Calculation of Equilibrium Concentrations
Under certain conditions, the equilibrium constant Kc
for the decomposition of PCl5
) into PCl3
) and Cl2
) is 0.0211. What are the equilibrium concentrations of PCl5
, and Cl2
in a mixture that initially contained only PCl5
at a concentration of 1.00 M
Use the stepwise process described earlier.
- Step 1.
Determine the direction the reaction proceeds.
The balanced equation for the decomposition of PCl5 is
Because only the reactant is present initially Qc = 0 and the reaction will proceed to the right.
- Step 2.
Develop an ICE table.
- Step 3.
Solve for the change and the equilibrium concentrations.
Substituting the equilibrium concentrations into the equilibrium constant equation gives
Appendix B shows an equation of the form ax2 + bx + c = 0 can be rearranged to solve for x:
In this case, a = 1, b = 0.0211, and c = −0.0211. Substituting the appropriate values for a, b, and c yields:
The two roots of the quadratic are, therefore,
For this scenario, only the positive root is physically meaningful (concentrations are either zero or positive), and so x = 0.135 M.
The equilibrium concentrations are
- Step 4.
Confirm the calculated equilibrium concentrations.
Substitution into the expression for Kc (to check the calculation) gives
The equilibrium constant calculated from the equilibrium concentrations is equal to the value of Kc given in the problem (when rounded to the proper number of significant figures).
Check Your Learning
Acetic acid, CH3
H, reacts with ethanol, C2
OH, to form water and ethyl acetate, CH3
The equilibrium constant for this reaction with dioxane as a solvent is 4.0. What are the equilibrium concentrations for a mixture that is initially 0.15 M in CH3CO2H, 0.15 M in C2H5OH, 0.40 M in CH3CO2C2H5, and 0.40 M in H2O?
[CH3CO2H] = 0.18 M, [C2H5OH] = 0.18 M, [CH3CO2C2H5] = 0.37 M, [H2O] = 0.37 M
Check Your Learning
A 1.00-L flask is filled with 1.00 moles of H2
and 2.00 moles of I2
. The value of the equilibrium constant for the reaction of hydrogen and iodine reacting to form hydrogen iodide is 50.5 under the given conditions. What are the equilibrium concentrations of H2
, and HI in moles/L?
[H2] = 0.06 M, [I2] = 1.06 M, [HI] = 1.88 M