For the reaction \(\mathrm{A}(g)+\mathrm{B}(g) \longrightarrow \mathrm{AB}(g),\) how many unique collisions between \(A\) and \(B\) are possible if 1.01 mol of \(\mathrm{A}(g)\) and \(2.12 \mathrm{~mol}\) of \(\mathrm{B}(g)\) are present in the vessel?

In a chemical reaction, molecules must collide for the reaction to occur. Not every collision leads to a reaction, but for those that do, the orientation and energy of the molecules are crucial. Molecules A and B must collide properly to form the product AB, and this concept is key to understanding many reactions.

To calculate unique collisions, consider the number of each type of molecule present. Each molecule of A can potentially collide with every molecule of B. Thus, by knowing the number of molecules of A and B, we can determine the total unique collisions possible.
First, the number of molecules is calculated using Avogadro's number for the given moles. Then multiply the two results to get the total unique collisions during the reaction.

Avogadro's number is a fundamental constant in chemistry, defined as the number of atoms, ions, or molecules in one mole of a substance. This number is approximately \(6.022 \times 10^{23} \) particles per mole. It allows chemists to count entities at the atomic scale by relating amounts to macroscopic measurements.

In the exercise, here's how Avogadro's number is used:
1. Calculate the number of molecules of A:
\[ N(A) = 1.01 \text{ mol} \times 6.022 \times 10^{23} \text{ molecules/mol} \]
\[ N(A) \backsimeq 6.082 \times 10^{23} \text{ molecules} \]
2. Calculate the number of molecules of B:
\[ N(B) = 2.12 \text{ mol} \times 6.022 \times 10^{23} \text{ molecules/mol} \]
\[ N(B) \backsimeq 1.276 \times 10^{24} \text{ molecules} \]
After finding the number of molecules using Avogadro's number, you can use these values to calculate the unique collisions between the molecules.

Stoichiometry involves the calculation of reactants and products in chemical reactions. It provides the quantitative relationships derived from the balanced chemical equations.

For the reaction representing the formation of the product AB from reactants A and B, stoichiometry helps in understanding how many molecules of A and B react to form AB. In our example, 1 mole of A reacts with 1 mole of B:
\[ \text{A}(g) + \text{B}(g) \rightarrow \text{AB}(g) \]
Knowing the moles of A and B, stoichiometry ensures the calculation of the unique collisions according to the balanced equation.
From the given moles of A and B, we derive the number of molecules using Avogadro's number. Then, using these quantities, we understand how they interact in a stoichiometric ratio to form the product AB. This method demonstrates the integral role of stoichiometry in chemical reactions and quantitative predictions.