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# 19.1: Introduction to Equilibrium

Difficulty Level: At Grade Created by: CK-12

## Lesson Objectives

The student will:

• describe what is happening in a system at equilibrium.
• explain what is meant by dynamic equilibrium.
• state the conditions necessary for a system to be in equilibrium.

## Vocabulary

• dynamic equilibrium
• equilibrium
• irreversible reaction
• macroscopic properties
• reversible reaction

## Introduction

Consider this generic reaction: A+BC+D\begin{align*}A + B \rightarrow C + D\end{align*}. Based on what we have learned so far, you might assume that the reaction will keep going forward, forming C and D until either A or B (or both) is completely used up. When this is the case, we would say that the reaction “goes to completion.” Reactions that go to completion are referred to as irreversible reactions.

Some reactions, however, are reversible, meaning that products can also react to re-form the reactants. In our example, this would correspond to the reaction C+DA+B\begin{align*}C + D \rightarrow A + B\end{align*}. During a reversible reaction, both the forward and backward reactions are happening at the same time.

## Equilibrium

As we learned earlier, the rate of a reaction depends on the concentration of the reactants. At the very beginning of the reaction A+BC+D\begin{align*}A + B \rightarrow C + D\end{align*}, we would not expect the reverse reaction to proceed very quickly. If only a few particles of C\begin{align*}C\end{align*} and D\begin{align*}D\end{align*} have been created in a large flask of A\begin{align*}A\end{align*} and B\begin{align*}B\end{align*}, then it is very unlikely that they will find each other because the concentration of C\begin{align*}C\end{align*} and D\begin{align*}D\end{align*} is just too low. If C\begin{align*}C\end{align*} and D\begin{align*}D\end{align*} cannot find each other and collide with the correct energy and orientation, no reaction will occur.

However, as more and more C\begin{align*}C\end{align*} and D\begin{align*}D\end{align*} are created, it becomes more and more likely that they will find each other and react to re-form A\begin{align*}A\end{align*} and B\begin{align*}B\end{align*}. Conversely, as A\begin{align*}A\end{align*} and B\begin{align*}B\end{align*} are being used up, the forward reaction slows down for the same exact reason. The concentration of A\begin{align*}A\end{align*} and B\begin{align*}B\end{align*} decreases over the course of a reaction because there are less A\begin{align*}A\end{align*} and B\begin{align*}B\end{align*} particles in the same size flask. At some point, the rates for the forward and reverse reactions will be equal, at which point the concentrations will no longer change. If A\begin{align*}A\end{align*} and B\begin{align*}B\end{align*} are being destroyed at the same rate that they are being created, the overall amount should not change over time. At this point, the system is said to be in equilibrium. A qualitative description of this process for the reaction between hydrogen and sulfur to make dihydrogen sulfide is shown below.

Chemists use a double arrow to show that a reaction is in equilibrium. For the reaction above, the chemical equation would be:

2 H2(g)+ S2(g)2 H2S(g)\begin{align*}2 \ \text{H}_{2(g)} + \ \text{S}_{2(g)} \rightleftharpoons 2 \ \text{H}_2S_{(g)}\end{align*}

This indicates that both directions of the reaction are occurring. Note that a double-headed arrow (\begin{align*}\leftrightarrow\end{align*}) should not be used here because this has a different chemical meaning.

## Dynamic Equilibrium

One characteristic of a system at equilibrium is that the macroscopic properties do not change over time. Macroscopic properties are those that describe the system as a whole. These can be observed and measured without needing to investigate the system in terms of individual molecules.

One example of a macroscopic property is temperature. Although temperature can be explained on a microscopic level by the speed at which particles are moving around, individual molecules do not have a “temperature.” A glass of water with a constant temperature contains molecules with a large range of different speeds, and the speed of any individual molecule is constantly changing as it collides with other molecules and gains or loses kinetic energy. However, if you average out the properties of all these molecules (7.91×1024\begin{align*}7.91 \times 10^{24}\end{align*}) for an 8 oz glass of water), the overall temperature appears constant, despite continuous changes on the microscopic level.

Concentration is another example of a macroscopic property. It describes the total amount of a substance, but it does not make any statement about what is occurring on a molecular level. When a reaction is at equilibrium, the concentration of each component is constant over time. As we saw before, both the forward and reverse reactions are still taking place, but since they are moving at the same rate, there is no change for the system as a whole. The term dynamic equilibrium refers to a state where no net change is taking place, despite the fact that both reactions are still occurring. Individual molecules are still being formed and broken down, but the system as a whole is not changing over time.

