To determine the correct formula for the product of the reaction [tex]\(3 A_2 + B_2 \rightarrow 2\)[/tex] units of product, let's analyze the stoichiometry and the given choices step-by-step.
1. Understand the Reaction:
The reaction given is:
[tex]\[ 3 A_2 + B_2 \rightarrow 2 \text{ units of product} \][/tex]
This implies that 3 moles of [tex]\(A_2\)[/tex] react with 1 mole of [tex]\(B_2\)[/tex] to produce 2 moles of the product.
2. Break Down the Molecules and Stoichiometry:
- Each molecule of [tex]\(A_2\)[/tex] contains 2 atoms of A.
- Each molecule of [tex]\(B_2\)[/tex] contains 2 atoms of B.
Therefore, in the reaction:
- [tex]\(3 A_2\)[/tex] provides [tex]\(3 \times 2 = 6\)[/tex] atoms of A.
- [tex]\(1 B_2\)[/tex] provides [tex]\(1 \times 2 = 2\)[/tex] atoms of B.
3. Determine the Total Atoms in the Product:
The total atoms involved in the reaction are 6 atoms of A and 2 atoms of B.
4. Form the Product:
These atoms are rearranged to form 2 moles of the product. Therefore, each mole of the product must contain half the total number of each type of atom.
- Since we have two moles of the product containing a total of 6 atoms of A, each mole of the product must contain [tex]\(6 / 2 = 3\)[/tex] atoms of A.
- Similarly, since we have two moles of the product containing a total of 2 atoms of B, each mole of the product must contain [tex]\(2 / 2 = 1\)[/tex] atom of B.
5. Write the Simplified Product Formula:
Given these proportions, the product must have the formula where there is 1 atom of A for each atom of B. This corresponds to the simplest formula [tex]\(AB\)[/tex].
6. Choose the Correct Option:
Among the given options:
- [tex]\(A_2B\)[/tex]
- [tex]\(AB_2\)[/tex]
- [tex]\(A_3B\)[/tex]
- [tex]\(AB\)[/tex]
The correct formula based on the stoichiometric analysis is [tex]\(AB\)[/tex].
Hence, the correct answer is:
[tex]\[ AB \][/tex]
The correct formula for the product of the reaction is [tex]\(AB\)[/tex]. Therefore, the correct choice is:
[tex]\[ \boxed{AB} \][/tex]
