At 800 K, hydrogen iodide can decompose into hydrogen and iodine gases. 2HI(9) 2(9) +H2 (g) At this temperature, K = 0.0169. What are the partial pressures at equilibrium of the hydrogen and iodine if initially a sealed flask at 800 K contains only HI at a pressure of 0.226 atm? Partial pressure of hydrogen = atm Partial pressure of iodine = atm

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### Decomposition of Hydrogen Iodide at 800 K

At 800 K, hydrogen iodide (HI) can decompose into hydrogen (H₂) and iodine (I₂) gases according to the equilibrium reaction:

\[ 2HI(g) \rightleftharpoons I_2(g) + H_2(g) \]

At this temperature, the equilibrium constant, \( K \), is 0.0169. Given this information, we are asked to determine the partial pressures of hydrogen and iodine at equilibrium if initially a sealed flask at 800 K contains only HI at a pressure of 0.226 atm.

The problem can be broken down into the following steps:

1. **Initial Condition:**
   - Initial pressure of HI, \( P_{HI} \): 0.226 atm.
   - Initial pressure of H₂ and I₂: 0 atm (since initially only HI is present).

2. **Change at Equilibrium:**
   - Let the change in pressure of HI be \( -2x \) (since 2 moles of HI produce 1 mole each of H₂ and I₂).
   - The change in pressure of both H₂ and I₂ will be \( +x \).

3. **Equilibrium Condition:**
   - Equilibrium pressure of HI: \( 0.226 - 2x \) atm.
   - Equilibrium pressure of H₂: \( x \) atm.
   - Equilibrium pressure of I₂: \( x \) atm.

4. **Equilibrium Expression:**
   \[ K = \frac{(P_{I2})(P_{H2})}{(P_{HI})^2} \]
   Substituting the equilibrium conditions:

   \[ 0.0169 = \frac{(x)(x)}{(0.226 - 2x)^2} \]

5. **Solving for \( x \):**
   This equation needs to be solved to find the value of \( x \) which will give us the partial pressures at equilibrium.
   
6. **Substitute \( x \) into Equilibrium Pressures:**
   - Partial pressure of hydrogen \( P_{H₂} = x \) atm.
   - Partial pressure of iodine \( P_{I₂} = x \) atm.

### User Interaction

**Question:**
What are the partial pressures at equilibrium of the hydrogen and
Transcribed Image Text:### Decomposition of Hydrogen Iodide at 800 K At 800 K, hydrogen iodide (HI) can decompose into hydrogen (H₂) and iodine (I₂) gases according to the equilibrium reaction: \[ 2HI(g) \rightleftharpoons I_2(g) + H_2(g) \] At this temperature, the equilibrium constant, \( K \), is 0.0169. Given this information, we are asked to determine the partial pressures of hydrogen and iodine at equilibrium if initially a sealed flask at 800 K contains only HI at a pressure of 0.226 atm. The problem can be broken down into the following steps: 1. **Initial Condition:** - Initial pressure of HI, \( P_{HI} \): 0.226 atm. - Initial pressure of H₂ and I₂: 0 atm (since initially only HI is present). 2. **Change at Equilibrium:** - Let the change in pressure of HI be \( -2x \) (since 2 moles of HI produce 1 mole each of H₂ and I₂). - The change in pressure of both H₂ and I₂ will be \( +x \). 3. **Equilibrium Condition:** - Equilibrium pressure of HI: \( 0.226 - 2x \) atm. - Equilibrium pressure of H₂: \( x \) atm. - Equilibrium pressure of I₂: \( x \) atm. 4. **Equilibrium Expression:** \[ K = \frac{(P_{I2})(P_{H2})}{(P_{HI})^2} \] Substituting the equilibrium conditions: \[ 0.0169 = \frac{(x)(x)}{(0.226 - 2x)^2} \] 5. **Solving for \( x \):** This equation needs to be solved to find the value of \( x \) which will give us the partial pressures at equilibrium. 6. **Substitute \( x \) into Equilibrium Pressures:** - Partial pressure of hydrogen \( P_{H₂} = x \) atm. - Partial pressure of iodine \( P_{I₂} = x \) atm. ### User Interaction **Question:** What are the partial pressures at equilibrium of the hydrogen and
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