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Creating an Energy Efficient Engine

In a fuel cel...

Question

In a fuel cell, methanol is used as fuel and oxygen gas is used as an oxidizer.
The reaction is: $C H_{3} O H (l) + \frac{3}{2} O_{2} (g) \to C O_{2} (g) + 2 H_{2} O (l)$
At $298 K$ , standard Gibb's energies of formation for $C H_{3} O H (l), H_{2} O (l)$ and $C O_{2} (g)$ are $- 166.2, - 237.2$ and $- 394.4 k J m o 1^{- 1}$ respectively.
If standard enthalpy of combustion of methanol is $- 726 k J m o 1^{- 1}$ , efficiency of the fuel cell will be:

A

80 %

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B

87 %

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C

90 %

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D

97 %

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Solution

The correct option is D $97 %$
$Δ G = Δ G_{p r o d} - Δ G_{r e a c t} = 2 (- 237.2) - 394.4 + 166.2$

$= - 474.4 - 394.4 + 166.2 = 702.6 k J / m o l$
Efficiency $= \frac{Δ G}{Δ H} \times 100$

$= \frac{702.6}{726} \times 100$

$= 96.77 \approx 97$ %

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Similar questions

Q. If a fuel cell, methanol is used as fuel and oxygen gas is used as an oxidiser. The reaction is

C H_{3} O H_{(l)} + \frac{3}{2} O_{2} (g) \to C O_{2} (g) + 2 H_{2} O (g)

298 K

standard Gibb’s energies of formation for

C H_{3} O H (l), H_{2} O (l), and C O_{2} (g)

- 166.2, - 237.2

- 394.4 {kJ mol}^{- 1},

respectively. If the standard enthalpy of combustion of methanol is

- 726 {kJ mol}^{- 1}

, the efficiency of the fuel cell will be:

Q. In a fuel cell, methanol is used as a fuel and

O_{2}

is used as an oxidizer. The standard enthalpy of combustion of methanol is

- 726 {kJmol}^{- 1}

. The standard free energies of formation of

C H_{3} O H (l)

C O_{2} (g)

H_{2} O (l)

are − 166.3, −394.4 and

- 237.1 {kJmol}^{- 1}

respectively. The efficiency of the fuel cell will be:

Q. In a fuel cell, methanol is used as fuel and oxygen gas is used as an oxidiser. The reaction is:

{C H}_{3} O H (l) + \frac{3}{2} O_{2} (g) ⟶ \frac{1}{2} C O_{2} (g) + 2 H_{2} O (l)

Calculate standard Gibbs free energy change for the reaction that can be converted into electrical work. If the standard enthalpy of combustion for methanol is

- 726 k J {m o l}^{- 1}

, calculate the efficiency of conversion of Gibbs energy into useful work.

Δ G_{f}^{o}

{C O}_{2}, H_{2} O, {C H}_{3} O H, O_{2}

- 394.36; - 237.13; - 166.27

and zero respectively.

Q. In a fuel cell (the device used for producing electricity directly from a chemical reaction) methanol is used as a fuel and oxygen gas is used as an oxidizer. The standard enthalpy of combustion of methanol is

- 726 k J m o l^{- 1}

. The standard free energies of formation of

C H_{3} O H (l) . C O_{2 (g)}

H_{2} O (l)

- 166.3, - 394.4

- 237.1 k J m o l^{- 1}

respectively.
The standard free energy change of the reaction will be:

Calculate the standard enthalpy of formation of CH₃OH₍_l₎ from the following data:

CH₃OH₍_l₎ + O₂₍_g₎ CO₂₍_g₎ + 2H₂O₍_l₎ ; Δ_rH^θ = –726 kJ mol^–1

C₍_g₎ + O₂₍_g₎ CO₂₍_g₎ ; Δ_cH^θ = –393 kJ mol^–1

H₂₍_g₎ +O₂₍_g₎ H₂O₍_l₎ ; Δ_fH^θ = –286 kJ mol^–1.

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