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Let's break down the problem step by step to calculate the equilibrium constant \( K_c \).

### Reaction:
\[
\text{Ti}(s) + 2 \text{Cl}_2(g) \rightarrow \text{TiCl}_4(l)
\]
This is a heterogeneous equilibrium, which means that the solid (Ti) and liquid (\(\text{TiCl}_4\)) will not be included in the expression for \( K_c \), only the gaseous reactant \( \text{Cl}_2 \).

### Data provided:
- Volume of the vessel: \( 8.4 \, \text{L} \)
- Mass of Ti: \( 4.21 \, \text{g} \)
- Mass of \( \text{Cl}_2 \): \( 2.65 \, \text{g} \)
- Mass of \( \text{TiCl}_4 \): \( 3.41 \, \text{g} \)

### Step 1: Find the moles of each substance.
We need the molar masses:
- Molar mass of Ti: \( 47.87 \, \text{g/mol} \)
- Molar mass of \( \text{Cl}_2 \): \( 70.90 \, \text{g/mol} \)
- Molar mass of \( \text{TiCl}_4 \): \( 189.68 \, \text{g/mol} \)

Now calculate the number of moles for each substance:
\[
\text{Moles of Ti} = \frac{4.21 \, \text{g}}{47.87 \, \text{g/mol}} = 0.0879 \, \text{mol}
\]
\[
\text{Moles of Cl}_2 = \frac{2.65 \, \text{g}}{70.90 \, \text{g/mol}} = 0.0374 \, \text{mol}
\]
\[
\text{Moles of TiCl}_4 = \frac{3.41 \, \text{g}}{189.68 \, \text{g/mol}} = 0.0180 \, \text{mol}
\]

### Step 2: Write the equilibrium expression for \( K_c \).
Since \( K_c \) only includes the gaseous reactant \( \text{Cl}_2 \), the expression is:
\[
K_c = \frac{1}{[\text{Cl}_2]^2}
\]
Where \( [\text{Cl}_2] \) is the concentration of chlorine gas at equilibrium.

### Step 3: Calculate the concentration of \( \text{Cl}_2 \).
The concentration is given by:
\[
[\text{Cl}_2] = \frac{\text{Moles of Cl}_2}{\text{Volume of the vessel}} = \frac{0.0374 \, \text{mol}}{8.4 \, \text{L}} = 0.00445 \, \text{mol/L}
\]

### Step 4: Calculate \( K_c \).
Now plug the concentration of \( \text{Cl}_2 \) into the \( K_c \) expression:
\[
K_c = \frac{1}{(0.00445)^2} = \frac{1}{0.0000198} = 50505
\]
Rounding to 2 significant digits:
\[
K_c \approx 51000
\]

### Final answer:
The equilibrium constant \( K_c \) is approximately **51000**.

Would you like more details on any part of this solution? 

Here are 5 questions related to this topic:
1. How do we determine which substances to include in the equilibrium expression?
2. Why are solids and liquids not included in the expression for \( K_c \)?
3. What would happen to \( K_c \) if the volume of the container increased?
4. How does temperature affect the value of the equilibrium constant?
5. Can \( K_c \) be used to predict the direction of the reaction?

**Tip:** Always remember to use the molar mass to convert between grams and moles in equilibrium calculations.

Calculate the equilibrium constant for the reaction: Ti(s) + 2Cl2(g) → TiCl4(l) based on the provided masses of Ti, Cl2, and TiCl4 in a vessel with a volume of 8.4 L.

Learn how to calculate the equilibrium constant for the reaction Ti + Cl2 → TiCl4 using stoichiometry and molar mass. Includes step-by-step calculation of moles of Ti, Cl2, and TiCl4, with a final equilibrium constant value.

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