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2.3 Calculating equilibrium concentrations

6 min read•july 22, 2024

is all about balance. When reactions reach a steady state, the concentrations of reactants and products stabilize. Understanding this balance is key to predicting how reactions behave and calculating important values.

The is the star of the show. It tells us the ratio of products to reactants at equilibrium. By using K and some clever math tricks, we can figure out concentrations, pressures, and even pH levels for all sorts of chemical systems.

Equilibrium Concentrations and Pressures

Calculations with equilibrium constant

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Equilibrium constant (K) represents ratio of product of concentrations of products raised to their stoichiometric coefficients divided by product of concentrations of reactants raised to their stoichiometric coefficients
- For general reaction $aA + bB \rightleftharpoons cC + dD$ $a A + b B ⇌ c C + d D$ , is $K = \frac{[C]^c[D]^d}{[A]^a[B]^b}$ $K = \frac{[ C ] ^{c} [ D ] ^{d}}{[ A ] ^{a} [ B ] ^{b}}$
  - $[A]$ , $[B]$ , $[C]$ , and $[D]$ represent molar concentrations of species A, B, C, and D respectively
  - $a$ , $b$ , $c$ , and $d$ represent stoichiometric coefficients of species A, B, C, and D respectively
If or pressures are known, they can be substituted into equilibrium constant expression to calculate K
- For example, if $[A] = 0.1 M$ , $[B] = 0.2 M$ , $[C] = 0.3 M$ , and $[D] = 0.4 M$ at equilibrium for reaction $A + 2B \rightleftharpoons C + D$ , then $K = \frac{(0.3)(0.4)}{(0.1)(0.2)^2} = 3$
If equilibrium constant and all but one of equilibrium concentrations or pressures are known, unknown concentration or can be calculated using equilibrium constant expression
- For example, if $K = 3$ , $[A] = 0.1 M$ , $[B] = 0.2 M$ , and $[D] = 0.4 M$ at equilibrium for reaction $A + 2B \rightleftharpoons C + D$ , then $[C]$ can be calculated as $[C] = \frac{K[A][B]^2}{[D]} = \frac{(3)(0.1)(0.2)^2}{0.4} = 0.3 M$

ICE table method

used to solve for equilibrium concentrations or pressures when or pressures and equilibrium constant are known
consists of three rows:
1. Initial (I): concentrations or pressures of reactants and products before reaction starts
2. Change (C): changes in concentrations or pressures of reactants and products as reaction proceeds to equilibrium
3. Equilibrium (E): concentrations or pressures of reactants and products at equilibrium
or pressure for each species determined by stoichiometry of reaction and extent of reaction (x)
- For example, for reaction $A + 2B \rightleftharpoons C + D$ , if initial concentration of A is $[A]_0$ and extent of reaction is x, then change in concentration of A is -x, change in concentration of B is -2x, change in concentration of C is +x, and change in concentration of D is +x
Equilibrium concentrations or pressures are sum of initial concentrations or pressures and changes in concentrations or pressures
- For example, for reaction $A + 2B \rightleftharpoons C + D$ , if initial concentration of A is $[A]_0$ and extent of reaction is x, then of A is $[A] = [A]_0 - x$ , equilibrium concentration of B is $[B] = [B]_0 - 2x$ , equilibrium concentration of C is $[C] = x$ , and equilibrium concentration of D is $[D] = x$
Equilibrium concentrations or pressures substituted into equilibrium constant expression, and resulting equation solved for x
- For example, for reaction $A + 2B \rightleftharpoons C + D$ with $K = 3$ , $[A]_0 = 0.1 M$ , and $[B]_0 = 0.2 M$ , equilibrium constant expression is $3 = \frac{(x)(x)}{(0.1-x)(0.2-2x)^2}$ , which can be solved for x using quadratic formula or other methods
Value of x then used to calculate equilibrium concentrations or pressures of all species
- For example, if x = 0.0577 M for reaction $A + 2B \rightleftharpoons C + D$ with $[A]_0 = 0.1 M$ and $[B]_0 = 0.2 M$ , then equilibrium concentrations are $[A] = 0.1 - 0.0577 = 0.0423 M$ , $[B] = 0.2 - 2(0.0577) = 0.0846 M$ , $[C] = 0.0577 M$ , and $[D] = 0.0577 M$

