Chemical kinetics

Mathematical expression of reaction rate

In chemical kinetics, the reaction rate reflects how quickly starting materials (reactants) are consumed or final substances (products) accumulate. Let us consider this principle using the classic example of hydrogen iodide synthesis, where a hydrogen molecule interacts with an iodine molecule: $H_2 + I_2 = 2HI$.

Mathematically, this process is described by the ratio of the change in concentration ($\Delta c$) to a specific time interval ($\Delta t$). Since reactants are steadily consumed during the process, their concentration drops. To keep the final rate value positive, a minus sign is forcibly placed in front of the fraction for reactants in formulas:

• For hydrogen ($H_2$): $v_1 = - \frac{\Delta c(H_2)}{\Delta t}$
• For iodine ($I_2$): $v_2 = - \frac{\Delta c(I_2)}{\Delta t}$

For the reaction product (hydrogen iodide), the situation is the opposite: its concentration only increases over time. Therefore, a minus sign is not required here, and the formula takes the form: $v_3 = \frac{\Delta c(HI)}{\Delta t}$. Thus, the dynamics of the system can be tracked using any of its participants.

Nature of molecular collisions

Imagine a chemical process occurring in a gas mixture or liquid. In such states of aggregation, particles are in continuous random motion, leading to a colossal number of mutual contacts. To understand the scale: in ordinary air, each individual molecule undergoes about 400 million collisions in just one second.

If absolutely every such collision inevitably led to a chemical transformation, any reaction would be completed almost instantaneously. However, in real laboratory and natural practice, we see a completely different picture: most chemical processes proceed at a measurable, often very slow rate. The main reason for this phenomenon lies in the fact that the lion's share of occurring collisions is ineffective—particles simply repel each other, and this does not lead to a chemical transformation.

Energetics of an effective collision

For a molecular collision to be successful and lead to a reaction, a strict condition must be met. The colliding particles must possess a sufficient reserve of kinetic energy ($E_{kin} = \frac{m \cdot v^2}{2}$, taking into account mass and velocity).

The transformation process itself during an effective collision proceeds according to the following algorithm:

1. At the moment of physical contact, severe deformation of the electron shells of the particles occurs.
2. During this deformation, the kinetic energy of translational motion is transformed into the potential energy of the system.
3. If the final increase in potential energy turns out to be sufficiently large, a deep internal rearrangement is triggered.

As a result, the entire electronic structure changes: the old chemical bonds that held atoms in the initial reactants are irreversibly broken. Immediately thereafter, new bonds form, creating the product molecules of the reaction.

What else to study on this topic

• In-depth analysis of factors affecting reaction rate (temperature, pressure, concentration).
• The role of catalysts in altering the energy required for a successful collision.
• Mechanisms of gradual cleavage and simultaneous formation of new chemical bonds.
• The relationship between the kinetic energy of particles and the temperature of the reaction mixture.
• Active collision theory and calculation of the fraction of effective collisions.

Other topics in "Chapter 6. Patterns of Chemical Reactions"

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