Question

For the reaction \(\mathrm{A}(g)+\mathrm{B}(g) \longrightarrow \mathrm{AB}(g),\) how many unique collisions between \(\mathrm{A}\) and \(\mathrm{B}\) are possible if there are four particles of \(\mathrm{A}\) and three particles of \(\mathrm{B}\) present in the vessel?

Short answer

12 unique collisions are possible.

Step-by-step solution

Identify the particles

Identify the total number of particles of \(\text{A}\) and \(\text{B}\). Here, there are 4 particles of \(\text{A}\) and 3 particles of \(\text{B}\).

Understand unique collisions

Each particle of \(\text{A}\) can collide with each particle of \(\text{B}\). To find the total number of unique collisions, multiply the number of \(\text{A}\) particles by the number of \(\text{B}\) particles.

Calculate the total unique collisions

Multiply the number of \(\text{A}\) particles (4) by the number of \(\text{B}\) particles (3): \[ 4 \times 3 = 12 \]

Key concepts

Reaction Kinetics

Reaction kinetics is a central area of chemistry that deals with the rates of chemical reactions. Knowing how fast a reaction occurs can be crucial for various real-world processes, such as manufacturing and biological systems. In essence, reaction kinetics explores how molecules react and what factors influence the speed of those reactions.

Several factors can affect reaction rates:

• Concentration of reactants: Higher concentrations usually lead to faster reactions because there are more molecules to collide.
• Temperature: Increasing temperature typically increases reaction rates as molecules move faster and collide more often.
• Presence of a catalyst: Catalysts can lower the activation energy required, making reactions occur more quickly.

Understanding these factors can help control reactions for desired outcomes. For example, in industrial settings, carefully adjusting temperature and concentration can optimize production yield.

Molecular Collisions

In collision theory, the rate of a chemical reaction is proportional to the number of effective collisions between reactant molecules. For a reaction to occur, reactant particles must collide with sufficient energy and proper orientation.

Here’s how collisions between molecules work:

• Effective Collisions: Only collisions with enough energy to overcome the activation energy barrier and with proper orientation lead to a reaction.
• Activation Energy: This is the minimum energy required for reactants to transform into products. Without this energy, even if the molecules collide, a reaction won't occur.
• Collision Frequency: This is the number of collisions per unit time. Higher frequency increases the chances of effective collisions, thus raising the reaction rate.

In the given exercise, we calculated the total possible collisions between particles of A and B. With 4 particles of A and 3 particles of B, the total number of unique collisions is found by multiplying the number of A particles with the number of B particles:
\[4 \times 3 = 12\]]

Chemical Reactions

A chemical reaction is a process where reactants transform into products. This transformation involves breaking and forming chemical bonds, and is governed by principles such as conservation of mass and energy.

There are various types of chemical reactions:

• Synthesis reactions: Two or more reactants combine to form a single product, such as \(\text{A}+\text{B} \rightarrow \text{AB}\).
• Decomposition reactions: A single compound breaks down into two or more simpler substances.
• Single-replacement reactions: An element in a compound is replaced by another element.
• Double-replacement reactions: The ions of two compounds exchange places in an aqueous solution to form two new compounds.

In the exercise, we focus on a synthesis reaction where \(\text{A}(g) + \text{B}(g) \rightarrow \text{AB}(g)\). This reaction involves reactant A and B colliding and reacting to form a product AB. By understanding the type of reaction and factors influencing it, one can predict and control the outcome effectively.