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.
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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![**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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe31f0f84-4944-4abf-a4a5-e3674c4e8a30%2F8d132509-ad78-4dc6-ab84-63f04757638e%2Fsvbqsml_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**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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