Comprehensive Reaction Rate Notes

Reaction Rate

Importance

• The reaction rate is defined as how fast or slow a reaction takes place. It's determined by observing how much of a substance appears (e.g., $H_2$) or disappears (e.g., metal) over time.
• Understanding reaction rates is crucial for speeding up or slowing down chemical reactions in various applications.
• Examples of reactions that are:
  • Too slow: Some combustions, composting of organic waste, aging of wine.

Collision Theory

• A chemical reaction occurs when reacting molecules collide.
• Effective or successful collisions lead to a reaction and require:
  • Enough kinetic energy.
  • The right orientation.
• Non-effective collisions do not result in a reaction because they lack sufficient energy or proper orientation.

Activated Complex

• A chemical reaction results from effective collisions between particles, forming an activated complex.
• The activated complex is an intermediate phase with a higher energy content than the individual reactants.
• Activation energy ($E_A$) is required to convert reactants into the activated complex.
• $E_A$ is the energy that must be added to initiate the reaction.
• The formation of an activated complex is energetically more favorable compared to breaking all bonds in the reactants and then forming new ones.

Exothermic vs. Endothermic Reactions

• Exothermic reaction: Energy is released.
• Endothermic reaction: Energy is absorbed.

Definition of Reaction Rate

• Reaction rate = amount of successful collisions per second.
• Reaction rate is the change in concentration of one of the reactants or products per unit time, expressed in mol/L·s.
• Average reaction rate is the change in concentration of a substance over time.
• Example: $A + 2B \rightarrow C$
  • $<v> = -\frac{\Delta[A]}{\Delta t}$
  • $<v> = -\frac{\Delta[B]}{2\Delta t}$
  • $<v> = +\frac{\Delta[C]}{\Delta t}$
• Examples:
  • $CO + NO<em>2 \rightarrow CO</em>2 + NO$
    • $<v> = -\frac{\Delta[NO_2]}{\Delta t}$
  • $N<em>2O</em>4 \rightarrow 2NO_2$
    • $<v> = \frac{1}{2} \frac{\Delta[NO<em>2]}{\Delta t} = -\frac{\Delta[N</em>2O_4]}{\Delta t}$
• General Formula: $aA + bB \rightarrow cC + dD$
  • $<v> = -\frac{1}{a} \frac{\Delta[A]}{\Delta t} = -\frac{1}{b} \frac{\Delta[B]}{\Delta t} = \frac{1}{c} \frac{\Delta[C]}{\Delta t} = \frac{1}{d} \frac{\Delta[D]}{\Delta t}$
• Mathematically, is the slope of the straight line representing the change in concentration as a function of time.

Instantaneous Reaction Rate

• Instantaneous reaction rate is determined as the time interval approaches 0, expressed in mol/L·s.
• Formula: $v<em>t = \lim</em>{\Delta t \to 0} \frac{\Delta[NO<em>2]}{\Delta t} = \frac{d[NO</em>2]}{dt}$
• $v_t$ is the absolute value of the slope of the tangent line to the curve.

Average vs. Instantaneous Reaction Rate

• Example: $2A + B \rightarrow C + 2D$
• The instantaneous reaction rate at a specific moment (e.g., 3.25 s) can be read from the graph (e.g., 0.15 mol/L·s).

Concentration-Time Graph

• For the reaction $1A + 1B \rightarrow 1C + 1D$, the same concentration changes apply to substances with the same stoichiometric coefficients.
• The reaction stops when the limiting reagent is fully consumed.
• The changes in concentration are greatest at the beginning; the concentration-time graph is not a straight line.

Factors Affecting Reaction Rate

• Temperature:
  • A rise in temperature increases the mean velocity of molecules, raising their kinetic energy.
  • Higher temperatures lead to more frequent and forceful collisions, increasing the chance of successful collisions and a higher reaction rate.
  • Examples:
    • Refrigerators and freezers slow down food decay.
    • Fever enhances nail and hair growth.
    • Plant growth depends on seasonal temperatures.
• Concentration:
  • More particles in the solution raise the chance of successful collisions, increasing the reaction rate.
  • Examples:
    • Using pure oxygen instead of air in reanimation.
    • Risk of a too-high dose of medicines.
    • Creating an air stream to improve combustion.
• Light, Shock, and Radiation:
  • Energy is added to the system, allowing more molecules to reach the required kinetic energy threshold for effective collisions.
  • Examples:
    • Textiles and hair can discolor in the sun.
    • Storage of some products in brown bottles.
• Particle Size of Reactants, Dispersion Grade:
  • A higher dispersion grade means a higher contact surface, raising the chance of colliding with the right orientation, leading to a higher reaction rate.
  • Examples:
    • Chewing food facilitates digestion.
    • Dust explosions: Risks of explosive combustions of fine distributed combustible products.
    • Twigs and branches burn faster than a block of wood.
• Catalyst:
  • A catalyst is a substance that increases or decreases the rate of a chemical reaction without being altered.
  • Catalysts can act as the meeting place of the reactants, or promote the formation of an intermediate product.
  • In general, a reaction requires less minimal energy with a catalyst.
  • Examples:
    • Ethylene gas is used as a catalyst in fruit ripening.
    • Yeast is a catalyst in converting sugar to alcohol.
    • Enzymes facilitate chemical conversions in the body at a lower temperature.
• Homogeneous Catalysts:
• Heterogeneous Catalysts:

The Law of Mass Action (Guldberg and Waage)

• For a general reaction: $aA + bB + cC … \rightarrow … zZ$
• Rate equation: $v<em>t = k[A]</em>t^a[B]<em>t^b[C]</em>t^c$
  • Unit for $v_t$ is mol/L·s.
• Remarks:
  • Valid only in a homogeneous environment and with single-step reactions.
  • No solid substances in the equation.
  • $k$ = reaction rate constant.
• Example: $C<em>2H</em>4 + H<em>2 \rightarrow C</em>2H_6$
  • $v<em>t = k \cdot [C</em>2H<em>4]</em>t \cdot [H<em>2]</em>t$

Multiple-Step Reactions

• The law of mass action is not applicable to multiple-step reactions.
• Slow intermediate steps are decisive for the global reaction rate.
• If one intermediate step is much slower than the others, the total reaction rate is determined by that slowest step.
• The exponents are determined experimentally.
• Example: $2N<em>2O</em>5 \rightarrow 2N<em>2O</em>4 + O_2$
  • $v<em>t = k \cdot [N</em>2O<em>5]</em>t$

Reaction Rate Constant (k)

• Specific for each reaction.
• Influenced by temperature and catalysts.
• Unit is variable.

The Order of the Reaction

• The order of the overall reaction is determined by adding the valid values of the exponents in the rate equation.
• The order for a specific compound is the valid value of its accompanying exponent.
• Example: $C<em>2H</em>4 + H<em>2 \rightarrow C</em>2H<em>6$ with rate equation $v</em>t = k \cdot [C<em>2H</em>4]<em>t \cdot [H</em>2]_t$
  • Order of the global reaction: 2.
  • Order for the compound $C<em>2H</em>4$: 1.