What is $K_b$ for $C_5H_5N(aq) + H_2O(l) = C_5H_5NH^+(aq) + OH^-(aq)$?
A. $K_b = \frac{[C_5H_5N]}{[C_5H_5NH^+][OH^-]}$
B. $K_b = \frac{[C_5H_5NH^+ HOH^-]}{[C_5H_5N]}$
C. $K_b = \frac{[C_5H_5NH^+]}{[C_5H_5N]}$
D. $K_b = [C_5H_5N^+] |O^-|$
Answer (2)
The problem asks for the correct expression for K b of the given reaction.
K b is the base dissociation constant, which is the ratio of products to reactants.
For the reaction C 5 H 5 N ( a q ) + H 2 O ( l ) ⇌ C 5 H 5 N H + ( a q ) + O H − ( a q ) , the K b expression is K b = [ C 5 H 5 N ] [ C 5 H 5 N H + ] [ O H − ] .
None of the options exactly match the correct expression, indicating a possible typo in the question. The correct expression is K b = [ C 5 H 5 N ] [ C 5 H 5 N H + ] [ O H − ] .
Explanation
Understanding the Problem The reaction is: C 5 H 5 N ( a q ) + H 2 O ( l ) ⇌ C 5 H 5 N H + ( a q ) + O H − ( a q ) . We are asked to find the correct expression for K b (the base dissociation constant) for this reaction. The general form of K b is: K b = [ re a c t an t s ] [ p ro d u c t s ] . Water is a liquid and its concentration is not included in the K b expression.
Determining the Expression for Kb The products are C 5 H 5 N H + ( a q ) and O H − ( a q ) . The reactant is C 5 H 5 N ( a q ) . Therefore, the expression for K b is: K b = [ C 5 H 5 N ] [ C 5 H 5 N H + ] [ O H − ] .
Comparing with Given Options Now, let's compare the derived expression with the given options. Option A is K 6 = [ C 5 H 5 N H + ] [ O H − ] [ C 5 H 5 N ] . This is the inverse of the correct expression. Option B is K 0 = [ C 5 H 5 N ] [ O 5 H 5 N H + H O H − ] . This option is incorrect as it includes water and has an incorrect numerator. Option C is K b = [ C 6 H 5 N ] [ C 5 H 5 N H + ] . This is missing the hydroxide ion concentration in the numerator and has an incorrect formula. None of the options match the derived expression. However, if we look at the options carefully, we can see that option A is the inverse of what we expect, and option C is missing [ O H − ] in the numerator. The correct expression should have both [ C 5 H 5 N H + ] and [ O H − ] in the numerator and [ C 5 H 5 N ] in the denominator. It seems there might be a typo in the options. Assuming there is a typo in the options, let's derive the correct expression for K b .
Final Answer Based on the reaction C 5 H 5 N ( a q ) + H 2 O ( l ) ⇌ C 5 H 5 N H + ( a q ) + O H − ( a q ) , the correct expression for K b is: K b = [ C 5 H 5 N ] [ C 5 H 5 N H + ] [ O H − ] . Among the given options, none of them exactly matches the correct expression. However, option A is the closest if we consider its inverse. It seems there is a typo in the question.
Examples
Understanding base dissociation constants is crucial in various fields, such as environmental science, where it helps predict the behavior of pollutants in water, and in pharmacology, where it aids in understanding drug absorption and distribution in the body. For example, if a pharmaceutical company is developing a new drug that is a weak base, knowing its K b value can help predict how well it will be absorbed in the acidic environment of the stomach versus the more alkaline environment of the intestines. This knowledge can then be used to optimize the drug's formulation and dosage to ensure maximum effectiveness.
The correct K b expression for the reaction of 5-pyridine with water is given by K b = [ C 5 H 5 N ] [ C 5 H 5 N H + ] [ O H − ] . None of the provided options match this expression correctly. The closest option, however, is option A, which is the inverse of the expected expression.
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