Q: A solution contains $0.20$ M of a weak base $B$ with $K_b = 1.0 \times 10^{-6}$. What is the equilibrium concentration of $OH^-$? (Assume $x \ll 0.20$)

$[OH^-] \approx 4.5 \times 10^{-4}$ M

Question 1

Which of the following best describes the behavior of a weak base in aqueous solution?

Accepted Answer

It partially dissociates, establishing a dynamic equilibrium with its conjugate acid and hydroxide ions.

Question 2

Given the equilibrium: $\mathrm{B(aq) + H_2O(l) \rightleftharpoons BH^+(aq) + OH^-(aq)}$, which expression correctly represents the base dissociation constant $K_b$?

Accepted Answer

$K_b = \dfrac{[BH^+][OH^-]}{[B]}$

Question 3

A 0.65 M solution of pyridine ($\mathrm{C_5H_5N}$) has a $K_b$ of $1.7 	imes 10^{-9}$. What is the $pH$ of this solution? (Assume $x \ll 0.65$ and $pK_w = 14$)

Accepted Answer

$pH \approx 9.6$

Question 4

Which of the following steps is NOT required when calculating the $pH$ of a weak base solution?

Accepted Answer

Directly using the initial concentration as $[OH^-]$.

Question 5

If a weak base solution is at equilibrium, which of the following statements is true?

Accepted Answer

The rates of the forward and reverse reactions are equal.

Question 6

A student dissolves a salt in water and observes that the solution becomes basic. Which of the following best explains this observation?

Accepted Answer

The salt contains the conjugate base of a weak acid, which hydrolyzes to produce $OH^-$.

Question 7

Which of the following is the correct sequence of steps to calculate the $pH$ of a weak base solution?

Accepted Answer

Write the equilibrium equation, set up an ICE table, solve for $[OH^-]$ using $K_b$, calculate $pOH$, then $pH$.

Question 8

Which of the following would increase the $pH$ of a weak base solution?

Accepted Answer

Increasing the concentration of the weak base.

Question 9

A weak base has a $K_b$ of $2.5 	imes 10^{-5}$. What is the $pOH$ of a $0.10$ M solution of this base? (Assume $x \ll 0.10$)

Accepted Answer

$pOH \approx 3.3$

Question 10

Which of the following real-world scenarios best illustrates the concept of a weak base establishing equilibrium in water?

Accepted Answer

Ammonia-based household cleaners partially ionize in water, resulting in a solution with a basic $pH$ but not as high as a strong base.

Question 11

If the $K_b$ for a weak base is very small, what does this indicate about the base's strength and the $pH$ of its solution?

Accepted Answer

The base is weak and the $pH$ will be only slightly above 7.

Question 12

Which of the following is a correct statement about the relationship between $K_b$ and $K_a$ for a conjugate acid-base pair?

Accepted Answer

$K_a 	imes K_b = K_w$

Question 13

A solution contains $0.20$ M of a weak base $B$ with $K_b = 1.0 	imes 10^{-6}$. What is the equilibrium concentration of $OH^-$? (Assume $x \ll 0.20$)

Accepted Answer

$[OH^-] \approx 4.5 	imes 10^{-4}$ M

Question 14

Which of the following best explains why weak base solutions are considered dynamic equilibrium systems?

Accepted Answer

Both the forward and reverse reactions occur simultaneously and continuously.

Question 15

A salt solution is found to be acidic. Which of the following is the most likely explanation?

Accepted Answer

The salt contains the conjugate acid of a weak base, which hydrolyzes to produce $H^+$.

Question 16

Which of the following is a correct calculation for the $pH$ of a weak base solution after finding $[OH^-]$?

Accepted Answer

$pOH = -\log [OH^-]$, then $pH = 14 - pOH$

Question 17

Which of the following would NOT affect the position of equilibrium in a weak base solution?

Accepted Answer

Adding a catalyst.

Question 18

A weak base solution is prepared by dissolving $0.50$ mol of base in $1.0$ L of water. If the $K_b$ is $5.0 	imes 10^{-10}$, what is the $pH$ of the solution? (Assume $x \ll 0.50$ and $pK_w = 14$)

Accepted Answer

$pH \approx 8.0$

Calculations Involving Weak Bases and pH

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