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QUESTION

# Put mercury(II) oxide in a vacuum bottle and let it decompose at 500 °C. This equilibrium takes place: "2HgO(crystal)" ⇌ "2Hg(vapor)" + "O"_2("g"). What is ΔG for the reaction at 500 °C?

ΔG= "-9.35 kJ/mol"

We must calculate the equilibrium constant for the reaction, then calculate the free energy change.

Calculation of K_P

color(white)(mmmm)"2HgO(s)" ⇌ "2Hg(g)"+"O"_2("g") "I/atm:" color(white)(mmmmmmmml)0 color(white)(mmmll)0 "C/atm:" color(white)(mmmmmml)+2x color(white)(mll)+x "E/atm:"color(white)(mmmmmmmm)2x color(white)(mmm)x

K_P = P_"Hg"^2P_"O₂" = (2x)^2x = 4x^3

P_"tot" = P_"Hg" +P_"O₂" = (2x + x) "atm" = 3xcolor(white)(l) "atm" = "4.0 atm"

x = 4.0/3 = 1.33

K_P = 4x^3 = 4 × 1.33^3 = 9.48

Calculation of ΔG

ΔG = "-"RTlnK = "-8.314 J·"color(red)(cancel(color(black)("K"^"-1")))"mol"^"-1" × 500 color(red)(cancel(color(black)("K"))) ln(9.48) = "-9350 J·mol"^"-1" = "-9.35 kJ/mol"

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