Calculate Kb from Ka.
Understand the Problem
The question is asking how to calculate the base dissociation constant (Kb) from the acid dissociation constant (Ka), which involves using the relationship that Kb = Kw / Ka, where Kw is the ion product of water.
Answer
$K_b = \frac{K_w}{K_a}$
Answer for screen readers
The base dissociation constant ($K_b$) can be calculated using the value of $K_a$ and is given by the formula:
$$ K_b = \frac{K_w}{K_a} $$
Substituting the values will yield the specific value of $K_b$.
Steps to Solve
- Identify the values needed
To calculate the base dissociation constant ($K_b$), first identify the value of the acid dissociation constant ($K_a$) and the ion product of water ($K_w$).
- Use the relationship between $K_b$ and $K_a$
Apply the formula that relates the two constants:
$$ K_b = \frac{K_w}{K_a} $$
- Insert the known values
Assuming $K_w$ is given as $1.0 \times 10^{-14}$ at 25°C, plug in the value of $K_a$.
- Calculate $K_b$
Perform the calculation to find $K_b$ using the equation from step 2.
The base dissociation constant ($K_b$) can be calculated using the value of $K_a$ and is given by the formula:
$$ K_b = \frac{K_w}{K_a} $$
Substituting the values will yield the specific value of $K_b$.
More Information
The ion product of water ($K_w$) is $1.0 \times 10^{-14}$ at 25°C, which is essential in determining the relationship of acid and base dissociation constants.
Tips
- Confusing $K_a$ with $K_b$; always ensure to use the correct value corresponding to the type of acid or base.
- Forgetting to use the inverse relationship between $K_a$ and $K_b$, which is a common oversight. Always remember that $K_b = K_w / K_a$.
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