Respuesta :
Explanation:
The given data is as follows.
Temperature = [tex]25^{o}C[/tex], Total alkalinity = [tex]6.2 \times 10^{-4}[/tex] M
Alkalinity of phenolphthalein = [tex]1 \times 10^{-5}[/tex] M
pH = 7.6, Hardness = 30 mg/L
[tex][Mg^{2+}] = 1 \times 10^{-4}[/tex] M
It is known that total alkalinity is as follows.
Total alkalinity = [tex][HCO^{-}_{3}] + [CO^{2-}_{3}] + [OH^{-}] - [H^{+}][/tex]
Since, pH = 7.6. Hence, concentration of hydrogen ions will be calculated as follows.
pH = [tex]-log [H^{+}][/tex]
7.6 = [tex]-log [H^{+}][/tex]
[tex][H^{+}][/tex] = antilog (-7.6)
= [tex]2.51 \times 10^{-8}[/tex] M
As, pH + pOH = 14
pOH = 14 - pH
= 14 - 7.6
= 6.4
So, [tex][OH^{-}] = 10^{-6.4}[/tex]
= [tex]3.98 \times 10^{-7} M[/tex]
Phenolphthalein alkalinity = [tex][CO^{2-}_{3}][/tex]
[tex][HCO^{-}_{3}][/tex] = Total alkalinity - 2[CO^{2-}_{3}] - [OH^{-}] + [H^{+}][/tex]
= [tex]6.2 \times 10^{-4} - 2(1 \times 10^{-5}) - (3.98 \times 10^{-7}) + (2.51 \times 10^{-8})[/tex]
= [tex]5.9 \times 10^{-4} M[/tex]
[tex][Mg^{2+}] = 1 \times 10^{-4} M[/tex] = [tex]24 \times 10^{-4} g/L[/tex]
[tex][Mg^{2+}][/tex] = 2.4 mg/L
Ratio of molar mass of [tex]Ca^{2+}[/tex] and [tex][Mg^{2+}][/tex] with [tex]CaCO_{3}[/tex] is as follows.
[tex]\frac{M_{CaCO_{3}}}{M_{Ca}}[/tex] = [tex]\frac{100}{40}[/tex] = 25
[tex]\frac{M_{CaCO_{3}}}{M_{Mg}}[/tex] = [tex]\frac{100}{24}[/tex] = 4.2
Total hardness = [tex]2.5[Ca^{2+}] + 4.2 [Mg^{2+}][/tex]
[tex][Ca^{2+}] = \frac{\text{total hardness - 4.2(2.4)}}{2.5}[/tex]
= [tex]1.99 \times 10^{-4} mol/L[/tex]
[tex]CaCO_{3} \rightarrow Ca^{2+} CO^{2-}_{3}[/tex]
[tex][Ca^{2+}][CO^{2-}_{3}][/tex] = [tex](1.99 \times 10^{-4}) \times (1 \times 10^{-5})[/tex]
= [tex]1.99 \times 10^{-9}[/tex]
[tex]K_{sp}[/tex] of [tex]CaCO_{3}[/tex] = [tex]3.36 \times 10^{-9}[/tex]
Since, [tex][Ca^{2+}][CO^{2-}_{3}][/tex] > [tex]K_{sp}[/tex]
Hence, the water is slightly unsaturated with [tex]CaCO_{3}[/tex].
