Question

The mineral rutile is an oxide of titanium containing $39.95\%$ oxygen and is isomorphous with cassiterite ($Sn{O_2}$). The atomic weight of titanium is :
A.) $68.10$
B.) $58.10$
C.) $48.10$
D.) $38.10$

Answer 1

In this question, isomorphous compounds have the same crystal form. Therefore, the formula of oxide of tin will be $(Ti{O_2})$ that is similar to that of cassiterite. From the formula we can find the percentage of titanium because the percentage of oxygen is given.

Complete step by step answer:
In this question, two compounds are said to be isomorphous when they have almost similar crystalline structure , they are generally identical and have similar chemical formulas.
In the question, it is given that oxide of titanium is isomorphous with cassiterite that is ($Sn{O_2}$) . Therefore, as we know that isomorphous compounds have similar chemical formulas, as $Sn{O_2}$ has two oxygen atoms in it therefore, the oxide of titanium will also have two atoms of oxygen and one atom of titanium. Therefore, the chemical formula of titanium oxide can be written as $Ti{O_2}$.
As in the question it is given that titanium oxide ($Ti{O_2}$) has $39.95\%$ of oxygen.
It means that in $100g$ of $Ti$ there is $39.95g$ of oxygen
Now, Molecular weight of $Ti{O_2}$ $= x + 2 \times 16g = x + 32g$
Where $x$ is the mass of titanium
As we know that, $x + 32g$ of $Ti{O_2}$ will contain $32g$ of oxygen
$1g{\text{ of titanium}} = \dfrac{{32}}{{x + 32}}g{\text{ of oxygen}} \\\ {\text{100g of titanium}} = \dfrac{{32}}{{x + 32}} \times 100g{\text{ of oxygen}} \\\$
As we know that in $100g$ of $Ti$ there is $39.95g$ of oxygen. Therefore, we can rewrite the above equation as:
$39.95 = \dfrac{{32}}{{x + 32}} \times 100 \\\ x + 32 = \dfrac{{32 \times 100}}{{39.95}} \\\ x + 32 = 80.100 \\\ x = 80.100 - 32 \\\ x = 48.10g \\\$
Therefore, the required mass of titanium in titanium oxide ($Ti{O_2}$) is $48.10g$.

Hence, option C.) is the correct answer.

Note:

Do not get confused between polymorphism and isomorphism. Polymorphism occurs when a particular substance exists in more than two crystalline form like- calcium carbonate exists in two crystalline structure and isomorphism occurs when two substance have similar crystalline structure like- $Ti{O_2},Sn{O_2}$.