Titanium chloride `(TiCl_3)` is used as a catalyst in plastic industry. How many chlorine atoms are there in 38.6 g of `TiCI_3`?
[Given : Atomic mass of Ti = 48 u, Cl = 35.5 u ]

Options

A. `18.06 xx 10^(23)`
B. `3.12 xx 10^(23)`
C. `4.5 xx 10^(23)`
D. `1.5 xx 10^(23)`

Answer

To find the number of chlorine atoms in 38.6 g of titanium chloride (TiCl₃), we can follow these steps:

### Step 1: Calculate the molar mass of TiCl₃
The molar mass of TiCl₃ can be calculated by adding the atomic masses of titanium (Ti) and chlorine (Cl).

- Atomic mass of Ti = 48 u
- Atomic mass of Cl = 35.5 u

Since there are 3 chlorine atoms in TiCl₃, the calculation is as follows:

\[ \text{Molar mass of TiCl}_3 = \text{Atomic mass of Ti} + 3 \times \text{Atomic mass of Cl} \]
\[ = 48 + 3 \times 35.5 \]
\[ = 48 + 106.5 = 154.5 \text{ g/mol} \]

### Step 2: Calculate the number of moles of TiCl₃ in 38.6 g
Now, we can calculate the number of moles of TiCl₃ using the formula:

\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
\[ = \frac{38.6 \text{ g}}{154.5 \text{ g/mol}} \approx 0.249 \text{ moles} \]

### Step 3: Calculate the number of molecules of TiCl₃
To find the number of molecules, we use Avogadro's number, which is \(6.022 \times 10^{23}\) molecules/mol.

\[ \text{Number of molecules} = \text{Number of moles} \times \text{Avogadro's number} \]
\[ = 0.249 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mol} \approx 1.50 \times 10^{23} \text{ molecules} \]

### Step 4: Calculate the number of chlorine atoms
Since each molecule of TiCl₃ contains 3 chlorine atoms, we multiply the number of molecules by 3:

\[ \text{Number of Cl atoms} = \text{Number of molecules} \times 3 \]
\[ = 1.50 \times 10^{23} \text{ molecules} \times 3 \approx 4.51 \times 10^{23} \text{ Cl atoms} \]

### Final Answer
Thus, the number of chlorine atoms in 38.6 g of TiCl₃ is approximately \(4.51 \times 10^{23}\).

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