Phosphorus pentachloride decomposes according to the chemical equation PCI, (g) = PCI, (g) + Cl, (g) K. = 1.80 at 250 °C A 0.2950 mol sample of PCl, (g) is injected into an empty 4.75 L reaction vessel held at 250 °C. Calculate the concentrations of PCI, (g) and PCl,(g) at equilibrium. [PCI,] = M [PCI,] = M

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### Phosphorus Pentachloride Decomposition Reaction

Phosphorus pentachloride decomposes according to the chemical equation:

\[ \text{PCl}_5 (g) \rightleftharpoons \text{PCl}_3 (g) + \text{Cl}_2 (g) \quad \text{with} \quad K_c = 1.80 \text{ at } 250^\circ \text{C} \]

### Initial Conditions
A 0.2950 mol sample of PCl₅(g) is injected into an empty 4.75 L reaction vessel held at 250°C.

### Problem Statement
Calculate the concentrations of PCl₅(g) and PCl₃(g) at equilibrium.

#### Calculation Components
1. **ICE Table**: 
   Establish an ICE (Initial, Change, Equilibrium) table to handle the concentration changes.

2. **Initial Concentration**:
   \[
   [\text{PCl}_5]_{\text{initial}} = \frac{0.2950 \text{ mol}}{4.75 \text{ L}} = 0.0621 \text{ M}
   \]

3. **Equilibrium Expression**:
   For the equilibrium constant \( K_c \):
   \[
   K_c = \frac{[\text{PCl}_3][\text{Cl}_2]}{[\text{PCl}_5]}
   \]

4. **Equilibrium Concentrations**:
   Define the changes in concentrations and relate them using the stoichiometric coefficients.

### Equilibrium Concentration Calculation

\[
K_c = 1.80 \text{ at } 250^\circ \text{C}
\]

1. **Initial Concentration**:
   \[
   [\text{PCl}_5](\text{initial}) = 0.0621 \text{ M}
   \]
   \[
   [\text{PCl}_3](\text{initial}) = 0
   \]
   \[
   [\text{Cl}_2](\text{initial}) = 0
   \]

2. **Change**:
   \[
   [\text{PCl}_5] = 0.0621 - x
   \]
   \[
   [\text{PCl}_3] = x
   \
Transcribed Image Text:### Phosphorus Pentachloride Decomposition Reaction Phosphorus pentachloride decomposes according to the chemical equation: \[ \text{PCl}_5 (g) \rightleftharpoons \text{PCl}_3 (g) + \text{Cl}_2 (g) \quad \text{with} \quad K_c = 1.80 \text{ at } 250^\circ \text{C} \] ### Initial Conditions A 0.2950 mol sample of PCl₅(g) is injected into an empty 4.75 L reaction vessel held at 250°C. ### Problem Statement Calculate the concentrations of PCl₅(g) and PCl₃(g) at equilibrium. #### Calculation Components 1. **ICE Table**: Establish an ICE (Initial, Change, Equilibrium) table to handle the concentration changes. 2. **Initial Concentration**: \[ [\text{PCl}_5]_{\text{initial}} = \frac{0.2950 \text{ mol}}{4.75 \text{ L}} = 0.0621 \text{ M} \] 3. **Equilibrium Expression**: For the equilibrium constant \( K_c \): \[ K_c = \frac{[\text{PCl}_3][\text{Cl}_2]}{[\text{PCl}_5]} \] 4. **Equilibrium Concentrations**: Define the changes in concentrations and relate them using the stoichiometric coefficients. ### Equilibrium Concentration Calculation \[ K_c = 1.80 \text{ at } 250^\circ \text{C} \] 1. **Initial Concentration**: \[ [\text{PCl}_5](\text{initial}) = 0.0621 \text{ M} \] \[ [\text{PCl}_3](\text{initial}) = 0 \] \[ [\text{Cl}_2](\text{initial}) = 0 \] 2. **Change**: \[ [\text{PCl}_5] = 0.0621 - x \] \[ [\text{PCl}_3] = x \
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