Course Overview
0:00 - Overview and Preface: The course is introduced, and a special treat is mentioned later (0:00).
0:15 - Review of the last lecture on marking off the K2 as the slow step in a rate law. When the reverse step (minus one) is much faster than K2, this makes the expression simpler.
Today's Lecture Topic
0:36 - Overview of the lecture topic for today: Temperature and how it relates to earlier subjects.
Temperature's Impact on Reaction Rates
0:56 - Overarching observation: Rates tend to increase as temperatures rise. How to measure this effect on the rate constant will now be covered in the lecture.
The Plot and Arrhenius Equation
1:25 - Historical background: 1889 work by Svante Arrhenius. He plotted various rate constants against temperature.
- 1:50 - Arrhenius found that a straight line was produced when he plotted the natural log of the rate constant (ln K) versus the inverse temperature (1/T). Straight lines excite scientists because they show a relationship.
- 2:24 - The Arrhenius Plot: 1/T (in inverse Kelvin) on the x-axis versus ln K on the y-axis.
- 2:40 - The activation energy (EA) minus the gas constant (R) is the slope of the Arrhenius plot.
- 3:10 - The natural log of something called factor A (also called the Arrhenius factor or pre-exponential factor) is the y-intercept of the Arrhenius plot. The rate constant K and factor A have the same units.
- 3:57 - This plot demonstrated to Arrhenius that rate constants vary exponentially with inverse temperature. This was the first time that temperature and rate constants were quantitatively related.
Arrhenius Factor (A)
4:20 - The particular reaction under study determines the activation energy and factor A.
4:50 - Clicker Question: Does factor A depend on temperature? No is the response.
- 5:20 - Factor A Interpretation: It is the rate constant at a infinitely large temperature, or when 1/T is zero. For a given reaction at this fictitious infinite temperature, factor A is the fastest possible rate constant. Plotting data yields it.
EA (Activation Energy)
6:41 - Clicker Question: Does temperature affect activation energy? No is the response.
Plotting rate constants over different temperatures yields one activation energy value for a given reaction, as activation energy is largely independent of temperature (7:15). The materials and/or reactants involved do play a role.
- 7:44 - Arrhenius Equation Forms: The equation can be expressed either exponentially (K = A * e^(-EA/RT)) or linearly (ln K = ln A - EA/RT).
- 8:44 - A reminder to differentiate symbols from other units (such as the letter "A" in nuclear chemistry).
Forecasting Rate Constants with the Arrhenius Equation
As an illustration, consider the hydrolysis of sucrose during digestion (9:23).
10:09 - Given the rate constant at body temperature (1.0 x 10^-3 M^-1 s^-1 at normal body temperature) and activation energy (108 kJ/mol).
10:38 - Assignment: Determine the rate constant at 35°C, a lower temperature.
11:17 - Solution: To eliminate the unknown factor A, combine two versions of the Arrhenius equation (for K1 at T1 and K2 at T2).
11:57 - ln(K2/K1) = -EA/R * (1/T2 - 1/T1) is the combined equation.
12:45 - Entering values: Convert activation energy to Joules and temperatures to Kelvin.
13:24 - The computed result was a lower rate constant at the lower temperature (35°C) (7.6 x 10^-4 M^-1 s^-1).
13:38 - Verification: At lower temperatures, a lower rate is frequently seen. This clarifies the significance of body temperature for physiological functions such as digestion.
Activation Energy and Temperature Sensitivity
14:28 - The combined Arrhenius equation illustrates the relationship between EA and temperature sensitivity.
14:44 - The rate constants (K1 and K2) are extremely sensitive to temperature changes if EA is very large. Less sensitivity is indicated by a small EA.
The Impact of Cold Temperature
15:23 - Question: At liquid nitrogen temperatures, what happens to enzymes (such as those involved in digestion)? They either stop working ("frozen") or slow down significantly.
16:23 - Research application: Protein crystals are flash-frozen in liquid nitrogen after being soaked in reactants to record intermediate structures and investigate enzyme mechanisms. This stops the response.
17:16 - Inquiry: Do non-enzymatic reactions likewise slow down?
Demonstration with Glow Sticks
- 17:30 - Glow sticks glow as a result of a chemical reaction.
