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# 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"##