Question

Calculation: If you have a pH of 5.5 for a weak acid with a pKa of 4.76, then is there more A- or more HA in the solution? Explain why in words using your knowledge of positive or negative log numbers.

Answer 1

Answer:

lets set the ratio -A/HA as R:

pH = pKa + log(R,10) => pKa + log10(R)

pH = 5.5

pKa = 4.76

R => 10^(pH - 4.76)

10^(pH - 4.76) => 5.4954

Given R (-A/HA) a number bigger than 1, then the concentration of  -A is bigger than HA

Explanation:

Answer 2

Answer:

There is more A⁻ than HA in the solution  

Explanation:

The equation for the ionization of a weak acid is

HA + H₂O ⇌H₃O⁺ + OH⁻

When HA and A⁻ are present in comparable amounts, we can use the Henderson-Hasselbalch equation:

$\begin{array}{rcl}\text{pH} &=& \text{pK}_{\text{a}} + \log\dfrac{[\text{A}^{-}]}{\text{[HA]}}\\\\5.5 & = & 4.76 + \log\dfrac{[\text{A}^{-}]}{\text{[HA]}}\\\\0.74 & = & \log\dfrac{[\text{A}^{-}]}{\text{[HA]}}\\\end{array}$

0.74 is a positive number, and a number must be greater than one for its logarithm to be positive. That is,

$\begin{array}{rcl}\dfrac{[\text{A}^{-}]}{\text{[HA]}} & > & 1\\\\\textbf{[A]}^{-} & > & \textbf{[HA]}\\\end{array}$