1. Equilibrium Chemistry Tara LoPresti April 4, 2016 OLHS Chemistry
Session 23
4-4-16
Tara LoPresti
April 4, 2016

2. Equilibrium Define the term reversible reaction.
Describe chemical equilibrium.
Explain the equilibrium constant.
Calculate an equilibrium constant expression for a reaction.
Chemical equilibrium, the dynamic balance of reactants and products, is a key concept in chemistry.
In any closed system, a chemical reaction will result in a dynamic, ongoing balance between products and reactants. This lesson describes what chemical equilibrium is and how it can be achieved.

4. Keywords
chemical equilibrium the process by which the reactants form products and products form reactants at equal rates equilibrium constant the ratio between the concentrations of the products and the concentrations of the reactants reversible reaction a reaction in which there is a dynamic equilibrium between products and reactants

5. Content Equilibrium can be discussed in terms of chemical reactions.
Consider the following reaction:
H2 (g) + Cl2 (g)  2HCl (g)
When this reaction occurs, the reaction goes almost all the way to the right; that is, the reaction favors the products.
However, a small amount of the HCl product actually breaks back down into the reactants in a reverse of the reaction.
Such reactions are called reversible reactions.
Hydrogen Chloride: This reaction produces a gas that, when dissolved in water, produces hydrochloric acid. HCl (l) is widely used in industry.
Picture: Although this system at rest is 99% HCl, there is a dynamic situation in which the amounts of reactants and products have achieved a balance.

6. Content
Reversible reactions occur when the products of a reaction re-form into the reactants.
Consider the following equation:
2NO2  N2O4
Nitrogen dioxide gas (NO2), which is produced in automobile exhaust, is converted to dinitrogen tetroxide gas (N2O4).
If you placed NO2 in a closed container, you would expect that at some point the entire container would turn to N2O4.
But that doesn't happen.
The reason is that some of the N2O4 reverts to NO2 in a reversible reaction.
Picture: Products and reactants convert into each other, though one side of the equation is favored over the other.

7. Content
Chemical equilibrium is achieved when concentrations of reactants and products remain constant.
A dynamic interaction occurs in chemical reactions.
The term chemical equilibrium denotes that a chemical reaction exists as a dynamic, stable movement between products and reactants.
The term does not imply that the ratio of products to reactants is 1 : 1.
In fact, equilibrium exists in some reactions where the ratio of products to reactants is a million to one.
Equilibrium means that there exists a reversible reaction that over time remains in balance, as shown in the graph of the following reaction:
H2 + I2  2HI
Picture: As time passes, the amount of both reactants and products levels off and becomes stable.

8. Content A reaction at chemical equilibrium can be graphed.
One way to visualize equilibrium is to make a graph that compares the concentrations of reactants and products over time.
When you consider an equilibrium reaction graphically, keep two points in mind:
A reaction reaches equilibrium when the net concentrations of the reactants and products stop changing.
The concentrations of reactants and products do not need to be equal for equilibrium to occur.
Picture: Note that in a graph like this, equilibrium amounts need not be equal.

9. Content
The concentrations of the products and reactants at equilibrium in a reversible reaction can be expressed with the equilibrium constant.
The equilibrium constant, Keq, gives information about the equilibrium concentrations of reactants and products.
Each reaction has a value of Keq for any specific temperature.
The equation for determining the equilibrium constant is shown here, where A and B are the reactants; C and D are the products; and a, b, c, and d are the coefficients of the compounds.

10. Example Consider the general reaction aA + bB ⇋ cC + dD The equation
The value of Keq for this reaction is given by this equation:
𝐾 eq = [C] c [D] d [A] a [B] b
The alternative
It is sometimes useful to think of it as:
𝐾 eq = [products] [reactants]
Thinking about it this way will help you identify general trends and get a feel for what Keq means.

