# Question #542b5

##### 1 Answer

Here's what I got.

#### Explanation:

The problem provides you with the *number of moles* of each gas and with the *volume* of the reaction vessel, so right from the start you can use this information to calculate the concentration of the three gases.

So, molarity is defined as moles of solute divided by **liters** of solution, so your

#["H"_2] = "1 mole"/"1 L" = "1 M"#

#["I"_2] = "2 moles"/"1 L" = "2 M"#

#["HI"] = "3 moles"/"1 L" = "3 M"#

Next, use an **ICE table** to help you determine the *equilibrium concentrations* of the three species. Make sure that you write a **balanced** chemical equation for this equilibrium.

Before doing any calculations, take a look at the value of the equilibrium constant,

Since **product**, i.e. the equilibrium will lie to the **right**.

This means that you can expect the equilibrium concentrations of the two reactants to **decrease** compared with their initial values.

So, an ICE table for this equilibrium would look like this

#" ""H"_text(2(g]) " "+" " "I"_text(2(g]) " "rightleftharpoons" " color(red)(2)"HI"_text((g])#

By definition, the equilibrium constant for this reaction will be

#K_c = (["HI"]^color(red)(2))/(["H"_2] * ["I"_2])#

#K_c = (3 + color(red)(2)x)^color(red)(2)/((1-x)(2-x)) = 49.9#

Rearrange this to get

#9 + 12x + 4x^2 = 49.9 * (2 - 3x + x^2)#

#45.9x^2 - 161.7x + 90.8 = 0#

This quadratic equation will produce two *positive values* for

#{(color(red)(cancel(color(black)(x_1 = 2.82)))), (x_2 = 0.701 color(white)(a) color(green)(sqrt())):}#

Since equilibrium concentration (or any concentration, for that matter) **cannot** be negative, the first value of

This means that the equilibrium concentrations of the three species will be

#["H"_2] = 1 - 0.701 = color(green)("0.3 M")#

#["I"_2] = 2 - 0.701 = color(green)("1.3 M")#

#["HI"] = 3 + 2 * 0.701 = color(green)("4.4 M")#

Now, you *should* round these off to one sig fig, since that's how many sig figs you have for the initial number of moles of each species, but I'll leave them as-is.

Notice that the prediction is valid - the concentrations of the reactants *decreased* compared with their initial values.