An electrochemical cell is fueled by the combustion of butane at 1 bar and 298 K. Its cell potential is $\frac{\boldsymbol{X}}{\boldsymbol{F}} \times 10^{3}$ volts, where $\boldsymbol{F}$ is the Faraday constant. The value of $\boldsymbol{X}$ is ____. Use : Standard Gibbs energies of formation at 298 K are : $\Delta_{f} G_{\mathrm{CO}_{2}}^{\mathrm{o}}=-394 \mathrm{~kJ} \mathrm{~mol}^{-1}$; $\Delta_{f} G_{\text {water }}^{\mathrm{o}}=-237 \mathrm{~kJ} \mathrm{~mol}^{-1}$ ; $\Delta_{f} G_{\text {butane }}^{\mathrm{o}}=-18 \mathrm{~kJ} \mathrm{~mol}^{-1}$

JEE Advanced · 2025 · 18 May 2025 · Paper 2 · Redox Reactions and Electrochemistry

An electrochemical cell is fueled by the combustion of butane at 1 bar and 298 K. Its cell potential is

\frac{X}{F} \times 1 0^{3}

volts, where

F

is the Faraday constant. The value of

X

is ____.

Use : Standard Gibbs energies of formation at 298 K are :

Δ_{f} G_{CO_{2}}^{o} = - 394 kJ mol^{- 1}

;

Δ_{f} G_{water}^{o} = - 237 kJ mol^{- 1}

;

Δ_{f} G_{butane}^{o} = - 18 kJ mol^{- 1}

Answer: 105.5

Solution

Step 1: Write the combustion reaction:

C_{4} H_{10} (g) + \frac{13}{2} O_{2} (g) \to 4 C O_{2} (g) + 5 H_{2} O (l)

Step 2: Calculate ΔᵣG°:

Δ_{r} G^{\circ} = 4 Δ_{f} G_{C O_{2}}^{\circ} + 5 Δ_{f} G_{H_{2} O}^{\circ} - Δ_{f} G_{C_{4} H_{10}}^{\circ}

= 4 (- 394) + 5 (- 237) - (- 18)

= - 1576 - 1185 + 18 = - 2743 kJ/mol

Step 3: Calculate number of electrons transferred:
Butane oxidation: C₄H₁₀ → 4CO₂ involves transfer of 26 electrons
(Each C goes from -2.5 to +4, total change = 26e⁻)

Step 4: Use the relationship ΔᵣG° = -nFE°:

- 2743 \times 1000 = - 26 \times F \times E^{\circ}

E^{\circ} = \frac{2743000}{26 F} = \frac{105500}{F} = \frac{105.5 \times 1 0 ^{3}}{F} V

Therefore, X = 105.50

JEE Advanced · 2025 · 18 May 2025 · Paper 2 · Numerical answer

Practise more: all JEE Advanced PYQs on Redox Reactions and Electrochemistry →

JEE Advanced · 2025 · 18 May 2025 · Paper 2 · Redox Reactions and Electrochemistry

Solution

More JEE Advanced questions on Redox Reactions and Electrochemistry