For `Cr_2O_7^(2-) + 14 H^(+) + 6e^(-) to 2Cr^(+3) + 7H_2O, E^(@) = 1.33 V " At" [ Cr_2O_7^(2-)]=4.5` millimoles , `[Cr^(+3)]=15` millimole , E is 1.067V. The pH of the solution is nearly equal to

Options

A. 2
B. 3
C. 5
D. 4

Answer

A

Explanation

For ` Cr_2O_7^(2-) + 14^(+) + 6e^(-) to 2Cr^(+3) + 6H_2O`
`E=E^(@) - (2.303 RT)/(nF) log""([Cr^(+3)]^(2)[H_2O]^(7))/([Cr^(2)O_7^(2-)][H^(+)]^(14))`
` 1.067 =1.33 - (0.059)/(6) log""((15 xx 10^(-3))^(2) (1)^(7))/((4.5 xx 10^(-3))[H^(+)]^(14))`
`-0.263 = - (0.059)/(6) log""(225 xx 10^(-6))/((4.5 xx 10^(-3))[H^(+)]^(14))`
`-0.263 = - 0.0098 [ log 50 - log(H^(+))^(14)]`
`(-0.263)/(-0.0098) = 1.6990 + 14 pH implies 26.83-1.6990 = (25.1377)/(14)=1.7955 ~=2.0`