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Calculate the concentration of all species of significant concentration present in 0.1MH_(2)PO_(4) solution K_(a_(1))=6.2xx10^(-8),K_(a_(3))=3.6xx10^(-13).Take 0.075xx4.075=(0.555)^(2) |
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Answer» Solution :`{:(I step,H_(3)PO_(4) hArr H^(+)+H_(2)PO_(4)^(-),K_(a_(1))=7.5xx10^(-3)),(II step,H_(2)PO_(4)hArr H^(+)+HPO_(4)^(2-),K_(a_(2))=6.2xx10^(-8)),(III step,HPO_(4)^(2-)hArrH^(+)+PO_(4)^(3-),K_(a_(3))=3.6xx10^(-13)):}` For `I` step :`underset(0.1(1-alpha))underset(0.1)(H_(3)PO_(4))hArr underset(0.1alpha)underset(0)(H^(+))+underset(0.1alpha)underset(0)(H_(2)PO_(4)^(-))` `K_(a_(1))=([H^(+)][H_(2)PO_(4)^(-)])/([H_(3)PO_(4))]rArr(0.1alpha^(2))/((1-alpha))=7.5xx10^(-3)....(1)` Excepting `alpha ltlt1,alpha^(2)=7.5xx10^(-2):.alpha=0.274` (not negligible) so solve QUADRATIC equation (1) & GET=`alpha=0.24` `:.[H^(+)]=0.24MrArr [OH^(-)]=(10^(-14))/(0.024)=4.17xx10^(-13)M` ("insignificant") &`[H_(2)PO_(4)^(-)]=0.024M` Also `[H_(3)PO_(4)^(-)]=0.1-0.024=0.076M` The value of `K_(a_(2))` and `K_(a_(3))`.Also dissociations of `II` and `III` steps occur in present of `H^(+)` furnished in `I` step and thus ,dissocations of `II` and `III` steps are further suppressed due to common ion effect. For `II` step `underset(0.024-y)underset(0.024)(H_(2)PO_(4)^(-))hArr underset(0.024-y)underset(0.024)H^(+)+underset(y)underset(0)(HPO_(4)^(2))` The dissocation of `H_(2)PO_(4)^(-)` occurs in PRESENCE of `[H^(+)]` furnished in step `I`. Thus `K_(a_(2))=([H^(+)][HPO_(4)^(-)])/([H_(2)PO_(4)^(-)])` `6.2xx10^(-8)=((0.024+y)y)/((0.24-y))` `:.y` is small `:.0.024-y~~0.024` and neflecting `y^(2)` `6.2xx10^(-8)=(0.024y)/(0.024)` `y=6.2xx10^(-8)M` or `[HPO_(4)^(2-)]=K_(a_(2))=6.2xx10^(-8)M` (insignificant) for `III` step `underset((6.2xx10^(-5)-x))(HPO_(4)^(2-))hArr underset((0.024+x))(H^(+))+underset(x)(PO_(4)^(3-))` `K_(3)=([H^(+)][PO_(4)^(3-)])/([HPO_(4)^(2-)])=((0.24+x)x)/((6.2xx10^(-8)-x))` because `x ` is small :.Again neglecting `x^(2)` and assuming `6.2xx10^(-6)-x=6.2xx10^(-8)` `:.3.6xx10^(-13)=(0.024x)/(6.2xx10^(-8))` `:.x=(3.6xx10^(-13)xx6.2xx10^(-8))/(0.024)=9.3xx10^(-19)M` or `[PO_(4)^(3-)]=9.3xx10^(-19)M` (insufficant) Note: For weak polyprotic acid solution having no other electrolyte the anion concentration produced in step of dissocation is ALWAYS equal to`K_(a_(2))` if concentration is reasonable. |
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