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Equilibrium Constant and Standard Free Energy Change

For the react...

Question

For the reaction in equilibrium
(I) $C O (g) + \frac{1}{2} O_{2} (g) ⇌ C O_{2} (g)$
(II) $2 C O (g) + O_{2} (g) ⇌ 2 C O_{2} (g)$
Then,

Equilibrium constant Free energy change

$K_{1}$ $Δ G_{1}$

$K_{2}$ $Δ G_{2}$

A

K_{2} = K_{1}^{2}, Δ G_{2} = 2 Δ G_{1}

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B

K_{2} = 2 K_{1}, Δ G_{2} = 2 Δ G_{1}

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C

K_{1} = 2 K_{2}, Δ G_{1} = 2 Δ G_{1}

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D

K_{2} = K_{1}^{2}, Δ G_{2} = 2 Δ G_{1}^{2}

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Solution

The correct option is A $K_{2} = K_{1}^{2}, Δ G_{2} = 2 Δ G_{1}$
For the reaction,
$C O (g) + \frac{1}{2} O_{2} (g) ⇌ C O_{2} (g)$ ...(1)
$K_{1} = \frac{[C O_{2}]}{[C O] [O_{2}]^{\frac{1}{2}}}$
Again for the reaction,
$2 C O (g) + O_{2} (g) ⇌ 2 C O_{2} (g)$
$K_{2} = \frac{[C O_{2}]^{2}}{[C O]^{2} [O_{2}]} = K_{1}^{2}$

We know,
$Δ G_{1} = - 2.303 R T l o g K_{1}$
$Δ G_{2} = - 2.303 R T l o g K_{2} = 2.303 R T l o g K_{1}^{2}$
$\Rightarrow Δ G_{2} = 2 \times (- 2.303 R T l o g K_{1}) = 2 Δ G_{1}$

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Similar questions

Q. For the reaction in equilibrium
(I)

C O (g) + \frac{1}{2} O_{2} (g) ⇌ C O_{2} (g)

2 C O (g) + O_{2} (g) ⇌ 2 C O_{2} (g)

Equilibrium constant	Free energy change
$K_{1}$	$Δ G_{1}$
$K_{2}$	$Δ G_{2}$

Q. At 1000 K, the equilibrium constants for the following equilibrium are

K_{1}

K_{2}

C O C l_{2} (g) ⇌ C O (g) + C l_{2} (g)

K_{1} = 0.329

2 C O (g) + O_{2} (g) ⇌ 2 C O_{2} (g)

K_{2} = 2.24 \times 10^{22}

For the equilibrium,

2 C O C l_{2} (g) + O_{2} (g) ⇌ 2 C O_{2} (g) + 2 C l_{2} (g)

, the equilibrium constant

K_{3}

Q. The change in free energy accompanied by the isothermal reversible expansion of 1 mole of an ideal gas when it doubles its volume is

Δ G_{1}

. The change in free energy accompanied by sudden isothermal irreversible doubling volume of 1 mole of the same gas is

Δ G_{2}

Δ G_{1}

Δ G_{2}

For the elementary reaction 2A $⇌$ B,The forward and backward rate constants are $k_{1}$ and $k_{2}$ respectively. Then the rate of disappearance of A is equal to:

298 K

equilibrium constant

K_{1}

K_{2}

of following reaction

S O_{2} (g) + 1 / 2 O_{2} (g) ⇌ S O_{3} (g)

2 S O_{3} (g) ⇌ 2 S O_{2} (g) + O_{2} (g)

-------- (2)
The relation between

K_{1}

K_{2}

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