At 298 K , a certain buffer solution contains equal concentrations of $X^{-}$and $HX$, $K_{b}$ for $X^{-}$ is $10^{-10}$. What is the pH of this buffer solution?

Question

Accepted Answer

B. 1. Since $X^{-}$ is the conjugate base of the weak acid $HX$, the two constants are related by **$K_a 	imes K_b = K_w$**.

$$
K_a = \frac{K_w}{K_b} = \frac{10^{-14}}{10^{-10}} = 10^{-4}
$$

2. For a buffer made of a weak acid and its conjugate base, use the **Henderson–Hasselbalch equation**.

$$
pH = pK_a + \log\frac{[X^{-}]}{[HX]}
$$

3. Since the buffer contains equal concentrations of $X^{-}$ and $HX$, the ratio inside the log is $1$, and $\log 1 = 0$.

$$
pH = pK_a + 0
$$

Given $K_a=10^{-4}$, so $pK_a=4$.

$$
pH = 4
$$

Hence, the answer is **Option B**.

At 298 K , a certain buffer solution contains equal concentrations of X−X^{-}X−and HXHXHX, KbK_{b}Kb​ for X−X^{-}X− is 10−1010^{-10}10−10. What is the pH of this buffer solution?

At 298 K , a certain buffer solution contains equal concentrations of $X^{-}$ and $HX$ , $K_{b}$ for $X^{-}$ is $10^{-10}$ . What is the pH of this buffer solution?