Answer:
1) The solubility product of the lead(II) chloride is
.
2) The solubility of the aluminium hydroxide is
.
3)The given statement is false.
Explanation:
1)
Solubility of lead chloride = ![S=3.1\times 10^-2M](https://tex.z-dn.net/?f=S%3D3.1%5Ctimes%2010%5E-2M)
![PbCl_2(aq)\rightleftharpoons Pb^{2+}(aq)+2Cl^-(aq)](https://tex.z-dn.net/?f=PbCl_2%28aq%29%5Crightleftharpoons%20Pb%5E%7B2%2B%7D%28aq%29%2B2Cl%5E-%28aq%29)
S 2S
The solubility product of the lead(II) chloride = ![K_{sp}](https://tex.z-dn.net/?f=K_%7Bsp%7D)
![K_{sp}=[Pb^{2+}][Cl^-]^2](https://tex.z-dn.net/?f=K_%7Bsp%7D%3D%5BPb%5E%7B2%2B%7D%5D%5BCl%5E-%5D%5E2)
![K_{sp}=S\times (2S)^2=4S^3=4\times (3.1\times 10^{-2})^3=1.2\times 10^{-4}](https://tex.z-dn.net/?f=K_%7Bsp%7D%3DS%5Ctimes%20%282S%29%5E2%3D4S%5E3%3D4%5Ctimes%20%283.1%5Ctimes%2010%5E%7B-2%7D%29%5E3%3D1.2%5Ctimes%2010%5E%7B-4%7D)
The solubility product of the lead(II) chloride is
.
2)
Concentration of aluminium nitrate = 0.000010 M
Concentration of aluminum ion =![1\timed 0.000010 M=0.000010 M](https://tex.z-dn.net/?f=1%5Ctimed%200.000010%20M%3D0.000010%20M)
Solubility of aluminium hydroxide in aluminum nitrate solution = ![S](https://tex.z-dn.net/?f=S)
![Al(OH)_3(aq)\rightleftharpoons Al^{3+}(aq)+3OH^-(aq)](https://tex.z-dn.net/?f=Al%28OH%29_3%28aq%29%5Crightleftharpoons%20Al%5E%7B3%2B%7D%28aq%29%2B3OH%5E-%28aq%29)
S 3S
The solubility product of the aluminium nitrate = ![K_{sp}=1.0\times 10^{-33}](https://tex.z-dn.net/?f=K_%7Bsp%7D%3D1.0%5Ctimes%2010%5E%7B-33%7D)
![K_{sp}=[Al^{3+}][OH^-]^3](https://tex.z-dn.net/?f=K_%7Bsp%7D%3D%5BAl%5E%7B3%2B%7D%5D%5BOH%5E-%5D%5E3)
![1.0\times 10^{-33}=(0.000010+S)\times (3S)^3](https://tex.z-dn.net/?f=1.0%5Ctimes%2010%5E%7B-33%7D%3D%280.000010%2BS%29%5Ctimes%20%283S%29%5E3)
![S=1.6\times 10^{-10} M](https://tex.z-dn.net/?f=S%3D1.6%5Ctimes%2010%5E%7B-10%7D%20M)
The solubility of the aluminium hydroxide is
.
3.
![Molarity=\frac{Moles}{Volume (L)}](https://tex.z-dn.net/?f=Molarity%3D%5Cfrac%7BMoles%7D%7BVolume%20%28L%29%7D)
Mass of NaCl= 3.5 mg = 0.0035 g
1 mg = 0.001 g
Moles of NaCl = ![\frac{0.0035 g}{58.5 g/mol}=6.0\times 10^{-5} mol](https://tex.z-dn.net/?f=%5Cfrac%7B0.0035%20g%7D%7B58.5%20g%2Fmol%7D%3D6.0%5Ctimes%2010%5E%7B-5%7D%20mol)
Volume of the solution = 0.250 L
![[NaCl]=\frac{6.0\times 10^{-5} mol}{0.250 L}=0.00024 M](https://tex.z-dn.net/?f=%5BNaCl%5D%3D%5Cfrac%7B6.0%5Ctimes%2010%5E%7B-5%7D%20mol%7D%7B0.250%20L%7D%3D0.00024%20M)
1 mole of NaCl gives 1 mole of sodium ion and 1 mole of chloride ions.
![[Cl^-]=[NaCl]=0.00024 M](https://tex.z-dn.net/?f=%5BCl%5E-%5D%3D%5BNaCl%5D%3D0.00024%20M)
Moles of lead (II) nitrate = n
Volume of the solution = 0.250 L
Molarity lead(II) nitrate = 0.12 M
![n=0.12 M]\times 0.250 L=0.030 mol](https://tex.z-dn.net/?f=n%3D0.12%20M%5D%5Ctimes%200.250%20L%3D0.030%20mol)
1 mole of lead nitrate gives 1 mole of lead (II) ion and 2 moles of nitrate ions.
![[Pb^{2+}]=[Pb(NO_2)_3]=0.030 M](https://tex.z-dn.net/?f=%5BPb%5E%7B2%2B%7D%5D%3D%5BPb%28NO_2%29_3%5D%3D0.030%20M)
![PbCl_2(aq)\rightleftharpoons Pb^{2+}(aq)+2Cl^-(aq)](https://tex.z-dn.net/?f=PbCl_2%28aq%29%5Crightleftharpoons%20Pb%5E%7B2%2B%7D%28aq%29%2B2Cl%5E-%28aq%29)
Solubility of lead(II) chloride = ![K_{sp}=1.2\times 10^{-4}](https://tex.z-dn.net/?f=K_%7Bsp%7D%3D1.2%5Ctimes%2010%5E%7B-4%7D)
Ionic product of the lead chloride in solution :
![Q_i=[Pb^{2+}][Cl^-]^2=0.030 M\times (0.00024 M)^2=1.7\times 10^{-9}](https://tex.z-dn.net/?f=Q_i%3D%5BPb%5E%7B2%2B%7D%5D%5BCl%5E-%5D%5E2%3D0.030%20M%5Ctimes%20%280.00024%20M%29%5E2%3D1.7%5Ctimes%2010%5E%7B-9%7D)
( no precipitation)
The given statement is false.