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Asked by: Francis
Created at: 2026-01-23 12:37:37
Final Answer:
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Let's solve the **step by step using the given data:
**Given:**
- Reversible reaction: \( \rightlefarpoons B \)
Isothermal at500 K
Equilibrium constant (\(K_c\)) at 500 K = **4**
- Initial concentration: \( [A]_ = 2 \) mol/L, \( [B]_ = \)
- Constant volume, ideal behavior
---
### (a) **Expression for the equilibrium constant in terms of concentration**
For the reaction \( A \rightleftharpoons B \):
\[
K_c = \frac{[B]_{eq}}{[A]_{eq}}
\]
---
### (b) **Equilibrium concentration of A (\([A]_{eq}\))**
Let \( x \) be the amount of A that reacts at equilibrium:
- Initial: \( [A]_ = 2 \), \( [B]_ = \)
- Change: \( -x \) for A, \( +x \) for B
- At equilibrium: \( [A]_{eq} = 2 - x \), \( [B]_{eq} = x \)
Substitute into the equilibrium expression:
\[
K_c = \frac{[B]_{eq}}{[A]_{eq}} = \frac{x}{2-x} = 4
\]
Solve for \( x \):
\[
x = 4(2-x)
\]
\[
x = 8 - 4x
\]
\[
x + 4x = 8
\]
\[
5x = 8
\]
\[
x = \frac{8}{5} = 1.6
\]
Thus,
\[
[A]_{eq} = 2 - x = 2 - 1.6 = .4 \text{ mol/L}
\]
---
### (c) **Equilibrium concentration of B (\([B]_{eq}\))**
\[
[B]_{eq} = x = 1.6 \text{ mol/L}
\]
---
### (d) **Equilibrium conversion of A**
Conversion of A, \( X \):
\[
X = \frac{\text{moles of A reacted}}{\text{initial moles of A}} = \frac{x}{2} = \frac{1.6}{2} = .8 \text{ or } 80\%
\]
---
### (e) **Total concentration of the system at equilibrium**
Total concentration = \( [A]_{eq} + [B]_{eq} = .4 + 1.6 = 2. \) mol/L
---
### (f) **Effect of increasing temperature if the reaction is exothermic**
For an **exothermic reaction**, increasing temperature **shifts equilibrium toward the reactant (A)**, thus favoring formation of A (less B formed). This is due to Le Chatelier’s principle: system tries to absorb added heat by favoring the endothermic (reverse) reaction.
---
### **Final Answers Summary**
(a) \( K_c = \frac{[B]_{eq}}{[A]_{eq}} \)
(b) \( [A]_{eq} = .4 \) mol/L
(c) \( [B]_{eq} = 1.6 \) mol/L
(d) Conversion of A = .8 (or 80%)
(e) Total concentration at equilibrium = 2. mol/L
(f) Increasing temperature favors formation of **A** (reactant) if the reaction is exothermic.
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