# Question baa36

Aug 7, 2016

Here's what I get.

#### Explanation:

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"#

$K = {e}^{\text{-4.177" = "0.015 34}}$

Step 3. Calculate the pressure of ${\text{CO}}_{2}$ at equilibrium

$\text{Ni" + "CO"_2 ⇌ "NiO" + "CO}$

${K}_{P} = {P}_{\text{CO"/P_"CO₂}}$

${P}_{\text{tot" = P_"CO₂" + P_"CO" = "1 atm}}$

Let ${P}_{\text{CO" = xcolor(white)(l) "atm}}$. Then ${P}_{\text{CO₂" = (1-x) color(white)(l)"atm}}$.

Then

${K}_{P} = \frac{x}{1 - x} = \text{0.015 34}$

$x = \text{0.015 34"(1-x) = "0.015 34 - 0.015 34} x$

$\text{1.015 34"x = "0.015 34}$

$x = \text{0.015 34"/"1.015 34" = "0.015 11}$

$1 - x = \text{1 - 0.015 11} = 0.985$

∴ At equilibrium, ${P}_{\text{CO₂" = "0.985 atm}}$.

This is the minimum pressure of ${\text{CO}}_{2}$ that will cause $\text{Ni}$ to be oxidized.