The acid-dissociation constant, Ka, for gallic acid is 4.57 × 10-3. What is the base-dissociation constant, Kb, for gallate ion?
To find the base-dissociation constant (Kb) for the gallate ion, we need to use the relationship between acid-dissociation constant (Ka) and base-dissociation constant (Kb) for the conjugate acid-base pair.
The equation is as follows:
Ka × Kb = Kw
Where Kw is the ion product of water (1.0 × 10^-14 at 25°C).
Rearranging the equation, we have:
Kb = Kw / Ka
Substituting the given values:
Kb = (1.0 × 10^-14) / (4.57 × 10^-3)
Calculating the value:
Kb ≈ 2.19 × 10^-12
Therefore, the base-dissociation constant (Kb) for the gallate ion is approximately 2.19 × 10^-12.
To determine the base-dissociation constant, Kb, for gallate ion, we need to use the relationship between Ka and Kb for a conjugate acid-base pair.
When a species donates a proton (H+), it behaves as an acid. Conversely, when a species accepts a proton, it behaves as a base. In this case, gallic acid (HB) donates a proton to form the gallate ion (B-).
The relationship between Ka and Kb for a conjugate acid-base pair can be expressed by the equation:
Ka × Kb = Kw
where Kw is the ion product of water, which is equal to 1.0 × 10^-14 at 25°C.
Rearranging the equation, we get:
Kb = Kw / Ka
Now, we can substitute the known value of Ka (4.57 × 10^-3) into this equation to calculate Kb:
Kb = (1.0 × 10^-14) / (4.57 × 10^-3)
Calculating this expression, we find:
Kb ≈ 2.19 × 10^-12
Therefore, the base-dissociation constant, Kb, for gallate ion is approximately 2.19 × 10^-12.