We can calculate Kb for the carbonate ion if we know the Ka values of carbonic acid(H2CO3).
a) Is Ka1 or Ka2 of carbonic acid used to calculate Kb for the carbonate ion? Explain.
b) Calculate Kb for the carbonate ion.
c) Is the carbonate ion a weaker or stronger base than ammonia?
The Correct Answer and Explanation is :
Let’s go step by step.
a) Is Ka1 or Ka2 of carbonic acid used to calculate Kb for the carbonate ion?
To calculate the base dissociation constant (Kb) for the carbonate ion (CO₃²⁻), we must consider the relationship between Ka and Kb. Specifically, Kb can be calculated using the equation:
[
K_b = \frac{K_w}{K_a}
]
Where:
- ( K_w ) is the ionization constant for water (1 × 10⁻¹⁴ at 25°C),
- ( K_a ) is the acid dissociation constant.
For carbonate, the carbonate ion (CO₃²⁻) is the conjugate base of bicarbonate (HCO₃⁻), which is the conjugate base of carbonic acid (H₂CO₃). To calculate the Kb for CO₃²⁻, we use Ka2, the second dissociation constant of carbonic acid.
This is because the carbonate ion comes from the dissociation of HCO₃⁻, and HCO₃⁻ dissociates in the second step of carbonic acid dissociation (Ka2). Therefore, Ka2 is the relevant value when calculating Kb for the carbonate ion.
b) Calculate Kb for the carbonate ion
The dissociation steps for carbonic acid are:
- First dissociation (Ka1):
[
H_2CO_3 \rightleftharpoons H^+ + HCO_3^-
]
Ka1 ≈ ( 4.3 \times 10^{-7} ) - Second dissociation (Ka2):
[
HCO_3^- \rightleftharpoons H^+ + CO_3^{2-}
]
Ka2 ≈ ( 5.6 \times 10^{-11} )
Now we can use the formula:
[
K_b = \frac{K_w}{K_a2}
]
Since ( K_w = 1 \times 10^{-14} ) at 25°C, the calculation is:
[
K_b = \frac{1 \times 10^{-14}}{5.6 \times 10^{-11}} \approx 1.8 \times 10^{-4}
]
c) Is the carbonate ion a weaker or stronger base than ammonia?
The carbonate ion (CO₃²⁻) is a stronger base than ammonia (NH₃). This can be explained by comparing their base dissociation constants (Kb).
- For carbonate, we calculated Kb ≈ ( 1.8 \times 10^{-4} ).
- For ammonia, Kb ≈ ( 1.8 \times 10^{-5} ).
Since the Kb for carbonate is larger than the Kb for ammonia, it means carbonate is more likely to accept a proton (acting as a stronger base) compared to ammonia. A higher Kb value indicates a stronger base because it means that the base dissociates more readily in water, producing more hydroxide ions (OH⁻).
To summarize, carbonate (CO₃²⁻) is a stronger base than ammonia (NH₃), as it has a larger Kb value, implying it is more efficient at accepting protons in water.
I’ll now generate a visual for the carbonate ion’s base dissociation.
Here is a visual representation of the base dissociation of the carbonate ion in water, showing how it accepts a proton and produces hydroxide ions. This should help clarify the process. Let me know if you’d like further details or have any questions!
