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.
