# How would you write the equilibrium constant expression for the following #H_2O_((g))# #rightleftharpoons# #H_2##(g)# #+# #1/2# #O_2##(g)# ?

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P.S. I am totally open to the idea of just changing this equation...

BUT that would be a problem beacuse were supposed to answer this QUESTION

Also, if you could (pretty please) determine the units for the expression.

Thanks!

P.S. I am totally open to the idea of just changing this equation...

BUT that would be a problem beacuse were supposed to answer this QUESTION

Also, if you could (pretty please) determine the units for the expression.

Thanks!

##### 1 Answer

Here's what I got.

#### Explanation:

Your balanced chemical equation looks like this

#"H"_2"O"_text((g]) rightleftharpoons "H"_text(2(g]) + color(red)(1/2)"O"_text(2(g])#

As you know, the **equilibrium constant** is defined as the ratio between the *equilibrium concentrations* of the **products** and the equilibrium concentrations of the **reactants**, all raised to the power of their **stoichiometric coefficients**.

In this case, you have

#K_c = (["H"_2]^1 * ["O"_2]^color(red)(1/2))/(["H"_2"O"]^1) = (["H"_2] * ["O"_2]^color(red)("1/2"))/(["H"_2"O"])#

To determine the units for **molarity** is measured in *moler per liter*, or *molar*,

Using just the units, you would have

#K_c = (color(red)(cancel(color(black)("M"))) * "M"^color(red)("1/2"))/(color(red)(cancel(color(black)("M")))) = "M"^(1/2)#

Alternatively, you can write this as

#sqrt("M") = sqrt("mol L"^(-1)) = "mol"^(1/2) "L"^(-1/2)#

Notice what would happen to the equilibrium constant if you were to rewrite the equation as

#color(blue)(2)"H"_2"O"_text((g]) rightleftharpoons color(blue)(2)"H"_text(2(g]) + "O"_text(2(g])#

This time ,you would have

#K_c^' = (["H"_2]^color(blue)(2) * ["O"_2])/(["H"_2"O"]^color(blue)(2))#

This is actually equal to

#K_c^' = ((["H"_2] * ["O"+2]^("1/2"))/(["H"_2"O"]))^2 = K_c^2#

The units here would be

#K_c = (color(red)(cancel(color(black)("M"^2))) * "M")/color(red)(cancel(color(black)("M"^2))) = "M" = "mol L"^(-1)#