# M5-S3: Collision Theory in Equilibria

### Collision Theory

• Collision theory states that two molecules of gas will react to form product when they collide. The theory explains that rate of reaction depends on:
1. Rate of collision between gas molecules. Greater rate of collision leads to greater reaction rate. Collision rate is dependent on the temperature of the system. Higher temperature causes molecules to be more energetic and therefore, move around with greater speed.

2. Activation energy of the reaction. For a reaction to occur, the reactants must overcome a certain amount of activation energy. If the particles don’t have enough energy, reaction would not occur.

Figure: Molecular orientation is an important factor of reaction rate as stated by collision theory. If the orientation of reactants is not correct (effective) during collision, reaction does not occur.

3. Molecular orientation of reactants. Rate of reaction can increase if reactants collide in the right orientation. Conversely, rate can decrease if the orientation of molecules is not favourable for the formation of product(s).

### Chemical Equilibrium

• Chemical equilibrium is concerned with the reversibility of chemical reactions. Many reactions do not go to completion and instead both reactants and products are in dynamic equilibrium.
• A common reaction that exist in dynamic equilibrium is the conversion between nitrogen dioxide and dinitrogen tetroxide:

$$2NO_{2(g)} \rightleftharpoons N_2O_{4(g)}$$

• Equilibrium is attained when there is no net change in the concentration of reactants and products. At equilibrium the Gibbs free energy (DeltaG=0) of the reaction is zero.

Concentration & reaction rate

• Most reactions do not begin at equilibrium but with time, will reach equilibrium. A reaction can reach equilibrium with any starting quantities of reactants and products.

Figure: change in concentration of reactants and products of a reversible reaction. [N_2O_4] decreases while [NO_2] increases. A reaction can reach equilibrium starting with any quantities of reactants and products.

As a reaction proceeds, the concentration of reactants decreases which means the rate of collision between reactant also decreases. By collision theory, this reduces the rate of forward reaction.

At the same time, the concentration of products increases, and so does the rate of collision between products. This increases the rate of backward reaction.

Figure: change in reaction rate with time. At t1, rate of forward and backward reactions becomes equal, and equilibrium is reached.

Forward and backward reaction rates will continue to change until they become equal in value. When this occurs, the reaction reaches chemical equilibrium.

Figure: Reaction between dinitrogen tetroxide and nitrogen dioxide can be monitored by its colour change. Nitrogen tetroxide is colourless whereas nitrogen dioxide has a distinctive brown colour.

• Nitrogen dioxide (NO_2) has a distinctive brown colour while dinitrogen tetroxide (N_2O_4) is colourless.
• In the reaction above, the reaction mixture is pale brown as it consists of mostly N_2O_4. As the reaction approaches equilibrium, the concentration of NO_2 increases, making the mixture appear browner.

Figure: Change in rates of forward and reverse reactions. In the beginning only reactants are present. Since there are no products, collision rate between products is zero, and so is the reverse reaction rate.

• As the concentration of N_2O_4 decreases, the collision rate of forward reaction decreases. On the other hand, as concentration of NO_2 increases, the collision rate of reverse reaction increases. These changes continue until they become equal, which marks when a dynamic equilibrium is achieved.