Step 1. Calculate the value of #ΔG# at 1600 K
#ΔG = "37 850 J" +"11.69 J"·color(red)(cancel(color(black)("K"^"-1"))) × 1600 color(red)(cancel(color(black)("K"))) = "(37 850 + 18 704) J" = "56 554 J"#
Step 2. Calculate the value of the equilibrium constant
#ΔG = "-"RTlnK#
#lnK = ("-"ΔG)/(RT) = ("-55 564" color(red)(cancel(color(black)("J·mol"^"-1"))))/(8.314 color(red)(cancel(color(black)("J·K"^"-1""mol"^"-1"))) × 1600 color(red)(cancel(color(black)("K")))) = "-4.177"#
#K = e^"-4.177" = "0.015 34"#
Step 3. Calculate the pressure of #"CO"_2# at equilibrium
#"Ni" + "CO"_2 ⇌ "NiO" + "CO"#
#K_P = P_"CO"/P_"CO₂"#
#P_"tot" = P_"CO₂" + P_"CO" = "1 atm"#
Let #P_"CO" = xcolor(white)(l) "atm"#. Then #P_"CO₂" = (1-x) color(white)(l)"atm"#.
Then
#K_P = x/(1-x) = "0.015 34"#
#x = "0.015 34"(1-x) = "0.015 34 - 0.015 34"x#
#"1.015 34"x = "0.015 34"#
#x = "0.015 34"/"1.015 34" = "0.015 11"#
#1-x = "1 - 0.015 11" = 0.985#
∴ At equilibrium, #P_"CO₂" = "0.985 atm"#.
This is the minimum pressure of #"CO"_2# that will cause #"Ni"# to be oxidized.