11. Content
Determine the equilibrium expression for a reversible reaction.
Suppose you are given the chemical reaction shown.
How would you go about determining its equilibrium constant?
Picture: Remember that the equilibrium expression is the ratio of the concentration of the product to the concentration of the reactants.

12. Example
You are ready to calculate the equilibrium constant for an equation.
Start with this equation:
N2 (g) + 3H2 (g)  2NH3 (g)
This equation represents the reaction for the production of ammonia, a reaction known as the Haber process.
Nitrogen gas and hydrogen gas react to form ammonia gas.
Ammonia is an important component of fertilizers.
The reaction reaches equilibrium with the following concentrations:
[N2] = 0.8 M
[H2] = 0.6 M
[NH3] = 1.7 M
How do you find the equilibrium constant for this reaction at this temperature?

13. Example Gather Information
The general form of Keq for the reaction aA + bB ⇋ cC + dD is as follows:
𝐾 eq = [C] c [D] d [A] a [B] b
Apply the equation
So the Keq for the equation for the reaction N2 (g) + 3H2 (g) ⇋ 2NH3 (g)
𝐾 eq = [NH 3 ] 2 [N 2 ] [H 2 ] 3
Remember, the exponents come from the coefficients in the balanced chemical equation.
Calculate
To find Keq, plug in the equilibrium concentrations:
𝐾 eq = [NH 3 ] 2 [N 2 ] [H 2 ] 3 = [1.7] 2 [0.8] [0.6] 3 = 16.7
The equilibrium constant for this reaction at this temperature is 16.7

14. hydrogen iodide gas (HI)
Content
The equilibrium constant can reveal the nature of the chemical reaction.
The equilibrium constant is always a positive number.
It can range from extremely small to extremely large.
What does the value of Keq tell you about a reaction?
If a reaction creates far more products than reactants, the numerator is large and the denominator is small.
That means Keq will be relatively large, and equilibrium exists when the far right of the reaction is favored by nature.
By contrast, if few products form, and many reactants remain, the numerator is small and the denominator is large.
So a relatively small Keq means that equilibrium is far to the left.
Picture: The equilibrium constant for the Haber process for making ammonia gas is This large number indicates that the products are favored in the reaction.
hydrogen iodide gas (HI)

15. Recap
The equilibrium constant for a reaction describes the balance of reactants and products in a reaction system.
Many chemical reactions, such as the dissociation of a small amount of HCl in water, are irreversible.
In other words, the reaction proceeds only from left to right, and all the reactants are converted to products.
Chemical equations for irreversible reactions like these include only a single arrow that points from reactants to products.
However, many chemical reactions are not irreversible.
In these reactions, at the same time that reactants are being converted to products, some of the products are themselves reacting together and turning back into reactants.
This type of reaction is a reversible reaction.
Chemical equations for reversible reactions are indicated by a double arrow.
The reaction that proceeds from left to right is called the forward reaction.
The reaction that proceeds from right to left is called the reverse reaction.
A reaction is said to be at equilibrium when the rates of forward and reverse reactions are equal.
At equilibrium, the amounts of reactants and products stop changing with time.
The equilibrium constant for a reaction represents the ratio of products to reactants at equilibrium.

16. Remember… The Equilibrium Constant
The equilibrium constant K for a reaction has no units.
The concentrations used in the equilibrium constant calculation are concentrations in moles per liter.
The concentration of a solid does not appear in an equilibrium expression for a reaction.
The equilibrium constant for a forward reaction is the reciprocal of the equilibrium constant for the reverse reaction

17. Example 1 Write the Equilibrium Expression for a Reaction
Methanol (CH3OH) is a simple alcohol that can be used as a fuel or as a reactant in the production of some important industrial chemicals. Methanol can form from carbon monoxide (CO) and hydrogen (H2) in a reversible reaction, as shown below:
CO(g) + 2H2 (g) ⇋ CH3OH(g)
Write the equilibrium expression for this reaction.

