rightarrow B$ : $\text{Average Rate} = \frac{[B]_2 - [B]_1}{t_2 - t_1} = \frac{\triangle [B]}{\triangle t}$

Quantitative Data Example: Nitrogen Dioxide Decomposition

For the reaction $2NO_2(g) \rightarrow 2NO(g) + O_2(g)$ , use the following data to find the average rate of decomposition of $NO_2$ :

Time ( $s$ )	$[NO_2]$ ( $M$ )
0	0.500
50	0.394
100	0.325
150	0.275
200	0.241
250	0.210
300	0.190

Calculations for Disappearing-Cross Experiment

In these experiments, the reaction rate is estimated by taking the reciprocal of the time ( $t$ ) it takes for the cross to disappear: $\text{Rate} = \frac{1}{t}$
The unit for this rate is $s^{-1}$ (which is equivalent to per second, or $/s$ ).
A faster reaction results in a smaller time value and thus a larger calculated rate value.

Questions & Discussion

Discussion: Food Preservation

Question: Why does food remain usable much longer if kept in a freezer?
Response: Food spoils due to chemical reactions. Reducing temperature slows these reactions because there are fewer and "softer" (lower energy) collisions between molecules at lower kinetic energy states.

Discussion: The High-Five Analogy

Scenario: Model a reaction as LHC students high-fiving in GSC. How do you increase the rate using the following?
- Surface Area: (Analogous to spreading students out vs. being in a tight cluster).
- Concentration: Adding more students to the same room.
- Temperature: Making students run faster.
- Agitation: Pushing students around so they move through the crowd.
- Catalyst: Giving students a specific designated meeting point (surface) where high-fives can occur more easily.

Experimental Data Analysis: Sodium Thiosulfate and HCl Students recorded the mean time ( $s$ ) for a cross to disappear at various temperatures:

Temperature ( $^\circ C$ )	Trial 1 ( $s$ )	Trial 2 ( $s$ )	Trial 3 ( $s$ )	Mean Time ( $s$ )	Average RoR ( $s^{-1}$ )
20	84	80	82	82.0	$0.0122$
30	61	58	60	59.7	$0.0168$
40	43	40	42	41.7	$0.0240$
50	30	32	29	30.3	$0.0330$
60	22	20	21	21.0	$0.0476$

Conclusion: As temperature increases, the rate of reaction increases, as evidenced by the decreasing mean time and increasing $s^{-1}$ values.
Justification: Higher temperatures provide particles with more kinetic energy, increasing collision frequency and the proportion of particles exceeding the activation energy.