14.6
Calculating Equilibrium Concentrations
Being able to calculate equilibrium concentrations is essential to many areas of science and technology—for example, in the formulation and dosing of…
Unknown equilibrium concentrations can be determined from the initial concentration of the reactants and the equilibrium constant, K, for the reaction.
Consider the reaction where 0.30 molar nitrogen gas and 0.40 molar oxygen gas react to produce nitric oxide gas and where K is 0.10. To calculate the equilibrium concentrations, the known values are tabulated in an ICE table.
For the change in concentration, the increase or decrease for each product or reactant, respectively, is denoted by x times its stoichiometric coefficient. The sum or difference is used to find the equilibrium concentrations, which are then substituted into the equilibrium expression.
To solve for x, the expression is expanded and all the terms are put on one side to convert it into the form: ax2 + bx + c. This equation can be solved using the quadratic formula.
Solving results in two values for x: 0.047 and −0.065. As the negative concentration of a substance is impossible, the value can be rejected.
Using 0.047 for x, the equilibrium concentrations of nitrogen, oxygen, and nitric oxide equal 0.25, 0.35, and 0.094 molar, respectively.
The perfect square condition is one situation where a shortcut can be used to avoid the quadratic formula.
For example, if the initial concentrations of nitrogen and oxygen in the above reaction were 0.30 molar each, the equation becomes a perfect square. In such cases, the equation can be simplified by taking the square root of both sides to solve for x.
View the full transcript and gain access to JoVE Core videos
Q1: What is an ICE table and how is it used to find equilibrium concentrations?
An ICE table organizes initial concentrations, concentration changes, and equilibrium concentrations for a reaction. Initial concentrations of reactants and products are listed first. Changes are denoted by x times the stoichiometric coefficient. Equilibrium concentrations are calculated by adding or subtracting changes from initial values, then substituted into the equilibrium expression to solve for x.
Q2: How do you determine which solution for x is physically meaningful when using the quadratic formula?
When solving the quadratic equation ax² + bx + c = 0, you obtain two mathematical solutions. However, only positive values are physically meaningful because concentrations cannot be negative. Reject any negative x value, as it would produce impossible negative concentrations for reactants or products.
Q3: What role does the equilibrium constant play in calculating unknown concentrations?
The equilibrium constant K provides the quantitative relationship between products and reactants at equilibrium. Unknown equilibrium concentrations are determined by substituting the equilibrium expressions into the K equation. Solving this equation yields the value of x, which is then used to calculate the final equilibrium concentrations of all species.
Q4: When can you use the perfect square condition to avoid the quadratic formula?
The perfect square condition occurs when the equilibrium expression simplifies to a perfect square equation. In such cases, you can take the square root of both sides instead of expanding and using the quadratic formula. This shortcut significantly simplifies calculations when initial concentrations and stoichiometric coefficients create symmetric terms.
Q5: How do you confirm that calculated equilibrium concentrations are correct?
Substitute the calculated equilibrium concentrations back into the equilibrium constant expression. If the resulting value equals the given equilibrium constant (accounting for significant figures), your calculations are verified. This confirmation step ensures accuracy before using the concentrations for further analysis or applications.
Q6: Why is determining reaction direction important before setting up an ICE table?
Determining reaction direction tells you whether reactants or products will increase or decrease to reach equilibrium. Compare the reaction quotient Q to the equilibrium constant K: if Q is less than K, the reaction proceeds forward; if Q exceeds K, it proceeds backward. This determines the signs of concentration changes in your ICE table.
Q7: What pharmaceutical applications depend on calculating equilibrium concentrations?
After ingestion or injection, drugs undergo several chemical equilibria affecting their concentration in body systems. Calculating equilibrium concentrations allows pharmacists to determine dosages that produce desired therapeutic effects. Understanding quantitative equilibrium aspects is essential for formulating medications and ensuring proper drug delivery and efficacy.