**Equilibrium Constant Conversion**In this problem, we aim to convert the equilibrium constant from concentration-based (Kc) to pressure-based (Kp) for a chemical reaction at a given temperature. The reaction, along with its known Kc value and temperature, is as follows:**Reaction:**\[ \text{H}_2(g) + \text{I}_2(g) \rightleftharpoons 2 \text{HI}(g) \]**Given:**- Equilibrium constant, \(K_c = 4.2\)- Temperature, \( T = 448^\circ\text{C} \)**Task:**Find the value of \( K_p \) at the given temperature.**Formula and Relationship:**The relationship between \( K_c \) and \( K_p \) is given by the formula:\[ K_p = K_c (RT)^{\Delta n} \]Where:- \( R \) is the gas constant (0.0821 L·atm/mol·K)- \( T \) is the temperature in Kelvin (K)- \( \Delta n \) is the difference in the number of moles of gaseous products and reactants**Steps to Solve:**1. **Convert Temperature to Kelvin:** \( T = 448^\circ\text{C} + 273.15 = 721.15 \text{K} \)2. **Determine \( \Delta n \):** \[ \Delta n = (\text{moles of HI}) - (\text{moles of H}_2 + \text{moles of I}_2) \] \[ \Delta n = 2 - (1 + 1) = 0 \]3. **Calculate \( K_p \):** Since \( \Delta n = 0 \), the relationship simplifies to: \[ K_p = K_c (RT)^{0} \] \[ K_p = K_c \] Therefore: \[ K_p = 4.2 \]**Answer:**\[ K_p = 4.20 \]This simplified answer provides a clear understanding of how to convert between \( K_c \) and \( K_p \) for the specified temperature and reaction conditions.

Kc and Kp are the equilibrium constant at particular concentration and pressure respectively. The…

Answered: The reaction below was found to have a…

The reaction below was found to have a Kc = 4.2 at a 448°C. Find the value of K, at that temperature. H2(g) + 12(g) = 2HI(g) Give your answer with 3 significant digits.

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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Question

**Equilibrium Constant Conversion**

In this problem, we aim to convert the equilibrium constant from concentration-based (Kc) to pressure-based (Kp) for a chemical reaction at a given temperature. The reaction, along with its known Kc value and temperature, is as follows:

**Reaction:**
\[ \text{H}_2(g) + \text{I}_2(g) \rightleftharpoons 2 \text{HI}(g) \]

**Given:**
- Equilibrium constant, \(K_c = 4.2\)
- Temperature, \( T = 448^\circ\text{C} \)

**Task:**
Find the value of \( K_p \) at the given temperature.

**Formula and Relationship:**

The relationship between \( K_c \) and \( K_p \) is given by the formula:
\[ K_p = K_c (RT)^{\Delta n} \]

Where:
- \( R \) is the gas constant (0.0821 L·atm/mol·K)
- \( T \) is the temperature in Kelvin (K)
- \( \Delta n \) is the difference in the number of moles of gaseous products and reactants

**Steps to Solve:**

1. **Convert Temperature to Kelvin:**
\( T = 448^\circ\text{C} + 273.15 = 721.15 \text{K} \)

2. **Determine \( \Delta n \):**
\[ \Delta n = (\text{moles of HI}) - (\text{moles of H}_2 + \text{moles of I}_2) \]
\[ \Delta n = 2 - (1 + 1) = 0 \]

3. **Calculate \( K_p \):**
Since \( \Delta n = 0 \), the relationship simplifies to:
\[ K_p = K_c (RT)^{0} \]
\[ K_p = K_c \]
Therefore:
\[ K_p = 4.2 \]

**Answer:**
\[ K_p = 4.20 \]

This simplified answer provides a clear understanding of how to convert between \( K_c \) and \( K_p \) for the specified temperature and reaction conditions.

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