1.

100mL of a clear saturated solution of Ag_(2)SO_(4) is added to 250mL of a clear saturated solution of PbCrO_(4) .will any precipitate form and if so what ?Given K_(sp) values of Ag_(2)SO_(4),Ag_(2)CrO_(4),PbCrO_(4)& PbSO_(4) are 1.4xx10^(-5),2.4xx10^(-12),2.8xx10^(-13) and 1.6xx10^(-8) respectively.

Answer»

Solution :For `Ag_(2)SO_(4)hArr underset(2s)2Ag^(+)+underset(s)SO_(4)^(2-)`
`K_(sp)=4S^(3)or s=3sqrt((K_(sp))/(4))=sqrt((1.4xx10^(-5))/(4))=1.52xx10^(-2)M`
for `PbCrO_(4)hArr Pb^(2+)+CrO_(4)^(2-)`
`K_(sp)=s_(1)^(2) or s_(1)sqrt(K_(sp))=sqrt(2.85xx10^(-13))=5.29x10^(-7)M`
In solution concentration of each ION can be GIVEN as:
THUS `[Ag^(+)]=(2sxx100)/(350)=(2xx1.52xx10^(-2)xx100)/(350)=0.869xx10^(-2)M`
`[SO_(4)^(2-)]=(sxx100)/(350)=(1.52xx10^(-2)xx100)/(350)=0.43xx10^(-2)M`
`[Pb^(2+)]=(s_(1)xx250)/(350)=(5.29xx10^(-7)xx250)/(350)=3.78xx10^(-7)M`
`[CrO_(4)^(2-)]=(s_(1)xx250)/(350)=(5.29xx10^(-7)xx250)/(350)=3.78xx10^(-7)M`
It is thus evidence that,
`[Ag^(+)]^(2)[CrO_(4)^(2-)]=(0.869xx10^(-2))^(2)xx(3.78xx10^(-7))`
`=2.85xx10^(-11)(gtK_(sp)Ag_(2)CrO_(4))`
Thus `Ag_(2)CrO_(4)` will percipitate.


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