Unit 4: Rates of Reaction

Investigating the speed of chemical reactions and the factors that control them.

4.5 Simple Collision Theory & Activation Energy

For a chemical reaction to occur, reactant particles must collide. However, not all collisions lead to a reaction. Simple Collision Theory states that for a collision to be successful (or effective), two conditions must be met:

  • Collision Geometry: The particles must collide with the correct orientation, allowing the appropriate bonds to break and form.
  • Collision Energy: The colliding particles must possess a minimum amount of kinetic energy, known as the activation energy ($E_a$). This is the energy barrier that must be overcome to break existing bonds and initiate the reaction.

The rate of a reaction depends on the frequency of these effective collisions. The activation energy can be shown on an enthalpy profile diagram as an energy "hump" between reactants and products.

Solved Examples:
  1. What are the two requirements for an effective collision?
    Solution: The particles must collide with sufficient energy (equal to or greater than the activation energy) and with the correct orientation.
  2. What is activation energy ($E_a$)?
    Solution: The minimum amount of energy required for reactant particles to form products upon collision.
  3. Why do most collisions between reactant molecules not result in a reaction?
    Solution: Because most colliding particles lack the minimum activation energy, or they do not have the correct orientation for bonds to break and form.
  4. On an enthalpy profile diagram, where is the activation energy shown?
    Solution: It is shown as the energy difference between the reactants and the peak of the energy curve (the transition state).
  5. If a reaction has a very high activation energy, would you expect it to be fast or slow?
    Solution: Slow. A high activation energy means that only a very small fraction of colliding particles will have enough energy to react.
  6. What is the difference between collision frequency and the frequency of effective collisions?
    Solution: Collision frequency is the total number of collisions per unit time, whereas the frequency of effective collisions is the number of collisions that actually result in a reaction.
  7. Does the value of $\Delta H$ for a reaction affect its activation energy?
    Solution: No, $\Delta H$ is the overall energy difference between products and reactants. A reaction can be highly exothermic (large negative $\Delta H$) but still have a high activation energy and be very slow.
  8. Explain why a collision between two H₂ molecules is unlikely to form a new substance.
    Solution: The collision energy is typically not high enough to break the strong H-H covalent bonds, and even if it were, reforming H-H bonds is the most favorable outcome.
  9. How does activation energy relate to bond breaking?
    Solution: Activation energy provides the energy needed to overcome the repulsion between electron clouds and to break the chemical bonds within the reactant molecules, allowing new bonds to form.
  10. Two reactions have the same collision frequency. Reaction A is much faster than Reaction B. What can you conclude about their activation energies?
    Solution: Reaction A must have a lower activation energy than Reaction B, meaning a larger fraction of its collisions are effective.

4.6 Factors Affecting Rates I (Concentration, Pressure, Temperature)

Several factors can be manipulated to change the rate of a chemical reaction by altering the frequency of effective collisions.

  • Concentration: Increasing the concentration of reactants in a solution increases the number of particles per unit volume. This leads to more frequent collisions (higher collision frequency), thus increasing the reaction rate.
  • Pressure (for gases): Increasing the pressure of a gaseous system by reducing its volume forces the gas particles closer together. This is equivalent to increasing concentration, leading to a higher collision frequency and a faster reaction rate.
  • Temperature: Increasing the temperature increases the reaction rate for two reasons:
    1. Particles gain kinetic energy and move faster, leading to more frequent collisions.
    2. A significantly larger proportion of particles will have kinetic energy equal to or greater than the activation energy, making collisions much more likely to be effective. The second effect is more significant.
Solved Examples:
  1. Explain, using collision theory, why increasing concentration increases reaction rate.
    Solution: Higher concentration means more reactant particles are packed into the same volume. This increases the probability of particles colliding, so the collision frequency increases, leading to a higher rate of effective collisions.
  2. How does compressing a gas affect the rate of reaction between gaseous particles?
    Solution: Compressing a gas increases its pressure and concentration. The particles are closer together, leading to a higher collision frequency and a faster reaction rate.
  3. Why does a small increase in temperature (e.g., 10°C) often cause a large increase (e.g., doubling) in reaction rate?
    Solution: While collision frequency increases slightly, the main reason is that a 10°C rise causes a large increase in the number of particles that possess energy greater than the activation energy, leading to a much higher frequency of successful collisions.
  4. A reaction between an acid and a carbonate is faster with 2 M acid than with 1 M acid. Why?
    Solution: The 2 M acid has a higher concentration of H⁺ ions. This leads to more frequent collisions between H⁺ ions and the carbonate, increasing the reaction rate.
  5. Does increasing the temperature change the activation energy of a reaction?
    Solution: No. Temperature increases the kinetic energy of the particles, but it does not change the intrinsic energy barrier (activation energy) of the reaction itself.
  6. Why is food stored in a refrigerator to slow down spoilage?
    Solution: Spoilage is caused by chemical reactions. The low temperature in a refrigerator reduces the kinetic energy of reactant particles, slowing down the rate of these spoilage reactions.
  7. If you increase the volume of a container holding two reacting gases at constant temperature, what happens to the rate?
    Solution: The rate decreases. Increasing the volume decreases the pressure and concentration of the gases, leading to a lower collision frequency.
  8. How does concentration change over time in a typical reaction? How does this affect the rate?
    Solution: Reactant concentration decreases as the reaction proceeds. This causes the collision frequency to decrease, so the reaction rate slows down over time.
  9. Does pressure affect the rate of reactions in the aqueous phase?
    Solution: No. Pressure changes primarily affect the concentration of gases. The volume of liquids and solids is not significantly affected by pressure.
  10. Two identical reactions are run, one at 20°C and one at 40°C. Which factor is most responsible for the rate difference: collision frequency or collision energy?
    Solution: Collision energy. The increase in the fraction of molecules possessing energy greater than the activation energy is the most significant factor.

