A certain buffer solution contains equal concentrations of X⁻ and HX. The K_b for X⁻ is 10⁻¹⁰.
The pH of the buffer is:
1) 4
2) 7
3) 10
4) 14
Answer (1)
To find the pH of a buffer solution that contains equal concentrations of a weak acid (HX) and its conjugate base (X⁻), it's important to understand the relationship between the base dissociation constant (K_b) and the acid dissociation constant (K_a).
The given problem states that the conjugate base X⁻ has a K_b value of 1 0 − 10 . Using the relation between K_b and K_a for a conjugate acid-base pair:
K w = K a × K b
where K w is the ion-product constant of water ( 1 × 1 0 − 14 at 25°C).
First, we can calculate K a for HX:
K a = K b K w = 1 0 − 10 1 × 1 0 − 14 = 1 0 − 4
Since the buffer contains equal concentrations of HX and X⁻, we apply the Henderson-Hasselbalch equation for pH calculation:
\text{pH} = \text{pK}_a + \log\left(\frac{[\text{A}^-]}{[\text{HA}]\right) }
Given that [ A − ] = [ HA ] , the equation simplifies to:
pH = pK a
Now, calculate pK a :
pK a = − lo g ( K a ) = − lo g ( 1 0 − 4 ) = 4
Thus, the pH of the buffer is 4. The correct answer is the first option:
4