Multiple equilibria systems

In system with multiple equilibria, concentrations or pressures of species involved in each equilibrium affected by other equilibria
To solve for equilibrium concentrations or pressures in system with multiple equilibria:
1. Write equilibrium constant expressions for each equilibrium
2. Use ICE table method to set up equations for equilibrium concentrations or pressures of each species in terms of extent of reaction variables (x, y, etc.)
3. Substitute equilibrium concentrations or pressures into equilibrium constant expressions
4. Solve resulting system of equations for extent of reaction variables
5. Use values of extent of reaction variables to calculate equilibrium concentrations or pressures of all species
For example, consider system with two equilibria: $A \rightleftharpoons B$ with $K_1 = 2$ and $B \rightleftharpoons C$ with $K_2 = 3$ . If initial concentration of A is $[A]_0 = 0.1 M$ and initial concentrations of B and C are zero, then ICE tables for each equilibrium are: | Equilibrium 1 | A | $\rightleftharpoons$ | B | |:--|:--|:--|:--| | Initial | 0.1 | 0 | 0 |
| Change | -x | | +x | | Equilibrium | 0.1-x | | x |

Equilibrium 2	B	$\rightleftharpoons$	C
Initial	x		0
Change	-y		+y
Equilibrium	x-y		y

Equilibrium constant expressions are $K_1 = \frac{[B]}{[A]} = \frac{x}{0.1-x} = 2$ and $K_2 = \frac{[C]}{[B]} = \frac{y}{x-y} = 3$ . Solving system of equations gives x = 0.0667 M and y = 0.0429 M. Therefore, equilibrium concentrations are $[A] = 0.1 - 0.0667 = 0.0333 M$ , $[B] = 0.0667 - 0.0429 = 0.0238 M$ , and $[C] = 0.0429 M$ .

Equilibrium in acid-base reactions

are type of equilibrium reaction in which acid and base react to form salt and water
Equilibrium constant for acid-base reaction called acid dissociation constant (Ka) for forward reaction or for reverse reaction
- For general acid dissociation reaction $HA \rightleftharpoons H^+ + A^-$ $H A ⇌ H^{+} + A^{-}$ , acid dissociation constant expression is $K_a = \frac{[H^+][A^-]}{[HA]}$ $K_{a} = \frac{[ H ^{+} ] [ A ^{-} ]}{[ H A ]}$
  - $[HA]$ , $[H^+]$ , and $[A^-]$ represent molar concentrations of undissociated acid, hydrogen ion, and conjugate base respectively
- For general base dissociation reaction $B + H_2O \rightleftharpoons BH^+ + OH^-$ $B + H_{2} O ⇌ B H^{+} + O H^{-}$ , base dissociation constant expression is $K_b = \frac{[BH^+][OH^-]}{[B]}$ $K_{b} = \frac{[ B H ^{+} ] [ O H ^{-} ]}{[ B ]}$
  - $[B]$ , $[BH^+]$ , and $[OH^-]$ represent molar concentrations of base, conjugate acid, and hydroxide ion respectively
pH of solution at equilibrium can be calculated using equilibrium concentrations of $H^+$ $H^{+}$ and $OH^-$ $O H^{-}$
- $pH = -\log[H^+]$ $p H = - lo g [H^{+}]$
  - For example, if $[H^+] = 1 \times 10^{-7} M$ , then $pH = -\log(1 \times 10^{-7}) = 7$
- $pOH = -\log[OH^-]$ $pO H = - lo g [O H^{-}]$
  - For example, if $[OH^-] = 1 \times 10^{-7} M$ , then $pOH = -\log(1 \times 10^{-7}) = 7$
- $pH + pOH = 14$ $p H + pO H = 14$ at 25°C
  - For example, if $pH = 7$ , then $pOH = 14 - 7 = 7$
ICE table method can be used to solve for equilibrium concentrations of $H^+$ $H^{+}$ and $OH^-$ $O H^{-}$ in acid-base reaction, and then pH can be calculated
- For example, for dissociation of 0.1 M acetic acid ( $CH_3COOH$ ) with $K_a = 1.8 \times 10^{-5}$ , ICE table is: | | $CH_3COOH$ | $\rightleftharpoons$ | $H^+$ | + | $CH_3COO^-$ | |:--|:--|:--|:--|:--|:--| | Initial | 0.1 | | 0 | | 0 | | Change | -x | | +x | | +x | | Equilibrium | 0.1-x | | x | | x |