4.7 Factors Affecting Rates II (Physical State, Catalysts, Solvent)

Beyond concentration and temperature, other factors like the physical state of reactants and the presence of catalysts play a crucial role in determining reaction rates.

  • Physical State & Surface Area: Reactions involving solids can only occur at the surface. By breaking a solid into smaller pieces (e.g., powder vs. lump), the surface area is increased. This exposes more particles to collision, increasing the collision frequency and thus the reaction rate.
  • Catalyst: A substance that increases the rate of a chemical reaction without being consumed itself. Catalysts work by providing an alternative reaction pathway with a lower activation energy. This means a larger fraction of collisions will be effective, dramatically increasing the rate. A catalyst does not change the overall enthalpy change ($\Delta H$).
  • Solvent: For reactions in solution, the nature of the solvent can influence the rate by affecting how reactant particles are stabilized or interact with each other.
Solved Examples:
  1. Explain why a powdered antacid tablet works faster than a whole tablet.
    Solution: The powdered tablet has a much larger surface area than the whole tablet. This allows the stomach acid to collide with more particles of the antacid simultaneously, increasing the reaction rate.
  2. How does a catalyst increase the rate of a reaction?
    Solution: A catalyst provides an alternative reaction pathway with a lower activation energy. This allows more colliding particles to have sufficient energy to react, increasing the frequency of effective collisions.
  3. Does a catalyst increase the amount of product formed in a reaction?
    Solution: No. A catalyst only increases the rate at which the product is formed; it does not change the overall yield or the position of equilibrium.
  4. Draw an enthalpy profile diagram showing the effect of a catalyst.
    Solution: The diagram should show a second, lower "hump" for the catalyzed pathway, starting and ending at the same reactant and product enthalpy levels as the uncatalyzed path.
  5. Why do reactions in the gaseous or aqueous phase tend to be faster than in the solid phase?
    Solution: In gases and liquids, particles are in constant, random motion, allowing for frequent collisions throughout the substance. In solids, particles are fixed, and reactions can only happen at the surface.
  6. What effect does a catalyst have on the collision frequency?
    Solution: A catalyst has no effect on the collision frequency or the kinetic energy of the particles. It only lowers the activation energy barrier.
  7. Give an example of a biological catalyst.
    Solution: Enzymes are biological catalysts. For example, the enzyme catalase speeds up the decomposition of hydrogen peroxide.
  8. A lump of coal burns slowly, but coal dust can be explosive. Explain this difference in terms of reaction rate.
    Solution: Coal dust has an extremely large surface area compared to a lump of coal. This allows for an incredibly high frequency of collisions with oxygen, leading to a very rapid, explosive combustion reaction.
  9. Will a catalyst for a forward reaction also catalyze the reverse reaction?
    Solution: Yes. A catalyst lowers the activation energy for both the forward and reverse reactions by the same amount, speeding up the rate at which equilibrium is reached.
  10. How could you increase the rate of the reaction between a solid metal and an acid?
    Solution: You could increase the rate by (1) increasing the acid concentration, (2) increasing the temperature, or (3) grinding the metal into a powder to increase its surface area.

