Dynamics of Chemical Reactions: Kinetics, Energy, and Equilibrium

Fundamental Prerequisites for Chemical Dynamics

To understand the dynamics of chemical reactions, one must first master the symbolic language of chemistry. A substance is defined as matter consisting of molecules with the same chemical composition and properties. A pure substance can be categorized as a simple substance (enkelvoudige stof) if the molecules consist of atoms from only one chemical element, such as oxygen gas ($O_2$). Conversely, a compound substance (samengestelde stof) consists of atoms from two or more elements, such as carbon dioxide ($CO_2$). Within these formulas, the index indicates the specific number of atoms of that element present in the molecule.

Energy changes are central to chemical transformations. Endo-energetic reactions are substance conversions where energy is absorbed from the environment, while exo-energetic reactions are those where energy is released into the environment. This energy management is closely linked to the kinetic energy of the particles, which is directly proportional to the temperature of the substance. Furthermore, concentration is quantified via molaire concentratie, which is the number of moles per liter ($mol/dm^3$). One mole is equivalent to Avogadro’s number, which is approximately $6.023 \times 10^{23}$ particles.

The Chemical Reaction Equation

A chemical reaction represents the transformation of reagents into reaction products. It is symbolically represented as a set of reagents followed by a reaction arrow and finally the reaction products ($\text{Reagents} \rightarrow \text{Products}$). For a generalized reaction where substances $A$ and $B$ form products $C$ and $D$, the stoichiometry is represented using coefficients (voorgetallen) represented by $a$, $b$, $c$, and $d$ in the equation:

$aA + bB \rightarrow cC + dD$

These coefficients indicate the specific number of molecules required and produced in the reaction. A key governing principle is the Law of Conservation of Atoms (Wet van atoombehoud). This law states that during a chemical reaction, the types of atoms and the total number of atoms of each element remain preserved. For example, in the decomposition of water ($2H_2O \rightarrow 2H_2 + O_2$), there are four hydrogen atoms and two oxygen atoms on both the reagent and product sides of the equation.

An illustrative example of a chemical reaction is the combustion of magnesium. Magnesium ($Mg$) is a chemical element used in light bulbs, rims, aircraft, bath salts, gymnastics powder, and pigments. When magnesium reacts with oxygen gas ($O_2$), it undergoes a combustion reaction to form magnesium oxide ($MgO$) according to the equation:

$2Mg + O_2 \rightarrow 2MgO$

Reaction Energy and Activation Energy

Chemical reactions involve not only the transformation of matter but also the conversion of energy. Every molecule possesses a specific amount of internal energy ($U$). During a reaction, the internal energy of the products typically differs from that of the reagents. The difference between these states is the reaction energy ($\Delta U$), calculated as:

$\Delta U = U(\text{reaction products}) - U(\text{reagents})$

If the reaction energy is negative ($\Delta U < 0$), the process is exo-energetic, meaning energy is given off to the environment (e.g., the explosion of dynamite). If the reaction energy is positive ($\Delta U > 0$), the process is endo-energetic, meaning energy is absorbed from the environment (e.g., recharging a battery).

While energy diagrams show the start and end states, they do not illustrate the energy state during the reaction. During the transformation, reagents must form a high-energy transition state (overgangstoestand). To reach this state, the reacting particles require a minimum amount of kinetic energy called the activation energy ($E_a$). A reaction will only occur if sufficient activation energy is present. For instance, a Bunsen burner provides the activation energy necessary to ignite magnesium ribbon, whereas a smoldering cigarette might provide the activation energy required to start a forest fire.

The Collision Model (Botsingsmodel)

According to collision theory, particles must collide in order to react. There are two categories of collisions:

1. Elastic Collisions: Collisions where the particles do not react and bounce apart unchanged. This can happen if the molecules collide with the wrong orientation or if they lack sufficient kinetic energy to break existing bonds.

2. Effective Collisions: Collisions that result in a chemical reaction and the formation of new atom combinations. For a collision to be effective, two conditions must be met: the colliding particles must have the correct spatial orientation, and they must possess sufficient kinetic energy, which must be at least equal to the activation energy ($E_a$). If these conditions are met, a transition state is formed, leading to the creation of reaction products.

The Average Reaction Rate

The speed at which chemical reactions occur is highly variable and depends on the number of effective collisions. Some processes are very slow, such as the rusting of iron, where no visible change might be seen for months. Others are extremely rapid, such as the production of nitrogen gas to inflate an airbag, which occurs in only $30\,ms$. Other examples of fast reactions include the change of red cabbage juice as an indicator or the "elephant toothpaste" experiment, while the transformation of diamond into graphite is incredibly slow.

The average reaction rate ($v_{\text{gemiddeld}}$) is defined as the change in concentration ($\Delta[X]$) of reagents or products per unit of time ($\Delta t$). To ensure the rate is always a positive number, a minus sign is placed before the change in concentration of reagents (since their concentration decreases). For the general reaction $aA + bB \rightarrow cC + dD$, the rate is defined as:

$v_{\text{gemiddeld}} = -\frac{\Delta[A]}{a \cdot \Delta t} = -\frac{\Delta[B]}{b \cdot \Delta t} = \frac{\Delta[C]}{c \cdot \Delta t} = \frac{\Delta[D]}{d \cdot \Delta t}$

For example, in the synthesis of hydrogen iodide ($HI$) from hydrogen ($H_2$) and iodine ($I_2$):

$H_2 + I_2 \rightarrow 2HI$

If the concentration of $H_2$ changes from $2.0\,mol/l$ to $1.5\,mol/l$ over an interval of $5\,s$, the average rate is calculated as:

$v_{\text{gemiddeld}} = -\frac{(1.5 - 2.0)\,mol/l}{1 \cdot 5\,s} = 0.1\,mol/(l \cdot s)$

Factors Influencing Reaction Rate

Several factors can increase or decrease the frequency of effective collisions and thus affect the reaction rate:

1. Degree of Dispersion (Verdelingsgraad): This refers to how finely a solid substance is divided. A higher degree of dispersion increases the contact surface area between reagents, which leads to a higher total number of collisions and a higher reaction rate.

