Question

Elements A and B form two compounds ${{\text{B}}_{\text{2}}}{{\text{A}}_{\text{3}}}$ and ${{\text{B}}_{\text{2}}}\text{A}$ 0.05 moles of ${{\text{B}}_{\text{2}}}{{\text{A}}_{\text{3}}}$ weight 9.0 g and 0.10 mole of ${{\text{B}}_{\text{2}}}\text{A}$ weight 10 g. Atomic weight of A and B are -
(A) 20 and 30
(B) 30 and 40
(C) 40 and 30
(D) 30 and 20

Answer 1

Hint: An attempt to this question can be made by determining the molar mass of the two compounds using the data provided in the question. Now calculate the contribution of the elements in both of these compounds. Based on this you can apply the unitary method to determine the atomic weight of the two elements, A and B.

Complete step by step answer:
- The question is given that two elements A and B are forming two compounds by combining in various ratios and the weight of the number of moles of the substance is given. We have to find the atomic weight of the two elements.
- To find the solution for the question we will first determine the molar mass of the two compounds as suggested in the hint.
The weight of 0.05 moles of ${{\text{B}}_{\text{2}}}{{\text{A}}_{\text{3}}}$ is 9 grams, hence the molar mass of the compound is calculated as,
$\text{Molar}\,\text{mass}\,\text{of}\,{{\text{B}}_{\text{2}}}{{\text{A}}_{\text{3}}}\,\text{=}\,\dfrac{\text{9}}{\text{0}\text{.05}}\,\text{=}\,\text{180}$
$\text{2B}\,\text{+}\,\text{3A}\,\text{=}\,\text{180}$
This is because 2 moles of B and 3 moles of A are present in 1 mole of ${{\text{B}}_{\text{2}}}{{\text{A}}_{\text{3}}}$ .
Similarly, weight of 0.1 mole of ${{\text{B}}_{\text{2}}}\text{A}$ is 10 grams and hence the molar mass of compound is calculated as,$\text{Molar}\,\text{mass}\,\text{of}\,{{\text{B}}_{\text{2}}}{{\text{A}}_{\text{3}}}\,\text{=}\,\dfrac{\text{9}}{\text{0}\text{.05}}\,\text{=}\,\text{180}$
$\text{Molar mass of }{{\text{B}}_{\text{2}}}\text{A}\,\text{=}\,\dfrac{\text{10}}{\text{0}\text{.1}}\text{=100}$
$\text{2B}\,\text{+}\,\text{A}\,\text{=}\,\text{100}$
By solving the two equations we get,
$\text{2A=}\,\text{80}$
$\text{A}\,\text{=}\,\text{40}$
Substituting the value of A to obtain the value of B,
$\text{B = 30}$ The correct answer is option “C” .

Note: It is important to know that two elements can form more than one type of compound. This is in accordance with the law of multiple proportions. Earlier it was considered that two elements can combine in one type of ratio only as mentioned in Dalton's atomic theory.