How to Calculate Ka from pH and Absorbance

Henderson-Hasselbalch Equation with Absorbance:

\[ Ka = 10^{-pKa} \] \[ pKa = pH - \log\left(\frac{A - A_{HA}}{A_A - A}\right) \]

pH:

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Absorbance:

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Absorbance HA (Acid Form):

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Absorbance A⁻ (Base Form):

unitless

Acid Dissociation Constant (Ka):

pKa Value:

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1. What is Ka Calculation from pH and Absorbance?

This method combines the Henderson-Hasselbalch equation with Beer-Lambert law to determine the acid dissociation constant (Ka) of pH indicators using spectrophotometric measurements at different pH values.

2. How Does the Calculator Work?

The calculator uses the following equations:

\[ Ka = 10^{-pKa} \] \[ pKa = pH - \log\left(\frac{A - A_{HA}}{A_A - A}\right) \]

Where:

\( Ka \) — Acid dissociation constant (M)
\( pKa \) — Negative logarithm of Ka
\( pH \) — Measured pH value
\( A \) — Absorbance at measured pH
\( A_{HA} \) — Absorbance of acid form (HA)
\( A_A \) — Absorbance of base form (A⁻)

Explanation: The ratio of conjugate base to acid is determined from absorbance measurements using Beer-Lambert law, then applied to Henderson-Hasselbalch equation.

3. Importance of Ka Determination

Details: Accurate Ka determination is crucial for understanding acid-base behavior, designing pH indicators, pharmaceutical development, and biochemical research involving proton transfer reactions.

4. Using the Calculator

Tips: Enter pH value (0-14), measured absorbance, absorbance of pure acid form, and absorbance of pure base form. Ensure all absorbance values are measured at the same wavelength and path length.

5. Frequently Asked Questions (FAQ)

Q1: Why use absorbance instead of concentration?
A: Absorbance provides a direct experimental measurement that correlates with concentration through Beer-Lambert law, eliminating the need for precise concentration determinations.

Q2: What are typical Ka values for weak acids?
A: Weak acids typically have Ka values between 10⁻² and 10⁻¹⁰ M, corresponding to pKa values between 2 and 10.

Q3: When is this method most accurate?
A: Most accurate when pH is close to pKa (within ±1 unit) and when acid and base forms have significantly different absorption spectra.

Q4: What are common sources of error?
A: Temperature variations, ionic strength effects, wavelength selection, and incomplete knowledge of pure form absorbances.

Q5: Can this method be used for all indicators?
A: Best suited for indicators where acid and base forms have distinct absorption maxima and the isosbestic point is well-defined.