What is [tex]$K_{ a }$[/tex] for [tex]$H _2 CO _3(a q)= H ^{+}(a q)+ HCO _3{ }^{-}(a q)$[/tex]?
A. [tex]$K_2=\frac{\left[ H _2 CO _3\right]}{\left[ H ^{+}\right]\left[ HCO _3{ }^{-}\right]}$[/tex]
B. [tex]$\left.K_a=\left[ H _2 CO _3\right] H + NH HCO _3\right]$[/tex]
C. [tex]$K_{ a }=\left[ H ^{+}\right]\left[ HCO _3{ }^{-}\right]$[/tex]
D. [tex]$K_3=\frac{| H +| HCO -|}{\left| H _2 CO _3\right|}$[/tex]
Answer (2)
Define the acid dissociation constant, K a , as the ratio of products to reactants in the dissociation of a weak acid.
Apply the general formula for K a to the specific reaction: H 2 C O 3 ( a q ) ⇌ H + ( a q ) + H C O 3 − ( a q ) .
Identify the correct expression for K a as K a = [ H 2 C O 3 ] [ H + ] [ H C O 3 − ] .
Choose the correct option, which is D: K 3 = ∣ H 2 C O 3 ∣ ∣ H + ∣ H CO − ∣ .
Explanation
Understanding Acid Dissociation Constant The problem asks for the expression for the acid dissociation constant, K a , for the given reaction. The general form for the acid dissociation of a weak acid H A is given by the equilibrium: H A ( a q ) ⇌ H + ( a q ) + A − ( a q ) The acid dissociation constant, K a , is defined as the ratio of the concentrations of the products to the concentration of the reactant, each raised to the power of their stoichiometric coefficients. Therefore, the expression for K a is: K a = [ H A ] [ H + ] [ A − ] .
Applying to the Given Reaction For the given reaction, we have: H 2 C O 3 ( a q ) ⇌ H + ( a q ) + H C O 3 − ( a q ) Here, H 2 C O 3 is the weak acid H A , and H C O 3 − is its conjugate base A − . Therefore, the expression for K a for this reaction is: K a = [ H 2 C O 3 ] [ H + ] [ H C O 3 − ] .
Selecting the Correct Option Now, we compare the derived expression with the given options:
A. K 2 = [ H + ] [ H C O 3 − ] [ H 2 C O 3 ] - Incorrect (inverse of the correct expression).
B. K a = [ H 2 C O 3 ] H + N HH C O 3 ] - Incorrect (not a valid expression).
C. K a = [ H + ] [ H C O 3 − ] - Incorrect (missing the denominator).
D. K 3 = ∣ H 2 C O 3 ∣ ∣ H + ∣ H CO − ∣ - Correct (but uses absolute value notation, which is unnecessary and could be confusing).
Option D is the closest to the correct expression, but it uses absolute value notation, which is not standard for equilibrium constants. However, since concentrations are always positive, the absolute value signs don't change the value of the expression. Thus, option D is the correct answer.
Final Answer The correct expression for K a is: K a = [ H 2 C O 3 ] [ H + ] [ H C O 3 − ] . Therefore, the correct answer is D.
Examples
Understanding acid dissociation constants is crucial in many real-world applications, such as environmental science, medicine, and industrial chemistry. For instance, in environmental science, K a values help predict the acidity of rainwater and the buffering capacity of natural waters. In medicine, they are essential for understanding drug absorption and the behavior of biological buffers in the body. In industrial chemistry, K a values are used to optimize reaction conditions and control the pH of solutions in various processes. For example, if you're studying the effects of acid rain on a lake, knowing the K a of carbonic acid ( H 2 C O 3 ) helps you predict how the lake's pH will change as the concentration of H 2 C O 3 increases. This is because the K a tells you the ratio of products ( H + and H C O 3 − ) to reactants ( H 2 C O 3 ) at equilibrium, which directly influences the lake's acidity.
The acid dissociation constant, K a , for the reaction of carbonic acid is expressed as K a = [ H 2 C O 3 ] [ H + ] [ H C O 3 − ] . Among the provided choices, option D captures the essence of this relationship, making it the best choice despite some notation issues. Thus, the correct answer is option D.
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