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Acid-base titration curves

This online calculator builds theoretical titration curves for monoprotic acids and bases

The calculator below plots the theoretical titration curve for the acid-base titration of monoprotic acids and bases. It calculates how the curve should look like with KNOWN molarity or molar concentration of titrand, KNOWN molarity of titrant and, in some cases, KNOWN titrand ionization constant (acid dissociation constant for weak acids and base dissociation constant for weak bases).

All formulas for all cases covered by the calculator:

  • strong base/strong acid
  • strong acid/strong base
  • weak base/strong acid
  • weak acid/strong base

are described below the calculator.

PLANETCALC, Titration curves

Titration curves

Digits after the decimal point: 2
Titration curve
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Titration curves

Definitions

Titration (also known as titrimetry and volumetric analysis) is a common laboratory method of quantitative chemical analysis to determine the concentration of an identified analyte (a substance to be analyzed). A reagent, termed the titrant or titrator, is prepared as a standard solution of known concentration and volume. The titrant reacts with a solution of analyte (which may also be termed the titrand) to determine the analyte's concentration.1 An acid-base titration is a quantitative analysis method for determining the concentration of an acid or base by exactly neutralizing it with a standard solution of base or acid having a known concentration.2

A titration curve is a curve in the graph where the x-coordinate represents the volume of titrant added since the beginning of the titration (as the absolute volume or the degree of titration, the ratio of the quantity of added titrant to the quantity of titrand), and the y-coordinate which represents the concentration of the analyte at the corresponding stage of the titration. In an acid-base titration, the y-coordinate of the titration curve represents the pH of the solution.

Points on the acid-base titration curve fall into one of four categories:

  1. initial pH, degree of titration f = 0
  2. pH before the equivalence point, 0 < f < 1
  3. pH at the equivalence point, f = 1
  4. pH after the equivalence point, f > 1

There are separate formulas for each category.

Notation

Formulas below use the following notations:
C_0 - initial molar concentration of the analyte/titrand
C_t - initial molar concentration of titrant
f - degree of titration
K_w - water ionization constant 10^{-14}, or autoionization constant of water
K - ionization constant of analyte/titrand, i.e. acid dissociation constant for weak acids and base dissociation constant for weak bases
pX=-lgX

Strong base/Strong acid

  1. initial pH
    pH=14-pC_0

  2. pH before the equivalence point
    pH=14-pC_0-p(1-f)

  3. pH at the equivalence point
    pH=\frac{pK_w}{2}

  4. pH after the equivalence point
    pH=pC_t+p(f-1)

Strong acid/Strong base

  1. initial pH
    pH=pC_0

  2. pH before the equivalence point
    pH=pC_0+p(1-f)

  3. pH at the equivalence point
    pH=\frac{pK_w}{2}

  4. pH after the equivalence point
    pH=pK_w-pC_t-p(f-1)

Weak acid/Strong base

  1. initial pH
    pH=\frac{pK+pC_0}{2}

  2. pH before the equivalence point
    pH=pK+lg\frac{f}{1-f}

  3. pH at the equivalence point
    pH=\frac{pK+pK_w-pC_0}{2}

  4. pH after the equivalence point
    pH=pK_w-pC_t-p(f-1)

Weak base/Strong acid

  1. initial pH
    pH=pK_w-\frac{pK+pC_0}{2}

  2. pH before the equivalence point
    pH=pK_w-pK-lg\frac{f}{1-f}

  3. pH at the equivalence point
    pH=\frac{pK_w+pC_0-pK}{2}

  4. pH after the equivalence point
    pH=pC_t+p(f-1)

  1. Wikipedia: Titration ↩

  2. Wikipedia: Acid-base titration ↩

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