Titanium oxide `(TiO_(2))` is heated with excess hydrogen gas to give water and nee oxide `Ti_(x)O_(y)`. If `1.6 gm TiO_(2)` produces `1.44 g Ti_(x)O_(y)`, then select statement (Molar mass of titanium is `48 g//mol`):

Options

A. Volume of `x//y` is `(2)/(3)`
B. Moles of `H_(2)` used in reaction is `0.01` mol.
C. Moles of `H_(2)` formed is `0.02` mol.
D. Both `(1)` and `(3)`

Explanation

To solve the problem, we need to determine the new oxide formed when titanium oxide (TiO₂) is heated with excess hydrogen gas. We are given the mass of TiO₂ and the mass of the new oxide produced, and we need to find the ratio of titanium to oxygen in the new oxide.

### Step 1: Calculate the mass of oxygen lost
We start with the mass of titanium oxide (TiO₂) and the mass of the new oxide (TiₓOᵧ) produced:
- Mass of TiO₂ = 1.6 g
- Mass of TiₓOᵧ = 1.44 g

To find the mass of oxygen lost during the reaction, we subtract the mass of the new oxide from the mass of TiO₂:
\[ \text{Mass of oxygen lost} = \text{Mass of TiO₂} - \text{Mass of TiₓOᵧ} \]
\[ \text{Mass of oxygen lost} = 1.6 \, \text{g} - 1.44 \, \text{g} = 0.16 \, \text{g} \]

### Step 2: Calculate the moles of oxygen lost
Next, we need to convert the mass of oxygen lost into moles. The molar mass of oxygen (O) is 16 g/mol.
\[ \text{Moles of oxygen lost} = \frac{\text{Mass of oxygen lost}}{\text{Molar mass of oxygen}} \]
\[ \text{Moles of oxygen lost} = \frac{0.16 \, \text{g}}{16 \, \text{g/mol}} = 0.01 \, \text{mol} \]

### Step 3: Calculate the moles of TiO₂
Now, we will calculate the moles of TiO₂ used in the reaction. The molar mass of TiO₂ can be calculated as follows:
- Molar mass of titanium (Ti) = 48 g/mol
- Molar mass of oxygen (O) = 16 g/mol

Molar mass of TiO₂ = 48 g/mol + (2 × 16 g/mol) = 48 g/mol + 32 g/mol = 80 g/mol.

Now we can calculate the moles of TiO₂:
\[ \text{Moles of TiO₂} = \frac{\text{Mass of TiO₂}}{\text{Molar mass of TiO₂}} \]
\[ \text{Moles of TiO₂} = \frac{1.6 \, \text{g}}{80 \, \text{g/mol}} = 0.02 \, \text{mol} \]

### Step 4: Determine the new oxide formula
From the reaction, we know that TiO₂ loses oxygen to form TiₓOᵧ. The moles of titanium remain the same as in TiO₂, which is 0.02 mol. The moles of oxygen in the new oxide can be calculated by subtracting the moles of oxygen lost from the moles of oxygen in TiO₂:
- Moles of oxygen in TiO₂ = 2 × 0.02 mol = 0.04 mol
- Moles of oxygen in TiₓOᵧ = 0.04 mol - 0.01 mol = 0.03 mol

### Step 5: Calculate the ratio of titanium to oxygen in the new oxide
Now we can find the ratio of titanium (Ti) to oxygen (O) in the new oxide:
- Moles of titanium = 0.02 mol
- Moles of oxygen = 0.03 mol

The ratio \( \frac{X}{Y} \) can be calculated as follows:
\[ \frac{X}{Y} = \frac{0.02}{0.03} = \frac{2}{3} \]

### Conclusion
The new oxide formed is Ti₂O₃, which corresponds to the ratio of titanium to oxygen being 2:3.