The Ka of H2CO3 is 4.3 x 10-7. What is the Kb for its conjugate Base HCO3?
Hint: for acid-base conjugate pairs:
Ka. Kb Kw Kw 1×10-14
Pka+Pkb-14
2.3 x 108
6.3 x 10-8
53×108
45×108
The Correct Answer and Explanation is :
To calculate the Kb of the conjugate base HCO3^- for the acid H2CO3, we can use the relationship between the acid dissociation constant (Ka) and the base dissociation constant (Kb) for conjugate acid-base pairs. The equation we will use is:
[
K_a \times K_b = K_w
]
Where:
- ( K_a ) is the acid dissociation constant for H2CO3.
- ( K_b ) is the base dissociation constant for the conjugate base HCO3^-.
- ( K_w ) is the ionization constant for water, which is ( 1 \times 10^{-14} ) at 25°C.
Given:
- ( K_a = 4.3 \times 10^{-7} )
- ( K_w = 1 \times 10^{-14} )
To solve for ( K_b ):
[
K_b = \frac{K_w}{K_a} = \frac{1 \times 10^{-14}}{4.3 \times 10^{-7}}
]
Now let’s calculate it.
[
K_b = 2.33 \times 10^{-8}
]
Thus, the ( K_b ) for the conjugate base HCO3^- is ( 2.3 \times 10^{-8} ).
Explanation:
The relationship between the acid dissociation constant (Ka) and the base dissociation constant (Kb) for a conjugate acid-base pair is an important concept in acid-base chemistry. When an acid dissociates in water, it produces hydronium ions (H3O+), and its conjugate base can accept protons to form the original acid. In the case of H2CO3, the bicarbonate ion (HCO3-) is the conjugate base.
Using the equation ( K_a \times K_b = K_w ), we know that the product of the acid dissociation constant and the base dissociation constant for a conjugate pair must always equal the ionization constant of water, ( K_w = 1 \times 10^{-14} ). Therefore, by rearranging this equation and solving for ( K_b ), we can determine the base dissociation constant for the conjugate base HCO3^-.
The value of ( K_b = 2.3 \times 10^{-8} ) indicates that HCO3^- is a weak base, meaning it does not strongly accept protons.
Let me generate a visual to represent this calculation.
Here is the diagram that visually represents the relationship between ( K_a ), ( K_b ), and ( K_w ) for conjugate acid-base pairs, showing the calculation for ( K_b ) of HCO3^-.
Let me know if you need any more clarifications or additional help with this!
