Rates of Reaction Notes

Introduction - Rates of Reaction

The reaction of Zinc (Zn) with Hydrochloric acid (HCl) is affected by concentration.
- Examples are shown using 6M and 12M HCl, as well as 6M and 15M HNO3.
The reaction of Magnesium metal in acid.

Collision Theory: A reaction occurs between two molecules if they collide with:
- Correct orientation
- Sufficient energy to break chemical bonds.
The more reacting particles that need to collide simultaneously, the less likely a proper collision will occur.

A chemical system consists of particles in constant random motion at various speeds.
A chemical reaction requires collisions of particles with each other or the container walls.
Effective Collision:
- Sufficient energy
- Correct orientation (collision geometry)
- Leads to bond breaking and new bond formation.
Ineffective Collision: Particles rebound without changing.
Reaction Rate:
- Depends on the frequency of collisions.
- Depends on the fraction of effective collisions.
Reactions require sufficient activation energy.

The area under the curve represents the total number of particles.
The shaded area represents the number of molecules with sufficient energy for a successful collision.
Diagram Explanation:
- x-axis: Kinetic Energy
- y-axis: Number of molecules
- Curves for temperatures T1 and T2
- Activation Energy marked on the Kinetic Energy axis.

Chemical Kinetics: The study of how fast a reaction proceeds.
Reaction Rate: Change in consumption or production of a substance with time.
- Measured as: \frac{\Delta moles}{\Delta t}, \frac{\Delta mass}{\Delta t}, \frac{\Delta P}{\Delta t}, \frac{\Delta [conc]}{\Delta t}.
Why Increase Rate?
- Speed up cooking or drying paints
- Relieve pain or increase production of chemicals in industry.
Why Decrease Rate?
- Reduce food spoilage or spontaneous ignition
- Reduce combustion rate or corrosion of metals.

Methods involve measuring changes in:
- Direct concentrations of components
- Concentration-related properties like color (using a spectrophotometer), density, electric conductivity, pressure (for gases), pH, and volume.

Reactions Producing a Gas:
- Collect gas and measure volume or pressure as the reaction proceeds.
Reactions Involving Ions:
- Conductivity of the solution changes as the reaction proceeds.
Reactions Changing Color:
- Measure the intensity of a colored reactant or product using a spectrophotometer.

Reactions:
1. Ag^{+1} + Cl^{-1} \rightarrow AgCl (Almost instantaneous)
2. 3Fe^{+2} + NO3^{-1} + 4H^{+1} \rightarrow 3Fe^{+3} + NO + 2H2O (Much slower)
3. C8H{18} + 12.5O2 \rightarrow 8CO2 + 9H_2O (Does not proceed without ignition)

Concentration:
- Rate increases as reactant concentration increases.
- Example: Burning sulfur in air vs. pure O2.
- Collision Theory Explanation:
  - Reactions occur only if reacting species collide: A + B \rightarrow AB
  - Increased [A] and/or [B] leads to more collisions, thus increased rate.
Temperature:
- Rate increases as temperature increases.
- Molecules move faster, causing more collisions with greater force.
- General Rule: A 10°C rise in temperature doubles the reaction rate.

Catalysts:
- Substances that increase the reaction rate but are not consumed.
- Enzymes are biological catalysts.
Surface Area:
- Applies to heterogeneous reactions.
- A finely divided reactant (powder) has a greater surface area for collisions than a solid mass.
- Example: Wood chips burn faster than a log of wood; carbon powder explodes, while lumps of coal burn slowly.
Pressure:
- Increasing pressure increases the rate of reaction due to more collisions.

Rate of Reaction:
- rate = reaction rate
- \Delta c = concentration change
- \Delta t = elapsed time
Average reaction rate = \frac{change \, in \, concentration}{change \, in \, time}

The rate can be represented in terms of:
- Rate of disappearance of reactant
- Rate of appearance of product
Mole ratios are important.
Consider the reaction 2A \rightarrow 3B + C
For every 1 mole of C produced, 3 moles of B are produced.
The rate of production of B is 3 times greater than the rate of production of C.

Question: If the rate of production of B is 1.2 x 10^{-3} mol/s, calculate the rate of disappearance of A?
Since \frac{\Delta [A]}{\Delta t} = \frac{2}{3} \frac{\Delta [B]}{\Delta t}
Rate of A disappearing = \frac{2}{3} (1.2 x 10^{-3} mol/s) = 8.0 x 10^{-4} mol/s
Note: The rate can be expressed as a negative rate since the concentration of A decreases over time.

Rates of reaction are found experimentally where concentrations at specific times are plotted on a graph.
Average rate of reaction is the slope of the secant drawn between two points.

The graph shows [C] (mol/L x 10^3) versus Time (s).
Calculations:
- \frac{\Delta[C]}{\Delta t} = \frac{5.4 x 10^{-3} mol/L - 3.1 x 10^{-3} mol/L}{15.0 s - 5.0 s} = \frac{2.3 x 10^{-3} mol/L}{10.0 s} = 2.3 x 10^{-4} mol/(L.s)
- \frac{\Delta[C]}{\Delta t} = \frac{3.1 x 10^{-3} mol/L - 0.0 mol/L}{5.0 s - 0.0 s} = \frac{3.1 x 10^{-3} mol/L}{5.0 s} = 6.2 x 10^{-4} mol/(L.s)

For the reaction:
- Br2 (aq) + HCOOH (aq) \rightarrow 2Br^- (aq) + 2H^+ (aq) + CO2 (g)
Average rate = -\frac{\Delta [Br2]}{\Delta t} = -\frac{[Br2]{final} – [Br2]{initial}}{t{final} - t_{initial}}
Instantaneous rate = rate for a specific instance in time, found by the slope of the tangent. Note that the average and instantaneous rate formulas are the same but are calculated differently.