18. Example 1 Solution Strategize
The equilibrium expression for a reaction is equal to the ratio of products to reactants. Each species in the reaction is raised to a power equal to its stoichiometric coefficient in the balanced chemical equation. The expression includes the concentrations of products and reactants, not just their chemical formulas. For this reaction, the equilibrium expression will include the following terms: [CO], [H2]2, and [CH3OH]. The square brackets indicate concentration in moles per liter.
Solve
Methanol is the product, and CO and H2 are the reactants. Therefore, the correct equilibrium expression for this reaction is the one shown below:
[CH 3 OH] [CO] [H 2 ] 2

19. Example 2 Calculate the Equilibrium Constant for a Reaction
A scientist combines carbon dioxide and hydrogen in a reaction at 210ºC to produce methanol according to the equation in the prior example. At equilibrium, the concentrations of methanol, carbon monoxide, and hydrogen for the reaction are as follows:
[CH3OH] = mol/L
[CO] = mol/L
[H2] = mol/L
What is the equilibrium constant, K, for this reaction at 210ºC

20. Example 2 Solution Collect and Strategize
The equilibrium expression for the reaction is given below:
[CH 3 OH] [CO] [H 2 ] 2
To calculate the equilibrium constant for this reaction, substitute the equilibrium concentrations given in the problem into the equilibrium expression.
Solve
Substituting the given values and solving yields the following:
𝐾= [CH 3 OH] [CO] [H 2 ] 2 = (0.151) (0.151) 2 = ×10 −3 = 14.4

21. Example 3 Interpret an Equilibrium Constant for a Reaction
Does the reaction for the formation of methanol in the last two examples favor the products or the reactants?

22. Example 3 Solution Recall Relevant Information
Remember that the equilibrium constant, K, for the reaction is the ratio of products to reactants at equilibrium. The product of the reaction (methanol) is in the numerator, and the reactants (CO and H2) are in the denominator.
Solve
The equilibrium constant for the reaction is greater than 1. Therefore, at equilibrium, the products are favored over the reactants.
Tip: If the equilibrium constant for a reaction is greater than 1, the products of the reaction as written are favored. If the equilibrium constant is less than 1, the reactants of the reaction as written are favored.

23. Example 4
Write an Equilibrium Expression for a Reverse Reaction and Calculate its K’
A scientist places some methanol in a closed container. The methanol begins to decompose into carbon monoxide and hydrogen gas according to the equation below:
CH3OH(g) ⇋ CO(g) + 2H2 (g)
Write the equilibrium expression for this reaction, and calculate the equilibrium constant, K’, for the reaction at 210ºC. (This reaction is the reverse of the reaction in Example 1. Chemists often use K’ to represent the equilibrium constant for a reverse reaction.

24. Example 4 Solution Recall Relevant Information
For any reaction, the equilibrium expression is the ratio of products to reactants, with each species raised to a power equal to its stoichiometric coefficient in the balanced equation. In the reaction given, the products are CO and H2, and the reactant is methanol. Therefore, this reaction is the reverse of the reaction in Example 1. The equilibrium constant K for the reaction in Example 1 at 210ºC is 14.4.
Solve
The equilibrium expression is the ratio of products to reactants for the reaction as written, as shown below:
[CO] [H 2 ] 2 [CH 3 OH]
Notice that this is the reciprocal of the equilibrium expression for the reaction in Example 1. Therefore, the equilibrium constant K’ for this reaction must be the reciprocal of the equilibrium constant K calculated in Example 2, as shown below:
𝐾= 1 𝐾 = =0.0694

25. Example 5
Write an Equilibrium Expression for a Reaction Involving a Solid
Only a tiny amount of silver chloride (AgCl) can dissolve in water. The equation below shows what happens when silver chloride dissolves in water:
AgCl (s) ⇋ Ag+ (aq) + Cl− (aq)
Write an equation for the equilibrium constant, K, for this dissolution reaction

