Question

If pure phosgene at an initial pressure of 1.1 atm decomposes, what are the equilibrium pressures of all species?

Lexan is a plastic used to make compact discs, eyeglass lenses, and bullet-proof glass. One of the compounds used to make Lexan is phosgene (COCl2), an extremely poisonous gas.Phosgene decomposes by the following reaction for which Kp = 6.8 ✕ 10-9 at 100°C. COCl2(g) <=> CO(g) + Cl2(g).

Answer 1

`p_text(CO) = p_text(Cl₂) = 8.6 × 10^"-5" color(white)(l)"atm"; p_text(COCl₂) = "1.1 atm"`

Explanation:

We can solve this problem by setting up an ICE table.

`color(white)(mmmmll)"COCl"_2 ⇋ "CO" +color(white)(l) "Cl"_2`
`"I/atm": color(white)(mm)1.1color(white)(mmmll)0color(white)(mml)0`
`"C/atm": color(white)(mll)"-"xcolor(white)(mmml)"+"xcolor(white)(mll)"+"x`
`"E/atm": color(white)(ml)"1.1-"xcolor(white)(mmm)xcolor(white)(mml)x`

`K_text(c) = (p_text(CO)p_text(Cl₂))/(p_text(COCl₂)) = (x^2)/("1.1-"x) = 6.8 × 10^"-9"`

Check for negligibility

`1.1/(6.8 × 10^"-9") =1.6 × 10^8 > 400`. ∴ x ≪1.1.

Then

`x^2/1.1 = 6.8 × 10^"-9"`

`x^2 = 1.1 × 6.8 × 10^"-9"`

`x^2 = 7.48 × 10^"-9"`

`x = 8.65 × 10^"-5"`

`p_text(CO) = x color(white)(l)"atm" = 8.6 × 10^"-5" color(white)(l)"atm"`

`P_text(Cl₂) = x color(white)(l)"atm" = 8.6 × 10^"-5" color(white)(l)"atm"`

`p_text(COCl₂) = "1.1 -"xcolor(white)(l)"atm" = ("1.1 - 8.6" × 10^"-5")color(white)(l) "atm" = "1.1 atm"`

Check:

`(8.6 × 10^"-5")^2/1.1^2 = 6.8 × 10^"-9"`

It checks!