Consider the general reversible reaction. Lower A upper A plus lower B upper B double-headed arrow lower C upper C plus Lower d upper D. What is the equilibrium constant expression for the given system? K e q equals StartFraction lowercase C StartBracket upper C EndBracket lowercase d StartBracket upper D EndBracket over lowercase A StartBracket upper A EndBracket lowercase B StartBracket upper B EndBracket EndFraction. K e q equals StartFraction StartBracket upper C EndBracket StartBracket upper D EndBracket over StartBracket upper A EndBracket StartBracket upper B EndBracket EndFraction. K e q equals StartFraction StartBracket upper A EndBracket superscript lower a StartBracket upper B EndBracket superscript lower b over StartBracket upper C EndBracket superscript lower c StartBracket upper D EndBracket superscript lower D EndFraction. K e q equals StartFraction StartBracket upper C EndBracket superscript lower c StartBracket upper D EndBracket superscript lower D over StartBracket upper A EndBracket superscript lower a StartBracket upper B EndBracket superscript lower b EndFraction.
Real Tutor Solution
Tutor-Verified Answer
Quick Answer
\(K_ { \text { eq} } = \frac { [ C] ^ c [ D] ^ d} { [ A] ^ a [ B] ^ b} \)
Step-by-step Solution
UpStudy Free Solution:
For the given general reversible reaction:
\[aA + bB \rightleftharpoons cC + dD\]
The equilibrium constant expression (\(K_ { \text { eq} } \)) is given by the ratio of the product of the concentrations of the products, each raised to the power of their respective coefficients, to the product of the concentrations of the reactants, each raised to the power of their respective coefficients.
Thus, the correct equilibrium constant expression is:
\[K_ { \text { eq} } = \frac { [ C] ^ c [ D] ^ d} { [ A] ^ a [ B] ^ b} \]
Among the options provided, this corresponds to:
\[K_ { \text { eq} } = \frac { [ C] ^ c [ D] ^ d} { [ A] ^ a [ B] ^ b} \]
Supplemental Knowledge
In chemical equilibrium, the equilibrium constant (\(K_ { eq} \)) is a crucial concept that quantifies the ratio of concentrations of products to reactants at equilibrium for a reversible reaction. For a general reversible reaction:
\[aA + bB \rightleftharpoons cC + dD\]
The equilibrium constant expression is given by:
\[K_ { eq} = \frac { [ C] ^ c [ D] ^ d} { [ A] ^ a [ B] ^ b} \]
Here:
\([ A] , [ B] , [ C] , [ D] \) are the molar concentrations of the reactants and products.
\(a, b, c, d\) are the stoichiometric coefficients from the balanced chemical equation.
This expression indicates that at equilibrium, there is a specific ratio of product concentrations raised to their respective powers (stoichiometric coefficients) to reactant concentrations raised to their respective powers. The value of \(K_ { eq} \) provides insight into whether the reaction favors the formation of products or reactants at equilibrium. A large \(K_ { eq} \) suggests that products are favored, while a small \(K_ { eq} \) indicates that reactants are favored.
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