At 298 K, an acidic buffer solution containing a weak acid HY and its salt NaY has a pH of 5 . If the base dissociation constant ( K_b ) for the conjugate base Y⁻ is 10⁻¹⁰ , what is the ratio of the concentration of Y⁻ to HY in the buffer?

Step-by-step solution

Given K_b for the conjugate base Y⁻ = 10⁻¹⁰ . For a conjugate acid-base pair at 298 K, K_a K_b = K_w = 10⁻¹⁴ . K_a = 10⁻¹⁴ 10⁻¹⁰ = 10⁻⁴ The pK_a of the weak acid HY is: pK_a = - (K_a) = - (10⁻⁴) = 4 Using the Henderson-Hasselbalch equation for an acidic buffer: pH = pK_a + ( [Y⁻] [HY] ) Substitute the given values ( pH = 5 ): 5 = 4 + ( [Y⁻] [HY] ) ( [Y⁻] [HY] ) = 1 Taking the antilogarithm on both sides: [Y⁻] [HY] = 10^1 = 10 Thus, the ratio of the concentration of Y⁻ to HY is 10 : 1 . Answer: 10 : 1