## Chapter Solving Equilibrium Problems - Chemistry LibreTexts

Subsitute concentrations into the equilibrium expression. Assume that [A] - x = [A], simplify the equation, and solve for the change. Check to see if the change is less than 5% of the starting quantity, or within the limits set by your instructor. Calculate the equilibrium amounts if asked to do so. Check your work. A Systematic Approach to Solving Equilibrium Problems. Calculating the solubility of Pb(IO 3) 2 in a solution of Pb(NO 3) 2 is more complicated than calculating its solubility in deionized water. The calculation, however, is still relatively easy to organize, and the simplifying assumption fairly obvious. How Do I Solve It? This page contains links to guides to solving many of the the types of quantitative problems found in Chemistry If you don't know where to start, try the links with the same name as the chapter the problem comes from.

## How To Solve It

There are how to solve chemical equilibrium problems fundamental kinds of equilibrium problems: 1 those in which we are given the concentrations of the reactants and the products at equilibrium or, more often, how to solve chemical equilibrium problems, information that allows us to calculate these concentrationsand we are asked to calculate the equilibrium constant for the reaction; and 2 those in which we are given the equilibrium constant and the initial concentrations of reactants, and we are asked to calculate the concentration of one or more substances at equilibrium.

In this section, we describe methods for solving both kinds of problems. We saw in the exercise in Example 6 in Section Remember that equilibrium constants are unitless. A more complex example of this type of problem is the conversion of n -butane, an additive used to increase the volatility of gasoline, to isobutane 2-methylpropane.

This reaction can be written as follows:. At equilibrium, a mixture of n -butane and isobutane at room temperature was found to contain 0, how to solve chemical equilibrium problems.

Substituting these concentrations into the equilibrium constant expression. Thus the equilibrium constant for the reaction as written is 2. The reaction between gaseous sulfur dioxide and oxygen is a key step in the industrial synthesis of sulfuric acid:.

A mixture of SO 2 and O 2 was maintained at K until the system reached equilibrium. The equilibrium mixture contained 5. Calculate K and K p at this temperature. Given: balanced equilibrium equation and composition of equilibrium mixture. Asked for: equilibrium constant. Write the equilibrium constant expression for the reaction.

Then substitute the appropriate equilibrium concentrations into this equation to obtain K. Substituting the appropriate equilibrium concentrations into the equilibrium constant expression. To solve for K pwe use Equation Hydrogen gas and iodine react to form hydrogen iodide via the reaction. A mixture of H 2 and I 2 was maintained at K until the system reached equilibrium. The equilibrium mixture contained 1. Calculate K and K p for this reaction.

Chemists are not often given the concentrations of all the substances, and they are not how to solve chemical equilibrium problems to measure the equilibrium concentrations of all the relevant substances for a particular system. In such cases, we can obtain the equilibrium concentrations from the initial concentrations of the reactants and the balanced chemical equation for the reaction, as long as the equilibrium concentration of one of the substances is known.

Example 9 shows one way how to solve chemical equilibrium problems do this. The contents of the reactor were then analyzed and found to contain 0.

Calculate K at this temperature. Given: balanced equilibrium equation, amount of reactant, volume, how to solve chemical equilibrium problems, and amount of one product at equilibrium. Asked for: K. A Write the equilibrium constant expression for the reaction. Construct a table showing the initial concentrations, how to solve chemical equilibrium problems, the changes in concentrations, and the final concentrations as initial concentrations plus changes in concentrations.

B Calculate all possible initial concentrations from the data given and insert them in the table. C Use the coefficients in the how to solve chemical equilibrium problems chemical equation to obtain the changes in concentration of all other substances in the reaction.

Insert those concentration changes in the table. D Obtain the final concentrations by summing the columns. Calculate the equilibrium constant for the reaction. A The first step in any such problem is to balance the chemical equation for the reaction if it is not already balanced and use it to derive the equilibrium constant expression.

In this case, the equation is already balanced, and the equilibrium constant expression is as follows:. To obtain the concentrations of NOCl, NO, and Cl 2 at equilibrium, we construct a table showing what is known and what needs to be calculated. We begin by writing the balanced chemical equation at the top of the table, followed by three lines corresponding to the initial concentrations, the changes in concentrations required to get from the initial to the final state, and the final concentrations, how to solve chemical equilibrium problems.

B Initially, the system contains 1. The initial concentrations of NO and Cl 2 are 0 M because initially no products are present. Moreover, we are told that at equilibrium the system contains 0. We insert these values into the following table:. C We use the stoichiometric relationships given in the balanced chemical equation to find the change in the concentration of Cl 2the substance for which initial and final concentrations are known:.