2. Concentration: This is a measure of the number of particles per unit volume. Increasing the concentration increases the number of effective collisions, thus increasing the reaction rate. A practical application is fire safety: closing windows and doors during a fire prevents a continuous supply of oxygen gas ($O_2$), keeping its concentration low and preventing the fire from becoming more intense.

3. Temperature: An increase in temperature increases the kinetic energy of particles, causing them to move faster. This increases the number of effective collisions. Generally, the reaction rate approximately doubles for every increase of $10^\circ C$. Lowering the temperature, such as in a refrigerator, slows down the rate of reactions that cause food to rot. Energetically, a higher temperature allows reagents to reach the transition state more easily because their starting energy level is higher relative to the unchanged energy of the transition state.

4. Catalyst: A catalyst is a substance that increases the reaction rate by lowering the activation energy ($E_a$). It does not affect the overall reaction energy ($\Delta U$). After the reaction, the catalyst is released unchanged and can be reused. Enzymes are biological catalysts (proteins) that speed up body reactions by correctly orienting reagents. Another example is the catalytic converter in cars, which converts toxic gases like $NO$ and $CO$ into less harmful gases like $N_2$ and $CO_2$.

Chemical Equilibrium

Reactions can be classified into two types regarding their completion:

1. Final Reactions (Aflopende reactie): These proceed until at least one of the reagents is completely consumed. They are noted with a single arrow ($\rightarrow$).

2. Equilibrium Reactions (Evenwichtsreactie): These are reversible reactions where products can be converted back into reagents. They are noted with two half-arrows ($\rightleftharpoons$) representing the forward (heenreactie) and backward (terugreactie) processes.

An equilibrium reaction spontaneously reaches a state of dynamic equilibrium. In this state, the concentrations of reagents and products are detectable and remain constant over time. This is not because the reactions have stopped, but because the rate of the forward reaction ($v_1$) is exactly equal to the rate of the backward reaction ($v_2$), where $v_1 = v_2 \neq 0$.

A common example is the equilibrium of sparkling water in a closed bottle. Carbon dioxide ($CO_2$) reacted under pressure with water ($H_2O$) forms carbonic acid ($H_2CO_3$). Simultaneously, the acid decomposes back into water and gas. The resulting equilibrium is:

$CO_2 + H_2O \rightleftharpoons H_2CO_3$

Le Chatelier's Principle and Equilibrium Shifts

Le Chatelier’s Principle states that if a system at equilibrium is disturbed, the position of the equilibrium will shift to (partially) counteract that disturbance. This is comparable to the principle of communicating vessels. Disturbances include:

1. Concentration Changes: If you increase the concentration of a substance, the equilibrium shifts to consume it. If you decrease it, it shifts to produce more. In a sparkling water bottle, opening the lid allows $CO_2$ to escape (decreasing concentration). The equilibrium shifts to the left to produce more $CO_2$. Conversely, pumping $CO_2$ into mineral water increases concentration, shifting the equilibrium right and making the water more acidic.

2. Biological Application (Oxygen Transport): Hemoglobin binds to oxygen ($O_2$) to form oxyhemoglobin. In the lungs, where the concentration of oxygen is high, the equilibrium shifts to the right (binding). In the tissues, where the concentration of oxygen is low, the equilibrium shifts to the left, releasing oxygen for the cells to use.

3. Temperature Changes: To predict shifts, energy ($E$) can be treated as a component of the reaction equation. In an exotherm reaction ($W + X \rightleftharpoons Y + Z + E$), energy is a product. In an endotherm reaction ($W + X + E \rightleftharpoons Y + Z$), energy is a reagent.

   • Increasing temperature adds energy, shifting the equilibrium toward the endothermic side to consume it.
   • Decreasing temperature removes energy, shifting the equilibrium toward the exothermic side to produce it.     In the sparkling water equilibrium ($CO_2 + H_2O \rightleftharpoons H_2CO_3 + E$), increasing the temperature will shift the equilibrium to the left, promoting the endothermic backward reaction.

Questions & Discussion

True or False?

1. In a reaction equation, the reagents are placed to the left of the arrow and the products are placed to the right.    Answer: True

2. During a chemical reaction, new atoms are formed.    Answer: False (Atoms are conserved, only their combinations change)

3. An elastic collision results in a chemical reaction.    Answer: False (Only effective collisions result in reactions)

4. An effective collision occurs if particles have sufficient energy and correct orientation.    Answer: True

5. Chemical reactions always occur at a high speed.    Answer: False (Speeds vary greatly; some are very slow)

6. The average reaction rate is the change in concentration per unit of time.    Answer: True

7. The average reaction rate can be both negative and positive.    Answer: False (While changes in concentration for reagents are negative, the rate itself is defined to be a positive value)

8. A finely divided substance reacts faster than a bulky one due to increased surface area.    Answer: True

9. A catalyst increases the activation energy.    Answer: False (A catalyst decreases the activation energy)

10. At equilibrium, the rates of the forward and backward reactions are zero.    Answer: False (The rates are equal and non-zero)

11. Upon cooling an equilibrium mixture, the endothermic reaction is temporarily stimulated.    Answer: False (Cooling stimulates the exothermic reaction to produce heat)