Question

An element X forms two oxides. Formula of the first oxide is $X{{O}_{2}}$. The first oxide contains 50% of oxygen. If the second oxide contains 60% oxygen, the formula of the second oxide is:
A. $X{{O}_{3}}$
B. ${{X}_{2}}{{O}_{3}}$
C. ${{X}_{3}}{{O}_{2}}$
D. ${{X}_{2}}O$

Answer 1

Hint: To solve such problems, consider the molecular weight of the elements in the molecule. Find out the molecular weight of the element X first using the percentage formula. Then you can find out the formula of the second oxide.

Complete answer:
Given that,
An element denoted by X forms two oxides.
Formula of the first oxide is $X{{O}_{2}}$ and the first oxide contains 50% amount of oxygen.
The second oxide of this element has 60% oxygen and we have to find out the formula of this oxide.
So, first of all let us find out the molecular weight of the first oxide i.e. $X{{O}_{2}}$.
As we know, the atomic weight of oxygen is $16g$ and the oxide has two atoms of oxygen. So, the molecular weight of oxygen in the first oxide will be $32g$ and let the atomic weight of the element be X. So, the total weight of this oxide will be $32+X$.
The first oxide has 50% amount of oxygen.
By using the formula,
$%=\dfrac{\text{Molecular weight of the element}}{\text{Total weight of compound}}$
So, placing the values we will get:
$50%<=\dfrac{32}{32+X}$
Then, $\dfrac{32}{32+X}=0.5$
Then, $X=32$
So, the molecular weight of the element is $32g$.
Now, let the molecular formula of the second oxide of the element X be$X{{O}_{n}}$.
So, here the atomic weight of the oxygen will be $16n$ and the molecular weight of the oxide will be $32+16n$. Given that, the second oxide has 60% oxygen.
Similarly, by using the formula used above we get,
$\dfrac{16n}{32+16n}=0.6$
So, $n=3$
Therefore, the formula of the second oxide will be $X{{O}_{3}}$.

Hence, the correct option is A.

Note:
It is important to remember here that while calculating here, we are considering the molecular weight and the percentage of the element present in the compound. Molecular weight or molar mass is the weight of one mole of an element. So, if two atoms of an element are present (shown in subscript), the molecular weight of the element should be multiplied with two.