The standard electrode potential `E^(Theta)` and its temperature coefficent `((dE^Theta)/(d T))` for a cell are 2V and `-5xx10^(-4)VK^(-1)` at 300 K respectively. The cell reaction is `Zn(s)+Cu^(2+)(aq)to Zn^(2+)(aq) +Cu(s)`.
The standard reaction enthalpy `(Delta_(t)H^(Theta))` at 300 K is `4.12 xx10^(x) J//"mol"`. Numerical value of x is _________________ [Use `R=8JK^(-1)mol^(-1) and F=96,000 C "mol"^(-1)`].

Options

A. 206.4
B. `-384.0`
C. `-412.8`
D. `192.0`

Answer

C

Explanation

`Delta H^(@) = - n FE^(@) + n FT ""(dE^(@))/(dT)`
Cell reaction :
`Zn (s) + Cu^(2+) (aq) to Zn^(2+) (aq) + Cu (s)`
`DeltaH^(@) = -2 xx 96000 xx 2 + 2 xx 96000 xx 300 xx (-) 5 xx 10^(-4)`
`= - 2 xx 96000 (2 + 0.15)`
`= -412.8 xx 10^(3) J mol^(-1)`
`= -412 . 8 kJ mol^(-1)`