# How do you determine the equilibrium constant #K_c# for the reaction #X + 2Y rightleftharpoons Z#? The equilibrium concentrations are #"0.216 M"# for #Z#, #"0.06 M"# for #X#, and #"0.12 M"# for #Y#.

##### 1 Answer

#### Explanation:

The equilibrium constant is simply a ratio between two *multiplications*.

In the **numerator**, you have the multiplication of the **equilibrium product concentrations** raised to the power of the products' respective stoichiometric coefficients.

In the **denominator**, you have the multiplication of the **equilibrium reactant concentrations** raised to the power of the reactants' respective stoichiometric coefficients.

In your case, the equilibrium reaction looks like this

#"X" + 2"Y" rightleftharpoons "Z"#

which means that you have

#"Products:" #

#"Z " -> " no coefficient = coefficient of 1"#

#"Reactants:"#

#"X " -> " no coefficient = coefficient of 1"#

#"Y " -> " coefficient of 2"#

By definition, the equilibrium constant for this reaction will be

#K_c = (["Z"]^1)/(["X"]^1 * ["Y"]^2)#

which is equivalent to

#K_c = (["Z"])/(["X"] * ["Y"]^2)#

Plug in the values you have for the equilibrium concentrations of the three chemical species to find the value of the equilibrium constant--I'll leave the answer *without added units*

#K_c = (0.216)/(0.06 * 0.12^2) = color(darkgreen)(ul(color(black)(250)))#

I'll leave the answer rounded to two **sig figs**, but keep in mind that you only have one significant figure for the equilibrium concentration of