- 18:05 - Glow sticks are broken and activated.
- 18:36 - Seeing the glowing response. The glow stops when the reaction slows down.
- 19:04 - Putting glow sticks into liquid nitrogen to cool them down.
- 19:33 - The glow starts to stop as the reaction slows due to the cold temperature.
Liquid Nitrogen Properties Demonstration
- 20:07 - Liquid nitrogen also changes physical properties.
- 20:16 - Demonstrating the effect on a flower: A fresh flower vs. one soaked in liquid nitrogen.
- 20:48 - The liquid nitrogen-soaked flower becomes brittle and can be smashed.
- 21:14 - Anecdotes about working with liquid nitrogen and minor burns.
- 22:34 - Conclusion: Everything slows down in the cold in terms of elementary reactions; rate constants slow down.
Activation Energy and Reaction Coordinate Diagrams
- 22:50 - Presenting the idea of the reaction coordinate: combining reactants to create products.
- 23:18 - Presenting the concepts of transition state and activation complex.
- 23:34 - Collision theory: Although molecules collide, they don't always produce products.
- 23:54 - The collision energy must be greater than a critical energy for the reaction to occur (also known as activation energy EA or E_min).
- 24:33 - Why is this vital energy required? to break bonds, create new bonds, and distort bonds throughout the reaction.
- 25:02 - The system's potential energy rises to create a transition state or activated complex.
- 25:38 - Whether the activated complex breaks down back into reactants or continues to form products depends on the critical energy.
Analogy: Relationships and Activation Energy
26:10 - Analogy: Relationships that need work to overcome obstacles.
- 27:32 - Relation to Temperature: Temperature has an impact on molecules' kinetic energy.
- 27:59 - Maxwell-Boltzmann distribution: Plot of kinetic energy versus fraction of molecules.
- 28:32 - Most molecules have low kinetic energy at low temperature, and only a small fraction have sufficient energy to cross the activation energy barrier.
- 29:13 - More molecules have higher kinetic energy at high temperature, and a much larger fraction have the energy required to react and break through the barrier.
Creating Diagrams of Reaction Coordinates
- 30:07 - The diagram's axes are the Reaction Coordinate on the x-axis and Potential Energy (PE) on the y-axis.
- 30:48 - Products end at a specific potential energy, while reactants begin at another. delta E is the difference.
- 31:20 - To become products, reactants need to get past an activation energy barrier.
- 31:55 - The activation energy for the reverse direction (EA_r) is another barrier to moving from products back to reactants.
- 32:17 - The transition state or <
or activated complex is represented by the diagram's peak.
Connection Between Energy Terms
Activation Energy: The activation energy of the forward reaction minus the activation energy of the reverse reaction (ΔE = EA_f - EA_r) is the energy change (delta E) between reactants and products. Although it is not on the equation sheet, this equation will be on the test.
Key Energy Terms
- Delta H: Enthalpy change is closely associated with delta E. For solids and liquids, they are roughly equal, while for gases, they vary by 1% to 2%.
- Calculation: If you know the other two energy terms, you can use this equation to calculate one.
- Example Computation: Given EA_r = 358 kJ/mol and EA_f = 132 kJ/mol.
Delta E was calculated to be -226 kJ/mol at 35:45.
Interpretation of Delta E
Exothermic Reaction: An exothermic reaction is indicated by a negative delta E.
Activation Energy Barriers
Crucial Point: The activation energy barrier (EA_f) must be overcome for the reaction to proceed, even in cases where the products of the reaction have less energy than the reactants.
Analogy for Activation Energy
The difficulty of beginning a task, such as writing a paper or grant, in contrast to simpler tasks, like cleaning (36:53). Deadlines or stress serve as the "energy" to overcome the obstacle. It may be easier after crossing the barrier ("smooth sailing").
Elementary Reactions
Barrier: An elementary reaction always has a barrier. EA is always a positive barrier.
Impact of Temperature
- Temperature Effect: Raising the temperature always increases the rate for an elementary reaction (occurs as written).
- Prediction Difficulty: The impact of temperature is more difficult to predict for an overall reaction (comprising several steps).
Reexamination of Reaction Mechanisms
Understanding Mechanisms: Thinking about overall reactions requires an understanding of reaction mechanisms.
