Energy Change and Reaction Rates Study Guide

Fundamental Concepts of Energy Change in Chemical Reactions

• All chemical reactions involve changes in energy because bonds are broken in the reactants and new bonds are formed in the products.

• The heat of reaction ($\Delta H$) is defined as the net change in chemical potential energy of a system during a chemical reaction.

• The overall energy change is determined by the balance between two specific energy processes:

  • Energy absorbed during the breaking of bonds.
  • Energy released during the formation of new bonds.

• The mathematical relationship for enthalpy change is formulated as:

  • $\Delta H = \text{energy absorbed (breaking bonds)} - \text{energy released (forming bonds)}$

• Bond strength influences energy requirements: stronger bonds require more energy to break and subsequently release more energy when they are formed.

Exothermic and Endothermic Reactions

• Exothermic Reactions:

  • Defined as reactions which transform chemical potential energy into thermal energy.
  • Chemical potential energy is converted into thermal energy, which is then released to the surroundings.
  • These reactions result in a net release of energy, where $\Delta H < 0$.
  • There is a net release of thermal energy to the surroundings, which causes the temperature of the surroundings to increase.
  • The products in an exothermic reaction have lower energy than the reactants.

• Endothermic Reactions:

  • Defined as reactions which transform thermal energy into chemical potential energy.
  • Thermal energy is absorbed from the surroundings and converted into chemical potential energy.
  • These reactions result in a net absorption of energy, where $\Delta H > 0$.
  • There is a net absorption of thermal energy from the surroundings, which causes the temperature of the surroundings to decrease.
  • The products in an endothermic reaction have higher energy than the reactants.

Activation Energy and the Activated Complex

• Activation Energy ($E_a$):

  • Defined as the minimum energy required to start a chemical reaction or the energy required to form the activated complex.

• Activated Complex:

  • Defined as a high energy, unstable, temporary transition state between the reactants and the products.

• Energy Profile Diagrams:

  • These diagrams represent energy changes over the course of a reaction.
  • The activated complex is represented by the peak of the curve.
  • Activation energy is the energy difference measured between the reactants and the peak (activated complex).
  • The change in enthalpy ($\Delta H$) is the energy difference between the reactants and the products.
  • In an exothermic energy profile, more energy is released than absorbed ($\Delta H < 0$), and the temperature of the reaction vessel increases as chemical potential energy converts to thermal energy.
  • In an endothermic energy profile, more energy is absorbed than released ($\Delta H > 0$), and the temperature of the reaction vessel decreases as thermal energy converts to chemical potential energy.

Reaction Rates: Definitions and Measurements

• The rate of reaction indicates the speed at which reactants are converted into products.

• Reactions occur at various speeds:

  • Very rapid reactions include precipitation reactions and the neutralization of an acid with a base.
  • Moderate speed reactions include zinc dissolving in acid.
  • Very slow reactions include the rusting of iron.

• Reaction Rate Definition:

  • The change in concentration per unit time of either a reactant or a product.
  • It measures how fast a reaction occurs by either the rate at which reactants are used up or the rate at which products are formed.

• Mathematical Formula for Rate:

  • $\text{Rate of reaction} = \frac{\text{change in concentration}}{\text{change in time}} = \frac{\text{final concentration} - \text{initial concentration}}{\Delta \text{time}}$

• Qualitative vs. Quantitative Observations:

  • Qualitative change is noted when relying only on visible observations to determine rate.
  • Quantitative change occurs when a specific measurement of reactants or products is taken over time to determine the rate.

• Quantitative Measurement Techniques:

  • Measuring gas production using a gas syringe.
  • Measuring the decrease in mass of a solid using a mass scale.
  • Measuring color change using a light or color meter.
  • Measuring precipitate formation (turbidity) using a light meter.
  • Measuring the change in pH using a pH meter.

Experimental Methods for Measuring Reaction Rates

• Measuring Mass Decrease Over Time:

  • A system consisting of calcium carbonate ($CaCO_3$) and hydrochloric acid ($HCl$) is placed in a conical flask on an electronic top-pan balance.
  • A cotton wool bung is used in the neck of the flask to prevent liquid from splashing out while allowing gas to escape.
  • As the reaction is exothermic, it also absorbs water vapor.
  • As carbon dioxide gas ($CO_2$) is produced and leaves the flask, the total mass of the system decreases.

