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Creating an Energy Efficient Engine

In a fuel cel...

Question

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 $C H_{3} O H (l) . C O_{2 (g)}$ and $H_{2} O (l)$ are $- 166.3, - 394.4$ and $- 237.1 k J m o l^{- 1}$ respectively.
The standard free energy change of the reaction will be:

A

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

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B

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

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C

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

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D

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

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Solution

The correct option is C $- 465.2 k J m o l^{- 1}$
Solution:- (C) $- 465.2 k J / m o l$
${C H_{3} O H}_{(l)} + \frac{3}{2} {O_{2}}_{(g)} ⟶ {C O_{2}}_{(g)} + 2 {H_{2} O}_{(l)}$
Given:-
${Δ {G^{0}}_{f}}_{({C H_{3} O H}_{(l)})} = - 166.3 k J / m o l$
${Δ {G^{0}}_{f}}_{({C O_{2}}_{(l)})} = - 394.4 k J / m o l$
${Δ {G^{0}}_{f}}_{({H_{2} O}_{(l)})} = - 237.1 k J / m o l$
Therefore,
${Δ G^{0}}_{R e a c t i o n} = {\sum Δ {G^{0}}_{f}}_{(p r o d u c t)} - {\sum Δ {G^{0}}_{f}}_{(r e a c t a n t)}$
$\Rightarrow {Δ G^{0}}_{R e a c t i o n} = ({Δ {G^{0}}_{f}}_{({C O_{2}}_{(l)})} + {Δ {G^{0}}_{f}}_{({H_{2} O}_{(l)})}) - {Δ {G^{0}}_{f}}_{({C H_{3} O H}_{(l)})}$
$\Rightarrow {Δ G^{0}}_{R e a c t i o n} = ((- 394.4) + (- 237.1)) - (- 166.3)$
$\Rightarrow {Δ G^{0}}_{R e a c t i o n} = - 465.2 k J / m o l$
Hence the standard free energy change of the reaction will be $- 465.2 k J / m o l$ .

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Similar questions

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 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)

298 K

, standard Gibb's energies of formation for

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

C O_{2} (g)

- 166.2, - 237.2

- 394.4 k J m o 1^{- 1}

If standard enthalpy of combustion of methanol is

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

, efficiency of the fuel cell will be:

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 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.

Standard enthalpy and standard entropy for the oxidation of $N H_{3}$ at $298$ K are $- 382.64$ $kJ {mol}^{- 1}$ and $- 145.6$ $J {mol}^{- 1} K^{- 1}$ respectively. Standard free energy change (in ${kJ mol}^{- 1}$ ) for the same reaction at $298$ K is:

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