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Vant Hoff's Equation and Effect of Temperature on Equilibrium Constant

Δ G = 77.77 k...

Question

$Δ G = 77.77 k J {m o l}^{- 1}$ at $1000 K$ for the reaction $\frac{1}{2} N_{2} (g) + \frac{1}{2} O_{2} (g) = N O (g)$ . Partial pressure of $N O$ under equilibrium at $1000 K$ for air at 1 atm pressure containing 80% $N_{2}$ and 20% $O_{2}$ by volume is $X \times 10^{- 5}$ atm. $100 X$ is__________.

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Solution

$Δ G^{o} = - R T l n K$
$77770 = - 8.314 \times 1000 \times l n K$
$l n K = - 9.354$
$K = 8.66 \times 10^{- 5}$

$N_{2}$
$O_{2}$ $N O$
Initial moles
0.8
0.2
0
Moles at eqm
$0.8 - y$ $0.2 - y$ $2 y$

$\frac{2 y}{(0.8 - y)^{0.5} (0.2 - y)^{0.5}} = 8.66 \times 10^{- 5}$

$\frac{4 y^{2}}{(0.8 - y) (0.2 - y)} = 7.5 \times 10^{- 9}$

$y = 6.85 \times 10^{- 6}$

$2 y = 1.37 \times 10^{- 5} = X \times 10^{- 5}$

$X = 1.37$

$100 X = 137$

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