JEE MAIN - Chemistry (2006 - No. 7)
Given the data at 25oC,
Ag + I- $$\to$$ AgI + e- , Eo = 0.152 V
Ag $$\to$$ Ag+ + e-, Eo = -0.800 V
What is the value of log Ksp for AgI? (2.303 RT/F = 0.059 V)
Ag + I- $$\to$$ AgI + e- , Eo = 0.152 V
Ag $$\to$$ Ag+ + e-, Eo = -0.800 V
What is the value of log Ksp for AgI? (2.303 RT/F = 0.059 V)
–8.12
+8.612
–37.83
–16.13
Explanation
$$\left( i \right)\,\,\,Ag \to A{g^ + } + {e^ - }\,\,$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{E^ \circ } = - 0.800\,V$$
$$\left( {ii} \right)\,\,\,Ag + {{\rm I}^ - } \to Ag{\rm I} + {e^ - }$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{E^ \circ } = 0.152\,V$$
From $$(i)$$ and $$(ii)$$ we have,
$$Ag{\rm I} \to A{g^ + } + {{\rm I}^ - }$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{E^ \circ } = - 0.952\,\,V$$
$$E_{cell}^ \circ = {{0.059} \over n}\log \,K$$
$$\therefore$$ $$ - 0.952 = {{0.059} \over 1}\,\log \left[ {A{g^ + }} \right]\left[ {{{\rm I}^ - }} \right]$$
[ as $$\,\,\,k = \left[ {A{g^ + }} \right]\left[ {{{\rm I}^ - }} \right]$$
or $$\,\,\, - {{0.952} \over {0.059}} = \log \,{K_{sp}}$$
or $$\,\,\, - 16.13 = \log \,{K_{sp}}$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{E^ \circ } = - 0.800\,V$$
$$\left( {ii} \right)\,\,\,Ag + {{\rm I}^ - } \to Ag{\rm I} + {e^ - }$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{E^ \circ } = 0.152\,V$$
From $$(i)$$ and $$(ii)$$ we have,
$$Ag{\rm I} \to A{g^ + } + {{\rm I}^ - }$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{E^ \circ } = - 0.952\,\,V$$
$$E_{cell}^ \circ = {{0.059} \over n}\log \,K$$
$$\therefore$$ $$ - 0.952 = {{0.059} \over 1}\,\log \left[ {A{g^ + }} \right]\left[ {{{\rm I}^ - }} \right]$$
[ as $$\,\,\,k = \left[ {A{g^ + }} \right]\left[ {{{\rm I}^ - }} \right]$$
or $$\,\,\, - {{0.952} \over {0.059}} = \log \,{K_{sp}}$$
or $$\,\,\, - 16.13 = \log \,{K_{sp}}$$
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