For the cell Cd | CdCl₂ || AgCl | Ag; E°_cell = 0.675 V and dE^°_cell / dT = -6.5 × 10^-4 VK^-1 at 27°C. The ΔH (kJ mol^-1) value for the reaction Cd + 2AgCl → 2Ag + CdCl₂ is closest to:

Concept:

According to Gibb's Helmohltz equation,

 \(\Delta G\, =\, \Delta H\, -\, T\Delta S \)

\(\Delta G\, =\, -nFE \)

\(\Delta S\, =\, -\frac{d}{dT}\, \left ( \Delta G/\Delta T \right )\, =\, nF\, \frac{dE}{dT} \)

\(\frac{dE}{dT}\, =\, \frac{E_{2}-E_{1}}{T_{2}-T_{1}}\)= temperature coefficient of a cell

Where,

\(\Delta G,\, \Delta H,\, \Delta S \) are the change in free energy, change in enthalpy and change in entropy.

E₁, E₂ are the emf of the cell at temperature T₁ and T₂.

n is the number of electrons in the cell reaction, F is the Faraday i.e. 96485 C. mol^-1

Explanation:

Given,

E⁰ = 0.675 V,  \(\frac{dE^{0}}{dT}\)= -6.5\(\times\)10^-4 V K^-1 , T = 27 ⁰C = 300 K

\(\Delta G^{0}\, =\, -nFE^{0} \)

= -2 \(\times\) 96485 \(\times\) 0.675

= -130.25 kJ

For the reaction Cd + 2AgCl → 2Ag + CdCl2         n=2  

\(\Delta S\, =\, nF\, \frac{dE}{dT}\)

= 2 \(\times\) 96485 \(\times\) (-6.5\(\times\)10^-4)

= -0.125 kJ

\(\Delta H\, = \Delta G\, +\, T\Delta S \)

= -130.25 + 300 (-0.125)

= -167.75 kJ 

Conclusion: -

The ΔH (kJ mol-1) value for the reaction Cd + 2AgCl → 2Ag + CdCl2 is closest to -168.