33rd IChO Problem 2 Student code :
Official version
Phosphoric Acid
Phosphoric acid is of great importance in fertiliser production. Besides, phosphoric acid and its various salts have a number of applications in metal treatment, food, detergent and toothpaste industries.
2.1 The pK values of the three successive dissociations of phosphoric acid at 25C are:
pK1a = 2.12 pK2a = 7.21 pK3a = 12.32
Write down the conjugate base of dihydrogen phosphate ion and determine its pKb value.
2 marks Small quantities of phosphoric acid are extensively used to impart the sour or tart taste to many soft drinks such as colas and root beers. A cola having a density of 1.00 g mL–1 contains 0.05 % by weight of phosphoric acid.
Page 7 of 39 The conjugate base of dihydrogen phosphate(H2PO4) is monohydrogen
phosphate (HPO42) : (0.5)
H2PO4 + H2O
⇌
HPO42 + H3O+ K2aHPO42 + H2O
⇌
H2PO4 + OH K2b2 H2O
⇌
H3O+ + OH KwpK2a + pK2b = pKw = 14 (0.5)
pK2b = 6.79 (1.0)
33rd IChO Problem 2 Student code :
Official version
(1)
H3PO4 + H2O
⇌
H2PO4 + H3O+ 0.0051–x x + xpK1a = 2.12 givesK1a = 7.59 x 10–3 (0.5)
(1)
(1)
(0.5)
46 . 2 pH
10 49 . 3 ] O H [ x
x 0051 . 0
x ]
PO H [
] O H ][
PO H 10 [
59 . 7
3 3
2
4 3
3 4 3 2
2.2 Determine the pH of the cola (ignoring the second and the third dissociation steps for phosphoric acid). Assume that the acidity of the cola arises only from phosphoric acid.
4 marks
2.3 Phosphoric acid is used as a fertiliser for agriculture. 1.00 x 10–3 M phosphoric acid is added to an aqueous soil suspension and the pH is found to be 7.00.
Determine the fractional concentrations of all the different phosphate species present in the solution. Assume that no component of the soil interacts with any phosphate species.
Page 8 of 39
O f H f HX
O H K X
O f H f X
H
O H K HX
O f H
f X
H O H X K H
1 f f f f
3 2 3 2
3 3 a
3
3 1 2 2
3 2 a
2
3 o 1 3
3 a 2
1
3 2 1 o
denote the fractional concentrations of different phosphate species. C is the total initial concentration of H3X. (X= PO4)
These equations lead to
(2)
From the values of pK1a, pK2a, pK3a and pH, one gets
K1a = 7.59 x 10–3 ; K2a = 6.17 x 10–8 ; K3a = 4.79 x 10–13
[ H3O+] = 10–7 (1)
The fractional concentrations of different phosphate species are
H3PO4 (fo) = 8.10 x 10–6 H2PO4 (f1) = 0.618 HPO42 (f2) = 0.382
PO43 (f3) = 1.83 x 10–6 (2)
C f X C and
f HX
C , ] X H f [ C ,
X f H
3 3 2
2
1 2 o 3
M 0.0051 98
PO 0.5 H of ion
Concentrat 3 4
Let
33rd IChO Problem 2 Student code :
Official version
5 marks
Page 9 of 39
D K K f K
D , O H K f K
D O H f K
D , O f H
a 3 a 2 a 3 1 3
a 2 a 2 1
2 3 a 1 1 3
o 3
3
32 3 a 1 3
a 2 a 1 a 3 a 2 a
1 K K K K H O K H O H O
K D
where
33rd IChO Problem 2 Student code :
Official version
2.4 Zinc is an essential micronutrient for plant growth. Plants can absorb zinc in water soluble form only. In a given soil water with pH = 7.0, zinc phosphate was found to be the only source of zinc and phosphate. Calculate the concentration of [Zn2+] and [PO43-] ions in the solution. Ksp for zinc phosphate is 9.1 1033.
5 marks
Page 10 of 39 Let S mol L–1 be the solubility of Zn3(PO4)2 in soil water.
[Zn++] = 3 S (1)
Total concentration of different phosphate species = 2 S mol L–1
[PO43–] = f3 x 2S (1)
f3 can be determined from the relation derived in 2.3
For pH = 7, f3 = 1.83 x 10 –6 (1)
Ksp = [Zn2+]3 [PO43–]2
9.1 x 10–33 = (3S)3(f3 x 2S)2 (1)
Solubility of Zn3(PO4)2 = 3.0 x 10 –5 mol L–1 (0.5) [Zn2+]= 9 x 10 –5 mol L–1 (0.5) [PO43–] = 1.1 x 10 –10 mol L–1
