Question

What is the molar concentration of carbon dioxide in equilibrium with calcium carbonate at 519 K if `K_text(p) = 2` for the reaction `"CaCO"_3"(s)" ⇌ "CaO(s)" + "CO"_2"(g)"`?

Answer 1

`["CO"_2] = "0.03 mol/L"`

Explanation:

The equation for the equilibrium is

`"CaCO"_3"(s)" ⇌ "CaO(s)" + "CO"_2"(g)"`

`K_text(p) = p_text(CO₂) = 2`

We can use the Ideal Gas Law to determine the concentration of `"CO"_2`.

`color(blue)(bar(ul(|color(white)(a/a)pV = nRTcolor(white)(a/a)|)))" "`

or

`p = n/VRT`

The molar concentration `c` is given by

`c = n/V`

So,

`p = cRT`

and

`c =p/(RT)`

In this problem,

`p = "2 atm"`
`T = "819 K"`

∴ `c = (2 color(red)(cancel(color(black)("atm"))))/("0.082 06 L"·color(red)(cancel(color(black)("atm·K"^"-1")))"mol"^"-1" × 819 color(red)(cancel(color(black)("K")))) = "0.03 mol/L"`

Note: The answer can have only one significant figure, because that is all you gave for the value of `K_text(p)`.