Calculate: (a) ∆G° and (b) the equilibrium constant for the formation of NO 2 from NO and O 2 at 298 K. where - Wired Faculty

Question

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Calculate: (a) ∆G° and (b) the equilibrium constant for the formation of NO₂from NO and O₂ at 298 K.
$NO left parenthesis straight g right parenthesis space plus space 1 half straight O subscript 2 left parenthesis straight g right parenthesis space space space leftwards harpoon over rightwards harpoon space space space NO subscript 2 left parenthesis straight g right parenthesis$
where $increment subscript straight f straight G to the power of 0 space left parenthesis NO subscript 2 right parenthesis space equals space 52.0 space kJ divided by mol comma space space increment subscript straight f straight G to the power of 0 left parenthesis NO right parenthesis space equals space 87.0 space kJ divided by mol comma space$ $increment subscript straight f straight G to the power of 0 left parenthesis straight O subscript 2 right parenthesis space equals space 0 space kJ divided by mol.$

Solution

(a) We know,
$increment subscript straight r straight G to the power of 0 space equals space sum from blank to blank of increment subscript straight f straight G to the power of 0 space left parenthesis Products right parenthesis space minus space sum from blank to blank of increment subscript straight f straight G to the power of 0 left parenthesis Reactants right parenthesis$
$equals space increment subscript straight f straight G to the power of 0 left parenthesis NO subscript 2 right parenthesis space minus space open square brackets increment subscript straight f straight G to the power of 0 left parenthesis NO right parenthesis space plus space 1 half increment subscript straight f straight G to the power of 0 left parenthesis straight O subscript 2 right parenthesis close square brackets space equals space 52.0 space minus space open parentheses 87.0 space plus space 1 half cross times 0 close parentheses space equals space minus 35.0 space kJ space mol to the power of negative 1 end exponent$
$space left parenthesis straight b right parenthesis space space We space know comma space space space increment straight G to the power of 0 space equals space minus 2.303 space RT space log space straight K space minus 35000 space straight J space mol to the power of negative 1 end exponent space equals space minus 2.303 space cross times space left parenthesis 8.314 space JK to the power of negative 1 end exponent space mol to the power of negative 1 end exponent right parenthesis space cross times space left parenthesis 298 straight K right parenthesis space cross times space log space straight K or space space space log space straight K space equals space 6.1341 or space space space space straight K space equals space antilog space left parenthesis 6.1341 right parenthesis space equals space 1.361 space cross times space 10 to the power of 6$

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Equilibrium

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