According to the coefficients in the balanced chemical equation, 2 mol of NO are produced for every 1 mol of Cl 2so the change in the NO concentration is as follows:. We can now calculate the equilibrium constant for the reaction:. At equilibrium, the mixture contained 0. What is K p? The original laboratory apparatus designed by Fritz Haber and Robert Le Rossignol in for synthesizing ammonia from its elements. A metal catalyst bed, where ammonia was produced, is in the large cylinder at the left.

The Haber-Bosch process used for the industrial production of ammonia uses essentially the same process and components but on a much larger scale. To describe how to calculate equilibrium concentrations from an equilibrium constant, we how to solve chemical equilibrium problems consider a system that contains only a single product and a single reactant, the conversion of n -butane to isobutane Equation If we begin with a 1.

We need to calculate the equilibrium concentrations of both n -butane and isobutane. Because it is generally difficult to calculate final concentrations directly, we focus on the change in the concentrations of the substances between the initial and the final equilibrium conditions. This is because the balanced chemical equation for the reaction tells us that 1 mol of n -butane is consumed for every 1 mol of isobutane produced.

We can then express the final concentrations in terms of the initial concentrations and the changes they have undergone. Substituting the expressions for the final concentrations of n -butane and isobutane from the table into the equilibrium equation.

Rearranging and solving for x. We obtain the final concentrations by substituting this x value into the expressions for the final concentrations of n -butane and isobutane listed in the table:. We can check the results by substituting them back into the equilibrium constant expression to see whether they give the same K that we used in the calculation:.

This is the same K we were given, so we can be confident of our results. Example 10 illustrates a common type of equilibrium problem that you are likely to encounter. The water—gas shift reaction is important in several chemical processes, such as the production of H 2 for fuel cells.

If a mixture of gases that initially contains 0. Given: balanced equilibrium equation, Kand initial concentrations. Asked for: final concentrations. A Construct a table showing what is known and what needs to be calculated. Define how to solve chemical equilibrium problems as the change in the concentration of one substance.

Then use the reaction stoichiometry to express the changes in the concentrations of the other substances in terms of x. From the values in the table, calculate the final concentrations. B Write the equilibrium equation for the reaction. Substitute appropriate values from the table to obtain x. C Calculate the final concentrations of all species present. Check your answers by substituting these values into the equilibrium constant expression to obtain K.

Just as before, we will focus on the change in the concentrations of the various substances between the initial and final states. We can use the stoichiometry of the reaction to express the changes in the concentrations of the other substances in terms of x.

We enter the values in the following table and calculate the final concentrations. B We can now use the equilibrium equation and the given K to solve for x :, how to solve chemical equilibrium problems. We could solve this equation with the quadratic formula, but it is far easier to solve for x by recognizing that the left side of the equation is a perfect square; that is.

How to solve chemical equilibrium problems quadratic formula is presented in How to solve chemical equilibrium problems Skills 7 in Section Taking the square root of the middle and right terms. C The final concentrations of all species in the reaction mixture are as follows:.

We can check our work by inserting the calculated values back into the equilibrium constant expression:. To two significant figures, this K is the same as the value given in the problem, so our answer is confirmed. Hydrogen gas reacts with iodine vapor to give hydrogen iodide according to the following chemical equation:.

In Example 10, the initial concentrations of the reactants were the same, which gave us an equation that was a perfect square and simplified our calculations. Under these conditions, there is usually no way to simplify the problem, and we must determine the equilibrium concentrations with other means.

Such a case is described in Example In the water—gas shift reaction shown in Example 10, a sample containing 0. What is the composition of the reaction mixture at equilibrium? Given: balanced equilibrium equation, concentrations of reactants, and K.

Asked for: composition of reaction mixture at equilibrium. A Write the equilibrium equation. Construct a table showing the initial concentrations of all substances in the mixture. Complete the table showing the changes in the concentrations x and the final concentrations.

B Write the equilibrium constant expression for the reaction. A Systematic Approach to Solving Equilibrium Problems. Calculating the solubility of Pb(IO 3) 2 in a solution of Pb(NO 3) 2 is more complicated than calculating its solubility in deionized water. The calculation, however, is still relatively easy to organize, and the simplifying assumption fairly obvious. How Do I Solve It? This page contains links to guides to solving many of the the types of quantitative problems found in Chemistry If you don't know where to start, try the links with the same name as the chapter the problem comes from. Subsitute concentrations into the equilibrium expression. Assume that [A] - x = [A], simplify the equation, and solve for the change. Check to see if the change is less than 5% of the starting quantity, or within the limits set by your instructor. Calculate the equilibrium amounts if asked to do so. Check your work.