SATHEE: Thermodynamics and Thermochemistry 1 Question 10

Thermodynamics and Thermochemistry 1 Question 10

10. The standard electrode potential $E^{Θ}$ and its temperature coefficient $(\frac{d E^{Θ}}{d T})$ for a cell are $2 V$ and $- 5 \times 10^{- 4} {VK}^{- 1}$ at $300 K$ respectively. The cell reaction is

$Zn (s) + {Cu}^{2 +} (a q) \to {Zn}^{2 +} (a q) + Cu (s)$

The standard reaction enthalpy $(Δ_{r} H^{Θ})$ at $300 K in kJ {mol}^{- 1}$ is, $[Use, R = 8 {JK}^{- 1} {mol}^{- 1}$ and $F = 96, 000 C {mol}^{- 1}$ ]

(a) -412.8

(b) -384.0

(d) 192.0

(2019 Main, 12 Jan I)

Thermodynamics and Thermochemistry

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Solution:

Given,

$\begin{aligned} E^{\circ} & = 2 V, (\frac{d E^{\circ}}{d T}) = - 5 \times 10^{- 4} {VK}^{- 1} T & = 300 K, R = 8 {JK}^{- 1} {mol}^{- 1} F & = 96000 {Cmol}^{- 1} \end{aligned}$

According to Gibbs-Helmholtz equation,

$Δ G = Δ H - T Δ S$

$Also, Δ G = - n F E^{\circ} cell$

On substituting the given values in equation (ii), we get

$Δ G = - 2 \times 96000 C {mol}^{- 1} \times 2 V$

$[∵ n = 2$ for the given reaction $]$

$= - 4 \times 96000 J {mol}^{- 1}$

$= - 384000 J {mol}^{- 1}$

Now, $Δ S = n F (\frac{d E^{\circ}}{d T})$ or

$\begin{aligned} Δ S & = 2 \times 96000 C {mol}^{- 1} \times (- 5 \times 10^{- 4} {VK}^{- 1}) & = - 96 {JK}^{- 1} {mol}^{- 1} \end{aligned}$

Thus, on substituting the values of $Δ G$ and $Δ S$ in Eq. (i), we get $- 384000 J {mol}^{- 1}$

$\begin{aligned} = Δ H - 300 K \times (- 96 {JK}^{- 1} {mol}^{- 1}) Δ H & = - 384000 - 28800 {Jmol}^{- 1} & = - 412800 J {mol}^{- 1} & = - 412.800 kJ {mol}^{- 1} \end{aligned}$

Thermodynamics and Thermochemistry 1 Question 10

10. The standard electrode potential $E^{Θ}$ and its temperature coefficient $(\frac{d E^{Θ}}{d T})$ for a cell are $2 V$ and $- 5 \times 10^{- 4} {VK}^{- 1}$ at $300 K$ respectively. The cell reaction is

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Thermodynamics and Thermochemistry 1 Question 10

10. The standard electrode potential EΘ and its temperature coefficient (dEΘdT) for a cell are 2 V and −5×10−4VK−1 at 300 K respectively. The cell reaction is

Thermodynamics and Thermochemistry

Solution:

Engineering Preparation

Medical Preparation

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10. The standard electrode potential $E^{Θ}$ and its temperature coefficient $(\frac{d E^{Θ}}{d T})$ for a cell are $2 V$ and $- 5 \times 10^{- 4} {VK}^{- 1}$ at $300 K$ respectively. The cell reaction is