• Using equilibrium constant and initial quantities (concentrations) to solve for the equilibrium quantities.
• Using concentration to solve for the equilibrium constant

1. Using equilibrium constant and initial quantities (concentrations) to solve for the equilibrium quantities.

When hydrogen iodide (HI) is placed in a closed container it will decompose into its elements hydrogen and iodine and an equilibrium will be established:

If the initial concentration of HI and the equilibrium constant for the system are known, then we can calculate the equilibrium concentration for HI, H₂, and I₂. These type of calculations are generally performed using iCe tables (or reaction tables).

Initial concentration of HI: 0.025 mol/L

K_c=2.2x10^-3

iCe -table:

"x" is the change in concentration : reactants decrease and products increase by an amount "x".

We can write the equilibrium constant for the reaction

We need to solve for "x", the change in concentration. This can easily be done by taking the square root:

Solving for "x" yields

Now we can calculate the equilibrium concentrations:

Solving for "x" was particularly easy in this example since the equation could be solved by taking the square root on both sides of the equation. However, this is not always the case. An example is the decomposition of ammonia into its elements hydrogen and notrogen:

We can solve this equation by either

• rearranging the quadratic equation into the standard form (ax² + bx + c = 0) and solving for "x" (see appendix A in Kotz and Treichel for more information) or
• By making the assumption that the change "x" is much smaller than the initial concentration: (initial - x )~ initial, which simplifies our equation to

Now we can easily solve for "x". The assumption that x<<intial concentration can generally be used if the change in concentration is smaller than 5% of the initial concentration.
 
 

Exercise 1: Use equilibrium constant and initial concentrations to solve for the equilibrium quantities:

The extent of the change from CO and H₂O to CO₂ and H₂ is used to regulate the proportions syngas fuel mixtures. If 0.250 mol CO and 0.250 mol H₂O are placed in a 125 ml flask at 900 K, what is the composition of the equilibrium mixture? K_c = 1.56.

• Calculate the initial concentrations: in mol/L!!!
• Set up reaction iCe table:

Equilibrium Constant K_c = ----------------------------------------

Solving for "x":

Calculate equilibrium concentrations:

[CO] =

[H₂O] =

[CO₂] =

[H₂] =

Answ.: initial concentration [CO] = [H₂O] = 2.00 M

x = 1.11 M;

[CO] = [H₂] = 0.89 M
 

2. Use concentration to solve for the equilibrium constant

If we know the intial concentration of the reactants and determine the concentration of one of the products at equilibrium, then we can calculate the equilibrium constant K. This is shown in the following example, the decomposition of hydrogen fluoride

If the initial concentration of HI is 0.075 M, and the equilibrium concentration if I₂ is determined to be 0.0084, then set up an iCe table:

It is apparent that "x" equals 0.0084, therefore we can calculate the equilibrium concentrations for HF and H₂:

Now we can calculate the equilibrium constant K:

Exercise 2: Using partial pressure data to determine the equilibrium constant:

An evacuated vessel containing a small amount of powdered graphite is heated to 1080 K and then CO₂ is added to a pressure of 0.458 atm. Once the CO₂ is added, the system starts to produce CO. After equilibrium is reached, the total pressure inside the vessel is 0.757 atm. Calculate K_p.
Hint: Use partial pressures (P) in place of concentrations, and K_p in place of K_c.

Pressure [atm]	CO2(g)	C(s)	2 CO
initial	0.458	0	0
Change	-x		+ 2x
equlibrium	0.458 - x		2 x

P_total = 0.757 atm = P_CO2(eq) + P _CO(eq) = 0.458 atm – x + 2x

X = _________________

P_CO2(eq) = _____________

P_CO (eq) = ______________

Kp = -------------------------------
Answ.: x = 0.299 atm; P_CO2(eq) = 0.159 atm; P_CO (eq) =0.598 atm; Kp = 2.25