Answer:
The concentration of [tex]Hg^{2+}[/tex] is [tex][Hg^{2+}]= 1.26 *10^{-27} mol/L[/tex]
The number of [tex]Hg^{2+}[/tex] ion is [tex]A = 0.7588\ ions[/tex]
Explanation:
Generally the solubility product constant of HgS(s) is [tex]k_{sp} = 1.6*10^{-54}[/tex]
This solubility product constant is mathematically represented as
[tex]K_{sp} = [Hg^{2+}][S^{2-}][/tex]
Since the HgS is saturated it implies that the concentration of sulfur ion is the same as that of mercury ion s
[tex][Hg^{2+}]= [S^{2-}] = z[/tex]
=> [tex]K_{sp} =z^2[/tex]
=> [tex]z = \sqrt{K_{sp}}[/tex]
substituting values
[tex]z = \sqrt{1.6 *10^{-54}}[/tex]
[tex]z = 1.26*10^{-27}[/tex]
=> [tex][Hg^{2+}]= [S^{2-}] = 1.26 *10^{-27} mol/L[/tex]
From above [tex]1.26 *10^{-27}[/tex] mole of [tex][Hg^{2+}][/tex] is equal to 1 L
Then x mole of [tex][Hg^{2+}][/tex] will be equal to 1000 L
Therefore
[tex]x = \frac{1.26*10^{-27} *1000}{1}[/tex]
=> [tex]x = 1.26*10^{-24} \ moles[/tex]
Now the number of [tex]Hg^{2+}[/tex] ions are in 1000 L of the solution is mathematically represented as
[tex]A = x * \frac{N_A}{1 mole}[/tex]
Where [tex]N_A[/tex] is the avogadro's constant which has a value of
[tex]N_A = 6.022*10^{23} \ ions[/tex]
Substituting value
[tex]A = 1.26 *10^{-24} * \frac{6.022 *10^{23}}{1}[/tex]
[tex]A = 0.7588\ ions[/tex]