4.8 Measuring Rates of Reaction

The rate of reaction is defined as the change in concentration of a reactant or product per unit time. Its units are typically mol dm⁻³ s⁻¹. The rate is not constant; it is usually fastest at the beginning of the reaction and decreases as reactants are used up.

We can determine the rate experimentally by monitoring a measurable change over time, such as gas volume produced, mass loss, or change in concentration. Plotting concentration against time gives a curve. The rate at any specific time is found by calculating the gradient (slope) of the tangent to the curve at that point. The initial rate is the gradient of the tangent at time t=0.

Solved Examples:
  1. Define 'rate of reaction'.
    Solution: The change in concentration of a reactant or product per unit time.
  2. Why does the rate of reaction decrease over time?
    Solution: As the reaction proceeds, the concentration of reactants decreases. This leads to a lower frequency of collisions between reactant particles, slowing the rate.
  3. How can you find the initial rate of reaction from a concentration-time graph?
    Solution: By drawing a tangent to the curve at time t=0 and calculating the gradient of that tangent.
  4. A reaction produces 40 cm³ of gas in 20 seconds. What is the average rate in cm³/s?
    Solution: Average rate = $40 \, cm³ / 20 \, s = 2.0$ cm³/s.
  5. On a concentration-time graph for a reactant, is the gradient positive or negative?
    Solution: Negative, because the concentration of a reactant decreases over time. The rate, however, is always reported as a positive value.
  6. Suggest a method to monitor the rate of the reaction: $CaCO_3(s) + 2HCl(aq) \rightarrow CaCl_2(aq) + H_2O(l) + CO_2(g)$.
    Solution: You could monitor the rate by (1) measuring the volume of CO₂ gas produced over time with a gas syringe or (2) measuring the loss in mass of the flask over time as CO₂ escapes.
  7. If the gradient of a tangent at t=30s on a [product] vs. time graph is 0.05, what is the rate?
    Solution: The rate at 30 seconds is 0.05 mol dm⁻³ s⁻¹.
  8. Why is the initial rate often used to compare reactions?
    Solution: The initial rate is measured when the concentrations of reactants are known precisely and are at their highest, making it a reliable and reproducible point of comparison.
  9. How would the initial gradient of a concentration-time graph change if the temperature was increased?
    Solution: The initial gradient would be steeper, indicating a faster initial rate of reaction.
  10. A reaction's concentration drops from 0.8 M to 0.4 M in 50 seconds. What is the average rate of consumption of the reactant?
    Solution: Average rate = $\frac{-(0.4 - 0.8) M}{50 s} = \frac{0.4 M}{50 s} = 0.008$ mol dm⁻³ s⁻¹.

End of Topic Questions

Answer: Correct orientation and sufficient energy (greater than or equal to the activation energy).

Answer: It increases the rate by increasing both the collision frequency and, more importantly, the proportion of particles with energy exceeding the activation energy.

Answer: To provide an alternative reaction pathway with a lower activation energy.

Answer: The powdered zinc has a larger surface area, which increases the frequency of collisions with the acid.

Answer: The change in concentration of a reactant or product per unit time.

Answer: No, it only affects the activation energy.

Answer: By calculating the gradient of the tangent to the curve at that specific time.

Answer: Negligible effect, as the volume of liquids and solids is not significantly compressible.

Answer: The minimum kinetic energy that colliding particles must possess for a reaction to occur.

Answer: Because the concentration of reactants decreases, leading to fewer collisions per unit time.

Answer: The reaction rate will increase significantly because a much larger fraction of molecules will have energy exceeding the new, lower activation energy.

Answer: mol dm⁻³ s⁻¹.

Answer: No, it only affects the collision frequency.

Answer: At the beginning (t=0), where the curve is steepest.

Answer: Enzymes.

Answer: The temperature increases by 30°C (three 10°C intervals). The rate will be $2 \times 2 \times 2 = 8$ times faster.

Answer: The volume of oxygen gas produced over time.

Answer: A collision that has both the correct orientation and sufficient energy to result in a chemical reaction.

Answer: It exposes more particles to the other reactants, thereby increasing the collision frequency.

Answer: It would double the frequency of collisions between particles of A and B, likely doubling the initial rate.
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