Aqueous SrSO_4 has a solubility product K_sp of 344 times 10^-7 at 298 K. a) Ass

Question

Aqueous SrSO_4 has a solubility product K_sp of 344 times 10^-7 at 298 K. a) Assuming that the DHLL applies calculate the solubility of SrSO_4 in water at 298 K. b) Assuming that the DHLL applies calculate by successive approximations the solubility of SrSO_4 in 0.10 M MgCl_2. c) Assuming that the DHLL applies estimate by successive approximations the solubility of SrSO_4 in 0.10 M MgSO_4. d) Consider the cell: Cu' | Sr(s) | SrSO_4 (sat 'd, aq), MgSO_4(0.100 M) | Ag_2SO_4(s) | Ag(s) | Cu RHE: Ag_2SO_4 (s) + 2e' doubleheadarrow 2Ag(s) + SO^2-_4(aq) E degree = 0.654 V LHE: Sr^2+ (aq) + 2e^- doubleheadarrow Sr(s) E degree = -2.899 V Calculate the EMF of this cell at 298 K using the information found in part (c).

Explanation / Answer

a) let the solubiliy of SrSO4 in water at 298K be S

[SrSO4]=S=[Sr2+]=[SO42-]

SrSO4<--->Sr2+ +SO42-

ksp=[Sr2+][SO42-]=S^2

or,3.44*10^-7=S^2

S=5.86*10^-4M

b)MgCl2<--->Mg2+ + 2 Cl-

As there is no common ion so,the concentration of Sr2+ or SO42- is unaffected by the concentration of Mg2+ or Cl- ions.

ksp=[Sr2+][SO42-]=S^2

or,3.44*10^-7=S^2

S=5.86*10^-4M

c)MgSO4<--->Mg2+ +SO42-

[MgSO4]=[Mg2+]=[SO42-]=0.10M,so with this concentration of SO42- ion,

Let the solubiliy of SrSO4 in water at 298K be S"

[SO42-]=0.10M

S"=[SrSO4]=[Sr2+]

SrSO4<--->Sr2+ +SO42-

ksp=[Sr2+][SO42-]=S"*0.1M

or,3.44*10^-7 M^2=S"*0.1M

S"=3.44*10^-3M

d) Eo(cell)=Eo(cathode)-Eo(anode)

Eo or reduction potential of Ag2SO4|Ag|Cu is higher so it is the cathode.

Eo(cell)=0.654V-(-2.899V)=3.553V

E(cell)=Eo(cell) -RT/nF ln [ox]/[red]=Eo(cell) -2.303RT/nF log [ox]/[red]=Eo(cell) -0.0592/n log Q {at T=298K,F=faraday's constant=96485 C/mol,R=gas constant=8.314J/K.mol, Q=reaction quotient}

net cell rxn-

Sr(s)+Ag2SO4<--->Sr2+ +2Ag(s)+SO42-

Q=[Sr2+][SO42-](in the presence of MgSO4)=(3.44*10^-3M)(0.10M)

n=2 mol electrons exchanged

E(cell)=Eo(cell) -0.0592/n log Q=3.553V-0.0592/2 V log (3.44*10^-3M)(0.10M)=3.450V

Ecell=3.450V

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