A student ran the following reaction in the laboratory at 586 K: CO(g) + Cl2(g) COCI,(g) When she introduced 0.376 moles of CO(g) and 0.406 moles of Cl½(g) into a 1.00 liter container, she found the equilibrium concentration of COCI,(g) to be 0.337 М. Calculate the equilibrium constant, K, she obtained for this reaction. K =

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### Reaction Equilibrium Calculation at 586 K

A student conducted an experiment to study the following reaction at a temperature of 586 K:

\[ \text{CO(g)} + \text{Cl}_2\text{(g)} \rightleftharpoons \text{COCl}_2\text{(g)} \]

#### Initial Conditions

- **Moles of CO(g)**: 0.376 moles
- **Moles of Cl₂(g)**: 0.406 moles
- **Volume of container**: 1.00 liter

#### Observed Equilibrium Condition

- **Equilibrium concentration of COCl₂(g)**: 0.337 M

#### Calculation of Equilibrium Constant \( K_c \)

To find the equilibrium constant \( K_c \), we need to set up the reaction table and expressions for equilibrium concentrations and then apply the equilibrium constant formula.

1. **Initial Concentrations (in Moles per Liter):**
   - \([ \text{CO} ]_0 = \frac{0.376 \text{ moles}}{1.00 \text{ L}} = 0.376 \text{ M}\)
   - \([ \text{Cl}_2 ]_0 = \frac{0.406 \text{ moles}}{1.00 \text{ L}} = 0.406 \text{ M}\)

2. **Determination of Changes:**
   - At equilibrium, \[\text{COCl}_2 \text{(g)} = 0.337 \text{ M}\]
   - Assuming \(x\) moles of CO and \(x\) moles of Cl₂ react to form 0.337 M of the product, then:
     - \([ \text{CO} ] = 0.376\text{ M} - x\]
     - \([ \text{Cl}_2 ] = 0.406\text{ M} - x\]
     - \([ \text{COCl}_2 ] = 0.337 \text{ M}\)
     - Since \(x = 0.337 \text{ M}\), the remaining concentrations are:
       - \([ \text{CO} ] = 0.376\text{ M} - 0.337\text{ M} = 0.039 \text{ M}\)
Transcribed Image Text:### Reaction Equilibrium Calculation at 586 K A student conducted an experiment to study the following reaction at a temperature of 586 K: \[ \text{CO(g)} + \text{Cl}_2\text{(g)} \rightleftharpoons \text{COCl}_2\text{(g)} \] #### Initial Conditions - **Moles of CO(g)**: 0.376 moles - **Moles of Cl₂(g)**: 0.406 moles - **Volume of container**: 1.00 liter #### Observed Equilibrium Condition - **Equilibrium concentration of COCl₂(g)**: 0.337 M #### Calculation of Equilibrium Constant \( K_c \) To find the equilibrium constant \( K_c \), we need to set up the reaction table and expressions for equilibrium concentrations and then apply the equilibrium constant formula. 1. **Initial Concentrations (in Moles per Liter):** - \([ \text{CO} ]_0 = \frac{0.376 \text{ moles}}{1.00 \text{ L}} = 0.376 \text{ M}\) - \([ \text{Cl}_2 ]_0 = \frac{0.406 \text{ moles}}{1.00 \text{ L}} = 0.406 \text{ M}\) 2. **Determination of Changes:** - At equilibrium, \[\text{COCl}_2 \text{(g)} = 0.337 \text{ M}\] - Assuming \(x\) moles of CO and \(x\) moles of Cl₂ react to form 0.337 M of the product, then: - \([ \text{CO} ] = 0.376\text{ M} - x\] - \([ \text{Cl}_2 ] = 0.406\text{ M} - x\] - \([ \text{COCl}_2 ] = 0.337 \text{ M}\) - Since \(x = 0.337 \text{ M}\), the remaining concentrations are: - \([ \text{CO} ] = 0.376\text{ M} - 0.337\text{ M} = 0.039 \text{ M}\)
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