## Other Conditions Necessary for Equilibrium

In order for a reaction to reach an equilibrium state, it needs to take place in a closed system. Consider the following reaction:

H2CO3(aq)H2O(l)+ CO2(g)\begin{align*}\text{H}_2\text{CO}_{3(aq)} \rightleftharpoons \text{H}_2\text{O}_{(l)} + \ \text{CO}_{2(g)}\end{align*}

This equilibrium is established in a closed can of soda because neither the reactants nor the products can leave the system. However, when you open the soda, one of the products (CO2\begin{align*}\text{CO}_2\end{align*}) is free to escape into the atmosphere. If a molecule of CO2\begin{align*}\text{CO}_2\end{align*} escapes, it is no longer available to collide with the water molecules left behind, so it can no longer participate in the reverse reaction. Therefore, the forward reaction will eventually go to completion until there is no more H2CO3\begin{align*}\text{H}_2\text{CO}_3\end{align*} available. Note that since H2CO3\begin{align*}\text{H}_2\text{CO}_3\end{align*} is an acid, an open soda will become less acidic over time. Acidity is an important component of taste, so flat soda really does taste different for reasons other than texture.

Another requirement for a system to stay in equilibrium is that the temperature and pressure stay constant. As we learned in the previous chapter, temperature and pressure both have an effect on the rate of a reaction. However, the effect might be greater for the forward reaction than the reverse reaction, or vice versa. For example, in the reaction above, adding heat will favor the forward reaction more than the reverse, resulting in the production of more CO2\begin{align*}\text{CO}_2\end{align*}. This is true even if the can remains closed. Eventually, a new equilibrium will be established at the new temperature, but while the temperature is changing, the system is no longer in equilibrium.

## Lesson Summary

• Irreversible reactions will continue to form products until the reactants are fully consumed.
• Reversible reactions will react until a state of equilibrium is reached.
• A reaction is at equilibrium when there is no net change to the system over time.
• Dynamic equilibrium refers to an equilibrium where forward and reverse reactions are still occurring, but they are proceeding at the same rate, so there is no net change.

## Review Questions

1. What does the term dynamic equilibrium mean?
2. List all of the conditions for a dynamic equilibrium.
3. Of the following conditions, which is not required for a dynamic equilibrium?
1. rate of the forward reaction equals the rate of the reverse reaction.
2. reaction occurs in an open system
3. reaction occurs at a constant temperature
4. reaction occurs in a closed system
4. Which of the following systems, at room temperature and pressure, can be described as a dynamic equilibrium?
1. an open flask containing air, water and water vapor
2. a glass of water containing ice cube cubes and cold water
3. a closed bottle of soda pop
4. an open flask containing solid naphthalene
5. Is each of the following in a state of equilibrium? Explain.
1. Ice cubes are melting in a glass of water with a lid on it
2. Crystals of potassium dichromate were dissolved in water, and now the water is a uniform orange color with a small amount of crystal left in the closed container.
3. An apple that is left on the counter for a few days, it dries out and turns brown.
6. If the following table (Table below) of concentration vs. time was provided to you for the ionization of acetic acid, how would you know when equilibrium was reached?
Data Table For Problem 6
Time (min) [HC2H3O2]mol/L\begin{align*}[\text{HC}_2\text{H}_3\text{O}_2] \;\mathrm{mol/L}\end{align*}
0\begin{align*}0\end{align*} 0.100\begin{align*}0.100\end{align*}
0.5\begin{align*}0.5\end{align*} 0.099\begin{align*}0.099\end{align*}
1.0\begin{align*}1.0\end{align*} 0.098\begin{align*}0.098\end{align*}
1.5\begin{align*}1.5\end{align*} 0.097\begin{align*}0.097\end{align*}
2.0\begin{align*}2.0\end{align*} 0.096\begin{align*}0.096\end{align*}
2.5\begin{align*}2.5\end{align*} 0.095\begin{align*}0.095\end{align*}
3.0\begin{align*}3.0\end{align*} 0.095\begin{align*}0.095\end{align*}
3.5\begin{align*}3.5\end{align*} 0.095\begin{align*}0.095\end{align*}
4.0\begin{align*}4.0\end{align*} \begin{align*}0.095\end{align*}
\begin{align*}4.5\end{align*} \begin{align*}0.095\end{align*}
\begin{align*}5.0\end{align*} \begin{align*}0.095\end{align*}

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