The equilibrium constant, K., for the following reaction is 5.10x10-6 at 548 K. Calculate K, for this reaction at this temperature. NHẠCI(s) 2NH3(g) + HCl(g) Kp- =

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### Calculating \( K_p \) from \( K_c \)

The equilibrium constant, \( K_c \), for the following reaction is \( 5.10 \times 10^{-6} \) at 548 K. Calculate \( K_p \) for this reaction at this temperature.

\[ \text{NH}_4\text{Cl}(s) \rightleftharpoons \text{NH}_3(g) + \text{HCl}(g) \]

#### Provided Data:
- \( K_c = 5.10 \times 10^{-6} \)
- Temperature, \( T = 548 \) K

#### Formula to convert \( K_c \) to \( K_p \):
\[ K_p = K_c(RT)^{\Delta n} \]

Where:
- \( R = 0.0821 \ \text{L·atm·K}^{-1}\text{·mol}^{-1} \) (Ideal gas constant)
- \( \Delta n \) is the change in the number of moles of gas (products - reactants)

For the given reaction:
\[ \Delta n = (1 + 1) - (0) = 2 \]

### Calculation:
1. Substitute the known values into the formula:
   \[ K_p = K_c \times (R \times T)^{\Delta n} \]
   \[ K_p = 5.10 \times 10^{-6} \times (0.0821 \times 548)^2 \]

2. Calculate \( (0.0821 \times 548) \):
   \[ (0.0821 \times 548) = 44.991 \]

3. Raise this result to the power of 2:
   \[ (44.991)^2 = 2024.91 \]

4. Multiply by \( K_c \):
   \[ K_p = 5.10 \times 10^{-6} \times 2024.91 = 1.03 \times 10^{-2} \]

### Final Answer:
\[ K_p = 1.03 \times 10^{-2} \]
Transcribed Image Text:### Calculating \( K_p \) from \( K_c \) The equilibrium constant, \( K_c \), for the following reaction is \( 5.10 \times 10^{-6} \) at 548 K. Calculate \( K_p \) for this reaction at this temperature. \[ \text{NH}_4\text{Cl}(s) \rightleftharpoons \text{NH}_3(g) + \text{HCl}(g) \] #### Provided Data: - \( K_c = 5.10 \times 10^{-6} \) - Temperature, \( T = 548 \) K #### Formula to convert \( K_c \) to \( K_p \): \[ K_p = K_c(RT)^{\Delta n} \] Where: - \( R = 0.0821 \ \text{L·atm·K}^{-1}\text{·mol}^{-1} \) (Ideal gas constant) - \( \Delta n \) is the change in the number of moles of gas (products - reactants) For the given reaction: \[ \Delta n = (1 + 1) - (0) = 2 \] ### Calculation: 1. Substitute the known values into the formula: \[ K_p = K_c \times (R \times T)^{\Delta n} \] \[ K_p = 5.10 \times 10^{-6} \times (0.0821 \times 548)^2 \] 2. Calculate \( (0.0821 \times 548) \): \[ (0.0821 \times 548) = 44.991 \] 3. Raise this result to the power of 2: \[ (44.991)^2 = 2024.91 \] 4. Multiply by \( K_c \): \[ K_p = 5.10 \times 10^{-6} \times 2024.91 = 1.03 \times 10^{-2} \] ### Final Answer: \[ K_p = 1.03 \times 10^{-2} \]
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