Writing the K Expression

As shown in the previous simulation for H2 (g) + I2 (g) 2HI (g) the Keq expression is   or 

Of course, we could also write the equation for the reaction as (the coefficients are highlighted in red)

1H2 (g) + 1I2 (g) 2HI (g)

We just don't usually write in the coefficient when it is 1, but have done so here just for emphasis.  This means the equilibrium constant expression is really

A number raised to the power of 1 is just itself, so these two expressions are equivalent.

   =  

We almost always just write it in the first form, ignoring coefficients of 1.

Consider the following equilibrium equations (coefficients are shown in red, and coefficients of 1 are included for emphasis).  Each one is included with its K expression.  Can you detect the pattern for writing Keq expressions?

Equilibrium Equation Including all coefficients Usual Keq
1PCl5 (g)  1PCl3 (g) + 1Cl2 (g)
2NO2 (g)  1N2O4 (g)
1N2 (g) + 3H2 (g) 2NH3 (g)
1N2H4 (g) + 3O2 (g) 2NO2 (g) + 2H2O (g) kexpn6_r.gif (515 bytes) kexpn6.gif (432 bytes)

 

Click here if you need a hintIf you see the pattern, then you should be able to pick the correct value of K for these reactions:

1. N2 (g) + 2O2 (g) 2NO2 (g)     K = ?

2. 4NH3 (g) + 7O2 (g) 4NO2 (g) + 6H2O (g)     K = ?

The most general possible form of a chemical equation is:

aA + bB + cC ... equilsymbol.gif (859 bytes) ... + xX + yY + zZ

where the lower case letters are the coefficients, and the upper case letters represent the formulas of the reacting substances.  Then the Keq expression for this any reaction can be written:

The equilibrium constant expression is formed by multiplying all the product concentrations, raised to the power of the coefficient of each, all divided by the reactant concentrations, raised to the power of each.

Actually, since each of the above is written for concentrations (the square brackets [] always represent concentrations in chemistry), each of them is a Kc; that is, a K expressed in terms of concentrations.  In introductory chemistry, almost all the K's used are Kc.   Because Kc is the most common way of writing K in Mission to Mars, when you see the symbol K, assume it is a Kc, even if it is not identified as such.

Remember that the square brackets [] represent the molar concentration, and that the concentration of a pure liquid or solid is a fixed value.  Since the concentration cannot change, pure liquids and solids are not included in equilibrium constant expressions (in beginning chemistry we use concentrations, rather than the more accurate term activity).  However, anything that is gaseous (g) or in solution (aq) can change in concentration, so must be included.   Look at the following examples, and you should see how this rule is applied.

Equilibrium Equation Kc
AgCl (s) Ag+ (aq) + Cl- (aq) K= [Ag+][Cl-]
PbCl2 (s) Pb2+ (aq) + 2Cl- (aq) K= [Pb2+][Cl-]2
CaCO3 (s) CO2 (g) + CaO (s) K = [CO2]
CH3COOH (aq) + H2O (l) H3O+ (aq) + CH3COO- (aq)

 

Click here if you need a hintIf you see the pattern, then you should be able to pick the correct value of Kc for these reactions:

3. BaSO4 (s) Ba+2 (aq) + SO42- (aq)     Kc = ?

K = [BaSO4] K = [Ba2+][SO42-]

4. Ca(OH)2 (s) Ca2+ (aq) + 2OH- (aq)     Kc = ?

K = [Ca2+]2[OH-] K = [Ca2+][OH-]2

5. NH3 (g) + H2O (l) NH4+ (aq) + OH- (aq)     K = ?

K = [NH4+][OH-]

Summary:

The Kc expression is equal to the concentration of all of the products multiplied together, divided by all of the reactants multiplied together.  Solids and liquids are not included in the K expression.

The three most common beginning mistakes are: