A buffer solution is prepared by mixing 0.1 M of a weak acid HY and 1.0 M of its sodium salt NaY at 298 K. If the base dissociation constant ( K_b ) of the conjugate base Y^- is 10⁻⁸ , what is the pH of the buffer solution?

Step-by-step solution

For a conjugate acid-base pair at 298 K, K_a K_b = K_w = 10⁻¹⁴ . Given K_b(Y^-) = 10⁻⁸ , the acid dissociation constant K_a of HY is: K_a = 10⁻¹⁴ 10⁻⁸ = 10⁻⁶ The pK_a of the weak acid is: pK_a = - (10⁻⁶) = 6 Using the Henderson-Hasselbalch equation for an acidic buffer: pH = pK_a + ( [ Salt ] [ Acid ] ) Substituting the given concentrations, [ Salt ] = 1.0 M and [ Acid ] = 0.1 M: pH = 6 + ( 1.0 0.1 ) pH = 6 + (10) pH = 6 + 1 = 7 Answer: 7