Class 20: Greenhouse Gases and Integrated Rate Laws

Question 1

Use the method of initial rates to determine the order of a reaction with respect to an individual reactant or reactants and write the rate law.

Answer 1

• Vary concentration of one reactant at a time, hold others constant
• Measure initial rate at different concentrations
• For each reactant:
  
  • Plot rate vs [reactant] on log-log plot
  • Slope = order with respect to that reactant
• Overall order = sum of individual orders
• Rate law: Rate = k[A]^m[B]^n…
  
  • k is rate constant
  • m, n are orders with respect to A, B
• Calculate k by plugging in one rate/concentrations data point

Question 2

Use integrated rate laws for first- or second- order reactions to predict the amount of reactant leftover or the amount of product formed after a certain amount of time.

Answer 2

For a first-order reaction:
* Integrated rate law: ln([A]t/[A]0) = -kt
* To find [A]t at time t:
- Rearrange to: [A]t = [A]0e^(-kt)
- Plug in [A]0, k, t
* Amount A remaining = [A]t × Volume

For a second-order reaction:
* Integrated rate law: 1/[A]t - 1/[A]0 = kt
* To find [A]t at time t:
- Rearrange: 1/[A]t = 1/[A]0 + kt
- Plug in [A]0, k, t
* Amount A remaining = [A]t × Volume

For either order:
* Amount of product P = Initial amount A - Amount A remaining

Question 3

Interpret the data on an Arrhenius plot and use it to calculate the activation energy.

Answer 3

• Arrhenius equation: ln(k) = -Ea/RT + ln(A)
• Plot ln(k) vs 1/T
• Should give a straight line
• Slope = -Ea/R
• To calculate Ea:
  
  • Measure slope
  • Rearrange to: Ea = -Slope * R
  • Plug in gas constant R value
• Higher Ea means steeper line
  
  • Reaction is more temperature dependent
• Intercept = ln(A)
  
  • A is pre-exponential factor

Question 4

Use the Arrhenius equation to calculate the activation energy for a reaction.

Answer 4

• Arrhenius equation: k = A * e^(-Ea/RT)
  
  • k is rate constant
  • A is pre-exponential factor
  • Ea is activation energy (goal)
  • R is gas constant
  • T is absolute temperature
• Rearrange to: ln(k) = -Ea/RT + ln(A)
• Measure k at multiple temperatures
• Plot ln(k) vs 1/T
• Slope = -Ea/R
• Calculate Ea:
  
  • Measure slope
  • Ea = -Slope * R
  • Plug in gas constant R value
• Higher Ea means reaction is more temperature sensitive

Question 5

Explain, using Collision Theory, the mechanism by which temperature can increase reaction rate.

Answer 5

• Molecules must collide to react
• Collision must have enough energy (E > Ea)
• Higher temperature:
  
  • Molecules move faster
  • More frequent collisions
  • More collisions have E > Ea
  • So more effective collisions per unit time
• Higher temperature also:
  
  • Gives greater fraction of molecules proper orientation
  • Increases chance of successful collisions
• Therefore, higher temp leads to higher reaction rate
  
  • By increasing collision frequency
  • And increasing fraction of effective collisions

Question 6

Identify a rate-determining step from a reaction coordinate energy diagram, and relate the rate law to the reactants involved in the rate-determining step.

Answer 6

• Identify rate-determining step from energy diagram:
  
  • Step with highest energy barrier (Ea)
  • Slowest step, rate depends on concentration of reactants involved
• Relate rate law to rate-determining step:
  
  • Rate ∝ [Reactants in slow step]^n
    
    • Where n is order with respect to each reactant
  • Reactants not in slow step have 0 order
    
    • Their concentration doesn’t affect rate
• Examples:
  
  • If A + B → C (slow), C + D → E
    
    • Rate law is: Rate = k[A]^x[B]^y
  • If A + B → C, C + D → E (slow)
    
    • Rate law is: Rate = k[C]

Question 7

Interpret the data on an Arrhenius plot and use it to calculate the activation energy.

Answer 7

The Ea will be the slope
BE CAREFUL! If R and the neg sign is not taken into account then you need to multiply the slope by -8.314 to get just the Ea and not the -Ea/R

Question 8

Explain, using Collision Theory, the mechanism by which temperature can increase reaction rate.

Answer 8

As you increase temperature, you increase the amount of molecules with enough energy to collide
Temperature is a measure of the average kinetic energy in the system

Question 9

Identify a rate-determining step from a reaction coordinate energy diagram, and relate the rate law to the reactants involved in the rate-determining step.

Answer 9

The rate determining step is the step with the largest activation energy
Every step before that also affects the rate; i.e concentration of acid needed to react