User:Soulzqm/Diprotic acid

In chemistry, diprotic acid is a class of acids capable of donating two protons or hydrogen atoms per molecule when dissociating in aqueous solution.

General Structure

Sulfuric acid is a strong acid that is completely dissociated in aqueous solution in its first deprotonation process.

There are both organic (which is called dicarboxylic acids) and inorganic diprotic acids. Chromic acid (H2CrO4) and sulfuric acid (H₂SO₄) are common and widely-used inorganic acids. They have similar structures with two -OH groups which are able to donate two H⁺ ions linked to the center atom. Some other inorganic diprotic acids such as hydrosulfuric acid (H₂S) usually have two hydrogen atoms linked to a electronegative center. Diprotic carbonxylic acids have general molecular formula HOOC-R-COOH.

Dissociation and acid-dissociation equilibrium constants

Dissociation in water

The dissociation equation of a diprotic acid can be written as:

H₂A (aq) + H₂O(l)↔ H₃O⁺ (aq) + HA^- (aq) (1)

HA^- (aq) + H₂O(l)↔ H₃O⁺ (aq) + A^2- (aq) (2)

The dissociation of a diprotic acid does not happen all at once due to the two stages of dissociation having different Ka values. Hence, each kind of diprtotic acid has two different acid-dissociation equilibrium constants, Ka₁ and Ka_2. The corresponding conjugate base of each conjugate acid state also has a different base-dissociationequilibrium constant K_b1 and K_b2, respectively.

The constants Ka₁ and Ka₂ are defined 25°C in water and can be written as:

$K_{a1}={\frac {[H^{+}][HA^{-}]}{[H_{2}A]}}$

$K_{a2}={\frac {[H^{+}][A^{2-}]}{[HA^{-}]}}$

K_a values for common diprotic aicds

For most Diprotic acids, the value of Ka₁ is at least one hundred times larger than the value of Ka_2. This is mainly because that more energy is required for a positively charged proton to be removed from HA^- with a negative charge in the above equation (2) than from H₂A which is electric neutral in the above equation (1). It is also illustrated by Pauling's first rule.

See also: Pauling's rules

Acid-Dissociation Equilibrium Constants for Common diprotic Acids

Acid	Ka1	Ka2
sulfuric acid (H2SO4)	1.0 x 103	1.2 x 10-2
chromic acid (H2CrO4)	9.6	3.2 x 10-7
oxalic acid (H2C2O4)	5.4 x 10-2	5.4 x 10-5
sulfurous acid (H2SO3)	1.7 x 10-2	6.4 x 10-8
glycine (C2H6NO2)	4.5 x 10-3	2.5 x 10-10
carbonic acid (H2CO3)	4.5 x 10-7	4.7 x 10-11
hydrogen sulfide (H2S)	1.0 x 10-7	1.3 x 10-13
Malonic acid(H2C3H2O4)	1.5 x 10-3	2.0 x 10-6

pH calculation

Solution of H₂A

For a solution prepared by adding dipotic acid with initial concentration [H₂A]=F dissociating in water,the pH value at equilibrium can be calculated by simply treating as a monoprotic acid if K_a1 is greater than K_a2 by a factor of 10³ or larger.Then we can apply the equation (1):

$K_{a1}={\frac {[H^{+}][HA^{-}]}{[H_{2}A]}}$ (1）

For [H⁺]=[HA^-] at equilibrium, we can assume that [H⁺]=[HA^-]=x and then the equation (1) can be written as:

$K_{a1}={\frac {x\cdot x}{F-x}}$

Note if the diprotic acid is a weak acid which has a K_a1 value ≤10^-3, the equation above can be further simplified as:

$x={\sqrt {K_{a1}\cdot F}}$

By solving for x, we obtain the final concentration of the hydrogen ion of the solution. Finally, we can calculate the pH value by substituting x=[H⁺] into pH definition:

${pH}=-\log _{10}({{[H}^{+}]})$

Diprotic Buffers

see also: Henderson–Hasselbalch equation

A buffer made by a diprotic acid and its conjugate base can be treated in the same way as a buffer made by a monoprotic acid. We can write two Henderson–Hasselbalch equations:

$\mathrm {pH} =\mathrm {p} K_{\mathrm {a1} }+\log _{10}\left({\frac {[\mathrm {HA} ^{-}]}{[\mathrm {H_{2}A} ]}}\right)=\mathrm {p} K_{\mathrm {a2} }+\log _{10}\left({\frac {[\mathrm {A} ^{2-}]}{[\mathrm {HA^{-}} ]}}\right)$

Depending on the quantity we know, we can either substituting [HA^-] and [H₂A] or [HA^-] and [A^-] to calculate the pH value of the buffer.

See also

• Dicarboxylic acid
• Sulfuric acid
• Acid-dissociation constant
• Acid-base titration