Question

Element 'A reacts with oxygen to form a compound ${{A}_{2}}{{O}_{3}}$. If 0.359g of A reacts to give 0.559 gram of the compound, then the atomic weight of 'A' will be:
(A) 51
(B) 43.08
(C) 49.7
(D) 47.9

Answer 1

Assume the atomic weight of element a as $a\,g\,mo{{l}^{-1}}$ and find the ratio of A to that of compound. Use the information given in the question to find an equation containing unknown “a” and solve it.

Complete answer:
In order to answer the question, we need to know about moles and molar mass. Now, matter is made up of atoms, and as matter has mass, then the atoms should have an individual mass. Molar mass of an element or compound is the mass which houses $6\times {{10}^{23}}$ particles. For, example, the hydrogen molecule has a molar mass of 2 grams. This means 2 grams of hydrogen contains $6\times {{10}^{23}}$.
atoms, and this number is also called the Avogadro’s number.
Number of moles of an element or a compound is the ratio of its given mass taken by the user, to its molar mass. More is the number of moles, more is the concentration of the substance.
Now, let us come to the question. As element a is unknown, we can assume it’s atomic mass as $a\,g\,mo{{l}^{-1}}$. We know the atomic mass of oxygen which is $16g\,mo{{l}^{-1}}$. So, the mass of the compound ${{A}_{2}}{{O}_{3}}$ will be $(2a+48)g\,mo{{l}^{-1}}$. We now find the mass ratio of A in the compound which is $\dfrac{2a}{2a+48}$. 0.559 grams of the compound is obtained when 0.359 grams of A reacts with it. So, we can use the ratio to find an equation. We have:

& \dfrac{2a}{2a+48}=\dfrac{0.359}{0.559} \\\ & \Rightarrow \dfrac{a}{a+24}=\dfrac{359}{559} \\\ & \Rightarrow 559a=359a+8616 \\\ & \Rightarrow 200a=8616 \\\ & \Rightarrow a=\dfrac{8616}{200}=43.08 \\\ \end{aligned}$$ **So, we get the atomic weight of A as 43.08 gram which matches with option B.** **Note:** It is to be noted that in case of a molecule, to find out the molar mass, the masses of individual elements are added up. For example, molar mass is 18 grams.