Final answer:
The atomic weights of elements A and B are determined by using the given mass of compounds and the number of moles provided. By setting up and solving a system of linear equations using the molar masses of B₂A₃ and B₂A, we find that the atomic weight of A is 30 amu and of B is 40 amu.
Step-by-step explanation:
Finding the Atomic Weights of Elements A and B
To calculate the atomic weights of elements A and B from the given compounds B₂A₃ and B₂A, we apply concepts like the Law of Definite Proportions and the Law of Conservation of Mass. The molar mass of a compound is numerically equivalent to its formula weight in amu, an example being the reference isotope 12C, which has both a molar mass and atomic mass of 12 g/mol or 12 amu respectively.
Given that 0.05 moles of B₂A₃ weigh 9 grams, we can divide the total mass by the number of moles to find the molar mass (MM) of B₂A₃: (9 g / 0.05 mol) = 180 g/mol. For the compound B₂A, since 0.1 mole weighs 10 grams, its MM is (10 g / 0.1 mol) = 100 g/mol.
Using these molar masses, we can set up the following equations to solve for the atomic weights of A and B:
- 2(B) + 3(A) = 180
- 2(B) + 1(A) = 100
By solving this system of linear equations, we find that the atomic weight of A is 30 amu and the atomic weight of B is 40 amu respectively.