• Measuring Volume of Gas Produced Over Time:

  • Downward Displacement of Water: A conical flask containing magnesium ($Mg$) and dilute acid is connected via a delivery tube to a measuring cylinder placed upside down in a water trough. Gas produced displaces the water, allowing the volume to be measured over time.
  • Gas Syringe Method: This is required for gases that are soluble in water, such as carbon dioxide ($CO_2$). These gases cannot be collected via downward displacement because they would dissolve into the water rather than displacing it.

Analysis of Reaction Rate Graphs

• The gradient (slope) of a graph representing amount versus time indicates the rate of reaction.

  • A steep gradient indicates a high reaction rate.
  • A gentle gradient indicates a low reaction rate.

• Average Rate:

  • Indicates the overall rate of reaction over a specific period of time.
  • Shows the average amount of reactant used or product formed between two specific points on the graph.
  • $\text{Rate} = \frac{\Delta \text{measured quantity}}{\Delta \text{time}}$

• Instantaneous Rate:

  • Indicates the rate of reaction at a specific, exact moment in time.
  • Determined by the gradient of a tangent drawn to the graph at that specific point.

• Graph Trends:

  • Graphs are usually steepest at the start, indicating the highest rate.
  • The gradient decreases over time as the reaction proceeds and slows down.
  • The graph levels off (becomes horizontal) when the reaction stops.

Collision Theory

• An effective collision is one that results in a chemical reaction taking place.

• During an effective collision, reactant bonds break and new bonds form to produce products.

• Requirements for an Effective Collision:

  1. Correct Orientation: Particles must collide in the specific position required for bonds to break and new bonds to form.
  2. Sufficient Kinetic Energy: Particles must possess kinetic energy equal to or greater than the activation energy ($E_a$). If kinetic energy is lower than $E_a$, the particles will collide but no reaction will occur.

Maxwell-Boltzmann Distribution

• Particles in a system possess a range of different kinetic energies.

• Temperature is a measurement of the average kinetic energy of the particles.

• The Maxwell-Boltzmann distribution curve shows the distribution of kinetic energy among particles in a system:

  • The x-axis represents kinetic energy ($J$).
  • The y-axis represents the number of particles (moles).
  • Only particles in the shaded area to the right of the activation energy ($E_a$) mark have sufficient energy to react.
  • Success in a reaction depends on the number of successful collisions per unit time.

Factors Affecting Reaction Rate

• Five primary factors influence the rate of chemical reactions:
  1. Temperature of the reaction.
  2. Concentration of reactants (amount per volume for solutions; pressure for gases).
  3. Surface area (state of division) of solid reactants (e.g., fine powder vs. coarse grains).
  4. Presence of a catalyst or, in certain cases, light.
  5. The nature of the reactants.

Detailed Effects of Temperature, Concentration, and Pressure

• Temperature:

  • An increase in temperature increases the rate of all chemical reactions.
  • Average kinetic energy is directly proportional to temperature ($E_k \propto T$).
  • In general, a $10\,^{\circ}C$ (or $10\,K$) rise in temperature approximately doubles the reaction rate.
  • For example, an increase of $30\,^{\circ}C$ would cause the rate to increase by approximately $2 \times 2 \times 2 = 8$ times.
  • Collision Theory Explanation: Increased temperature increases average kinetic energy and particle speed, creating a two-fold effect: more particles have kinetic energy $\ge E_a$, and there are more collisions per unit time. This results in more effective collisions per unit time.

• Concentration:

  • Increasing the concentration of one or more reactants increases the reaction rate.
  • A higher concentration means more molecules per unit volume, which results in a greater frequency of molecular collisions.
  • Proportionality: If the concentration of one reactant is doubled, the rate doubles. If the concentrations of both reactants in a reaction ($A + B \rightarrow AB$) are doubled, the rate increases fourfold.
  • The rate of reaction is proportional to the product of the concentrations of the reactants.

• Pressure of Gases:

  • The pressure of a gaseous reactant affects the rate because pressure is inversely proportional to the volume of the reaction container.
  • Increased pressure results in higher particle density and a higher frequency of collisions.