# Finding initial concentration by using Kc and equilibrium concentration?!

## At a certain temp the Kc for the Equillibrium reaction ${H}_{2} + {I}_{2} r i g h t \le f t h a r p \infty n s 2 H I$ is 51,50. An unknown amount of HI was placed in a 1 dm^3 container. At equilibrium 0,218 mol of Hydrogen gas (H2) was present. i)How much HI was originally placed in the container? ii) How much I2 and HI were present at equilibrium?

Mar 26, 2017

Here's what I get.

#### Explanation:

This looks like the appropriate time to set up an ICE table.

$\textcolor{w h i t e}{m m m m m m m} \text{H"_2 + "I"_2 ⇌ "2HI}$
${\text{I/mol·dm}}^{3} : \textcolor{w h i t e}{m l l} 0 \textcolor{w h i t e}{m l l} 0 \textcolor{w h i t e}{m m m} y$
$\text{C/mol·dm"^3: color(white)(ll)"+"xcolor(white)(m)"+"xcolor(white)(mm)"-2} x$
$\text{E/mol·dm"^3: color(white)(l)"0,218"color(white)(ll)xcolor(white)(mml)y"-} 2 x$

The equilibrium concentration of ${\text{H}}_{2}$ is ${\text{0,218 mol/dm}}^{3}$, so $x \text{ = 0,218}$.

Our ICE table now becomes

$\textcolor{w h i t e}{m m m m m m m l} \text{H"_2color(white)(m) +color(white)(m) "I"_2color(white)(mm) ⇌color(white)(ml) "2HI}$
${\text{I/mol·dm}}^{3} : \textcolor{w h i t e}{m m} 0 \textcolor{w h i t e}{m m m m} 0 \textcolor{w h i t e}{m m m m m m} y$
$\text{C/mol·dm"^3: color(white)(ll)"+0,218"color(white)(m)"+0,218"color(white)(mmm)"-0,436}$
$\text{E/mol·dm"^3: color(white)(mll)"0,218"color(white)(mm)"0,218"color(white)(mml)y-"0,436}$

We can now insert these numbers into the equilibrium constant expression.

${K}_{\textrm{e q}} = \text{[HI]"^2/(["H"_2]["I"_2]) = (y" - 0,436")^2/("0,218" × "0,218") = "51,50}$

(y" - 0,436")^2= "0,218"^2 × "51,50" ="2,447"

$y \text{ - 0,436" = 1.564}$

$y = \text{1,564+ 0,436" = "2,000}$

["I"_2] = "0,218 mol·dm"^"-3"

["HI"] =(y" - 0,436") color(white)(l)"mol·dm"^"-3" = ("2,000 - 0,436")color(white)(l)"mol·dm"^"-3" = "1,56 mol·dm"^"-3"

The volume of the container was ${\text{1 dm}}^{3}$, so

$\text{i)"color(white)(m)"the initial amount of HI was 2,00 mol.}$
$\text{ii)"color(white)(ll) "the equilibrium amount of I"_2 color(white)(l)"was 0,218 mol} .$
$\textcolor{w h i t e}{m l l} \text{the equilibrium amount of HI was 1,56 mol.}$