7.1 Rates of Reactions

This topic explains the rate of reaction — what it is, how it is measured, and how it changes over time. It covers the mathematical expression of reaction rate and how to calculate it from experimental data.

Definition

Rate of reaction is the change in concentration of reactants or products per unit time.

Main Idea

Chemical reactions occur at different rates. The rate of reaction is defined as the change in concentration of a substance per unit time. The concentration of reactants decreases while the concentration of products increases with time. Therefore, the rate of a reaction can also be defined as the decrease in concentration of reactants per unit time or the increase in concentration of products per unit time.

Core Concept

Rate = Change in concentration of a substanceTime taken for change

• Unit of concentration: mol dm⁻³
• Unit of time: second (s)
• Unit of reaction rate: mol dm⁻³ s⁻¹

Detailed Explanation

What is Rate of Reaction?

• The rate of reaction is the change in concentration of reactants or products per unit time.
• Mathematically:
• The concentration of reactants decreases and concentration of products increases with the passage of time.
• Therefore, rate of a reaction can also be defined as the decrease in concentration of reactants per unit time or the increase in concentration of products per unit time.
• The unit of concentration is mole dm⁻³ and time is second, so unit of reaction rate is mole dm⁻³ s⁻¹.

Graphical Representation

For the general reaction: A → B

• The change in concentration of reactants and products can be represented graphically.
• The slope of the curve for both starting materials and products is steeper at the beginning than at later stages.
• This indicates a rapid decrease or increase in the concentration of reactant or product, respectively.
• As the reaction progresses, the slope becomes less steep, indicating a decrease in the reaction rate.
• Eventually the graph becomes horizontal and the reaction stops.

• The reaction rate is never constant.
• The concentration of reactants continuously decreases while the concentration of products increases with time.
• Therefore, the reaction rate also decreases continuously.
• The rate measured from a time interval is just the average reaction rate for that interval.

Instantaneous Rate of Reaction

If dx is a very small change in concentration of a product in a very small time interval dt, the rate of reaction is expressed as:

Rate of reaction = dxdt

Consider a general reaction: A → B

The rate of reaction can be expressed in terms of the rate of disappearance of reactant A or the rate of appearance of product B.

dxdt = -d[A]dt

dxdt = d[B]dt

Where d[A] and d[B] represent changes in the concentration of A and B respectively. The negative sign indicates a decrease in the concentration of the reactant A, whereas the positive sign indicates the increase in the concentration of product B.

Example 7.1: Determining the Rate of Reaction

Problem: Determine the rate of the following reaction: A + B → C

Rate of a chemical reaction between any two-time intervals can be determined from experimental data. For obtaining experimental data, you need to measure change in the concentration of reactants or products at different time intervals.

Data:

Solution:

Suppose you want to calculate the rate of reaction between time intervals 0.0 second and 20 seconds.

dt = Change in time = 20s - 0.0 = 20s

d[C] = Change in the concentration of C = 0.38 - 0.0 = 0.38 mol/dm³

dxdt = +d[C]dt = 0.3820 = 0.019 mol/dm³/s

Final Answer: Rate of reaction = 0.019 mol dm⁻³ s⁻¹

Note: Like this, rate of reaction can be determined between any two time intervals. Note that you can determine only the average rate of reaction between the given time intervals.

Formula

Rate = Change in concentrationTime taken

Units

mol dm^-3 s^-1

Rate Expression

For reaction A → B:

Rate = -d[A]dt = d[B]dt

• Negative sign: Reactant concentration decreases.
• Positive sign: Product concentration increases.

Graphical Analysis

• Slope steep at beginning → fast rate.
• Slope less steep later → slow rate.
• Graph horizontal → reaction stops.
• Rate decreases continuously.

Example 7.1

• Concentration of C at 0.0 s = 0.0 mol/dm³
• Concentration of C at 20 s = 0.38 mol/dm³

Required: - Rate of reaction

Solution: Rate = 0.38 - 0.020 - 0.0 = 0.3820 = 0.019 mol/dm³/s

Final Answer: 0.019 mol dm⁻³ s⁻¹

Important Points

• 1. Rate = change in concentration / time.
• 2. Unit: mol dm⁻³ s⁻¹.
• 3. Reactants decrease, products increase.
• 4. Rate is fastest at beginning.
• 5. Rate decreases continuously.
• 6. Rate is never constant.
• 7. Average rate measured over time interval.
• 8. Example: Rate = 0.019 mol dm⁻³ s⁻¹.

Remember

• - Rate: Change in concentration / time
• - Unit: mol dm⁻³ s⁻¹
• - Reactants: Decrease
• - Products: Increase
• - Rate: Fastest at beginning, decreases over time
• - Example: 0.019 mol dm⁻³ s⁻¹

Common Mistakes

• 1. Thinking rate is constant: It decreases over time.
• 2. Forgetting the negative sign for reactants: Reactants decrease.
• 3. Mixing up average and instantaneous rate: Average = over interval; Instantaneous = at a point.
• 4. Forgetting units: mol dm⁻³ s⁻¹.

Quick Revision

• Rate = change in concentration / time.
• Unit: mol dm⁻³ s⁻¹.
• Reactants decrease, products increase.
• Rate is fastest at beginning.
• Rate decreases continuously.
• Rate is never constant.
• Average rate measured over time interval.
• Example: Rate = 0.019 mol dm⁻³ s⁻¹.

60-Second Revision

• Rate: Change in concentration / time
• Unit: mol dm⁻³ s⁻¹
• Reactants: Decrease
• Products: Increase
• Rate: Fastest at beginning, decreases over time
• Example: 0.019 mol dm⁻³ s⁻¹

QUALITY VALIDATION

• Topic: 7.1 Rates of Reactions
• Chapter: 7 (Chemical Kinetics)

• Source re-read: PASS
• Source scope followed: PASS
• Knowledge level matched: PASS
• Important concepts covered: PASS
• Definitions checked: PASS
• Equations checked: PASS
• Derivations checked: N/A
• Examples checked: PASS
• Unsupported knowledge added: NO
• Unnecessary repetition: NO
• Notes format maintained: PASS
• Important source content omitted: NO

• Source limitations:
• NONE

NEXT TOPIC