Example Mechanism
The example mechanism is as follows: 2 NO + O2 → 2 NO2. Step 1: NO + NO ⇌ N2O2 (quick, reversible). Step 2: N2O2 + O2 → 2 NO2 (slow).
Rate Law
Based on Slow Step: Rate = k2 * [N2O2] * [O2].
Removing Intermediate
Intermediate Removal: The intermediate [N2O2] must be removed from the rate law.
Equilibrium Reaction
Initial Step: The initial step is close to an equilibrium reaction for a fast reversible step followed by a slow step.
Analogy for Gradual Process
Draining the Ocean: Attempting to drain the ocean with a tiny bucket (the gradual process has little effect on the ocean's "equilibrium").
Equilibrium Expression
Fast Reversible Step: The equilibrium expression for the fast reversible step can be used to solve for the intermediate. [N2O2] / [NO]^2 = K_eq.
Finding Intermediate Concentration
Finding [N2O2]: Finding [N2O2] = K_eq * [NO]^2.
Rate Law Entry
Slow Step Rate Law: Enter this as follows: Rate = 2 * k2 * K_eq * [NO]^2 * [O2] in the slow step rate law. The stoichiometry in the slow step is where the 2 originates. The observed rate constant (K_obs) = 2 * k2 * K_eq.
Impact of Temperature on Equilibrium Constants
- Elementary Rate Constant: The elementary rate constant (k2) is affected by temperature, rising as the temperature rises.
- Reaction Step Effect: Whether the reaction step is exothermic or endothermic determines the temperature effect on the equilibrium constant (K_eq).
- van't Hoff Equation: The
Key Concepts in Reaction Kinetics and Equilibrium
46:37 - The Arrhenius (ln K vs. 1/T, slope -EA/R) and van't Hoff (ln K_eq vs. 1/T, slope -ΔH/R) equations are very similar. Delta H versus activation energy.
47:04 - The equilibrium constant (K_eq) decreases with increasing temperature for an exothermic reaction (ΔH < 0). This is evident from the van't Hoff equation or can be remembered from earlier education.
Impact of Temperature on Rate Constants
47:29 - The Impact of Temperature on the Total Rate Constant (K_obs)
- 47:29 - K_obs = 2 * k2 * K_eq. The elemental rate constant, or k2, rises with temperature.
- 47:58 - K_eq falls but k2 rises for an exothermic step.
- 48:15 - The magnitude of ΔH for the equilibrium step and the magnitude of EA for k2 determine the overall effect on K_obs.
- 48:46 - Example: EA for k2 is small and positive (for the NO + O2 reaction). For the equilibrium step, ΔH is a large negative value (exothermic).
- 49:10 - A slight positive EA indicates that k2 only slightly rises with temperature. A large negative ΔH indicates that K_eq significantly drops with temperature.
- 49:29 - Conclusion for this particular reaction: Because the decrease in K_eq exceeds the increase in k2, increasing temperature actually decreases the observed rate constant (K_obs).
- 49:49 - General rule: The magnitudes of EAs and the signs/magnitudes of ΔHs for the steps involved determine how temperature affects any overall reaction.
- Large EA indicates that the rate constant is very sensitive to temperature (50:03).
- 50:18 - A large ΔH indicates that the equilibrium constant is extremely sensitive to temperature.
- 50:32 - Since EA is always positive, the rate always increases with temperature for an elementary rate constant.
- 50:54 - Because ΔH can be either positive or negative, an equilibrium constant may increase or decrease. The sign indicates the direction of change, while the magnitude indicates how much it changes.
Le Chatelier's Principle: Linking Kinetics and Equilibrium
51:29 - Returning to the Principle of Le Chatelier. According to Le Chatelier, a system reacts to reduce stress.
- 51:56 - Stress: Adding heat, raising the temperature.
- 52:16 - System response: Changes in the endothermic direction to minimize or expend the heat.
- 52:40 - We have already covered the impact of temperature on the equilibrium position. Today's objective is to use kinetics to provide a new explanation for why this occurs.
Using Activation Energies to Rationalize Le Chatelier's Principle
53:48 - Using Activation Energies to Rationalize Le Chatelier's Principle
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