How to calculate Ka given pH?
Understand the Problem
The question asks about the method to calculate the acid dissociation constant (Ka) using the pH value of a solution. This often involves determining the concentration of hydrogen ions in the solution and applying the formula related to Ka for weak acids.
Answer
$K_a \approx \frac{[H^+ ]^2}{[HA]_0}$
Answer for screen readers
To calculate Ka, use the formula $K_a \approx \frac{[H^+]^2}{[HA]_0}$ where $[H^+] = 10^{-\text{pH}}$.
Steps to Solve
- Use the pH to find the hydrogen ion concentration \([H^+]\)
Given the pH of the solution, we can find the hydrogen ion concentration using the formula:
$$[H^+] = 10^{-\text{pH}}$$
- Set up the equilibrium expression for the weak acid
For a weak acid that dissociates as HA ⇌ H extsuperscript{+} + A extsuperscript{-}, we can express the equilibrium concentrations in terms of \[H^+]\ and the initial concentration of the acid \[HA]_0\ .
- Write the expression for Ka
The acid dissociation constant \(K_a\) is given by:
$$K_a = \frac{[H^+][A^-]}{[HA]}$$
Assuming the initial concentration of HA is \[HA]_0\ and at equilibrium, the concentration of HA remaining is \[HA] = [HA]_0 - [H^+]\ (since \[H^+]\ is very small).
Therefore, we can approximate:
$$K_a = \frac{[H^+][H^+]}{[HA]_0 - [H^+]}$$
Since \[H^+]\ is very small compared to \[HA]_0\ , we usually approximate it as:
$$K_a \approx \frac{[H^+]^2}{[HA]_0}$$
- Calculate Ka using the given pH and initial concentration of HA
If we know \[HA]_0\ (the initial concentration of the acid) and we have found \[H^+]\ in step 1, we can substitute these values into our simplified expression for \[K_a\) to find its value.
To calculate Ka, use the formula $K_a \approx \frac{[H^+]^2}{[HA]_0}$ where $[H^+] = 10^{-\text{pH}}$.
More Information
In chemistry, the acid dissociation constant (Ka) is a quantitative measure of the strength of an acid in solution. The larger the Ka, the stronger the acid.
Tips
Common mistakes include not considering the small value of [H+] when it can be neglected in the denominator, and miscalculating the hydrogen ion concentration from the pH.