26. Example 5 Solution Recall Relevant Information
The equilibrium expression for a reaction is the ratio of products to reactants in the reaction. In this reaction, solid AgCl is the reactant, and Ag+ ions and Cl− ions are the products. The equilibrium expression includes the concentrations of the reactants and products. The concentration of a solid is a constant, unlike the concentrations of aqueous ions.
Collect
First, write the equilibrium expression in the usual way, as shown below:
𝐾= [Ag + ] [Cl − ] [AgCl]
Solve
K is a constant, and so is [AgCl]. Therefore, their product must be a constant, and they can be combined to eliminate [AgCl] from the expression, as shown below:
K × [AgCl] = [ Ag+][Cl−]
K = [ Ag+][Cl−]
It is conventional in chemistry to eliminate the concentrations of all solid species from equilibrium expressions in this way. The equilibrium constant for the dissolution of a salt is called the solubility product constant, or Ksp. Therefore, the Ksp for silver chloride is given by the equation Ksp = [Ag+][Cl−]

27. Problem Set 85
The equilibrium constant for the following reaction at 2,000 K is 0.154:
2CH4 (g) ⇋ C2H2 (g) + 3H2 (g)
Are the products or reactants favored in this reaction at 2,000 K? Explain your answer.
Write the equilibrium expression for the equation below:
N2 (g) + 3H2 (g) ⇋ 2NH3 (g)
The reaction between hydrogen and iodine at 700 K is described by the equation below:
H2 (g) + I2 (g) ⇋ 2HI (g)
For this reaction, 𝐾= [HI] 2 [H 2 ] [I 2 ] . At equilibrium, the concentration of H2 is mol/L, the concentration of I2 is mol/L, and the concentration of HI is 0.29 mol/L. Calculate the equilibrium constant for this reaction at 700 K. Are the products or reactants favored at equilibrium?
Explain why a chemical equilibrium is called a dynamic equilibrium.
H2 and Br2 are heated to give HBr according to the equation below:
H2 (g) + Br2 (g) ⇋ 2HBr (g)
At equilibrium, at a specific temperature, the concentration of H2 is mol/L, the concentration of Br2 is mol/L, and the concentration of HBr is mol/L. Calculate the equilibrium constant for this reaction at that specific temperature.

28. Problem Set 85
At 298 K, the equilibrium constant for the reaction 2SO2 (g) + O2 (g) ⇋ 2SO3 (g) is 7.2 × Are the products or the reactants favored?
Challenge The solubility product constant, Ksp, for silver chloride (AgCl) is 1.8 × 10–10 at 25°C. Use a scientific calculator to calculate the concentrations of Ag+ ions and Cl– ions in a saturated AgCl solution. (Hint: Use the balanced chemical equation for the dissolution of AgCl to find a relationship between [Ag+] and [Cl–].)
Challenge Nitrogen dioxide (NO2) can form from N2O4 according to the following reaction:
N2O4 (g) ⇋ 2NO2 (g)
At equilibrium at a certain temperature, the concentration of N2O4 is mol/L, and the concentration of NO2 is mol/L. Is the reactant or product favored at equilibrium?
Challenge Ethanol (C2H5OH) is manufactured by reacting ethane (C2H4) with steam according to the equation C2H4 (g) + H2O (g) ⇋ C2H5OH (g). The equilibrium constant for this reaction at a specific temperature is In a particular reaction system, the equilibrium concentrations of C2H4 and C2H5OH are mol/L and mol/L, respectively. What is the equilibrium concentration of H2O (g)?

29. Problem Set 85 Answers

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34. Lesson Summary In this lesson, you learned:
In chemical equilibrium, the products and reactants of a reversible reaction remain constant over time.
Reversible reactions reach chemical equilibrium.
If the rate at which the products and reactants are produced remains in a dynamic constancy, the reaction is at equilibrium.
Equations at equilibrium can be described quantitatively in terms of their equilibrium constant.

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