Equilibrium constant expression is $K_a = \frac{(x)(x)}{0.1-x} = 1.8 \times 10^{-5}$ . Solving for x gives x = $1.34 \times 10^{-3} M$ . Therefore, $[H^+] = 1.34 \times 10^{-3} M$ and $pH = -\log(1.34 \times 10^{-3}) = 2.87$ .

Key Terms to Review (35)

Acid dissociation constant ka: The acid dissociation constant, denoted as $k_a$, is a numerical value that quantifies the strength of an acid in solution by measuring its tendency to donate protons ($H^+$ ions$). A higher $k_a$ value indicates a stronger acid, meaning it dissociates more completely in water. Understanding $k_a$ is crucial for calculating equilibrium concentrations in acid-base reactions.

Acid-base reactions: Acid-base reactions are chemical processes that involve the transfer of protons (H$^+$) between reactants. In these reactions, acids donate protons, while bases accept them, leading to the formation of conjugate acids and bases. The understanding of acid-base reactions is crucial for calculating equilibrium concentrations, as it helps predict how changes in concentration affect the position of equilibrium in a chemical system.

Atm for gases: An atmosphere (atm) is a unit of pressure defined as being precisely equal to 101,325 pascals. It is commonly used in chemistry to express the pressure of gases in reactions and can significantly influence the behavior and equilibrium of gaseous systems.

Base Dissociation Constant (Kb): The base dissociation constant, denoted as Kb, measures the strength of a base in solution by quantifying its ability to accept protons from water and form hydroxide ions. It is a vital concept in understanding acid-base equilibria and helps in calculating the equilibrium concentrations of species in a reaction involving a weak base. The larger the Kb value, the stronger the base, which directly influences the pH of the solution and the extent of dissociation at equilibrium.

Change in concentration: Change in concentration refers to the variation in the amount of a substance present in a given volume of solution over time. It is an essential concept in understanding how reactions reach equilibrium, as it helps describe the shifts that occur when reactants are converted into products or vice versa.

Chemical Equilibrium: Chemical equilibrium is a state in a reversible reaction where the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products over time. This balance allows for a dynamic process where reactants are continuously converted to products and vice versa, without any net change in concentration. Understanding this concept is crucial for relating it to spontaneity and energy changes in reactions, as well as determining equilibrium concentrations in various chemical scenarios.

Chemical equilibrium: Chemical equilibrium is the state in which the concentrations of reactants and products in a chemical reaction remain constant over time, indicating that the forward and reverse reactions occur at equal rates. This balance reflects a dynamic process where the reactants are continuously converting to products and vice versa, making it essential for understanding reaction behavior and spontaneity in thermodynamics.

Common ion effect: The common ion effect refers to the reduction in the solubility of an ionic compound when a solution already contains one of the ions present in that compound. This phenomenon occurs due to Le Chatelier's principle, where the addition of a common ion shifts the equilibrium position, favoring the formation of solid precipitate rather than keeping the ionic compound dissolved in solution. It is significant in understanding precipitation reactions, calculating solubility product constants, and determining equilibrium concentrations.

Concentration change: Concentration change refers to the alteration in the amount of reactants or products in a chemical system at equilibrium, impacting the system's position according to Le Chatelier's Principle. When the concentration of either reactants or products is modified, the equilibrium will shift to counteract that change, either favoring the forward or reverse reaction to restore balance. Understanding this concept is crucial for calculating new equilibrium concentrations when disturbances occur.

Concentration changes: Concentration changes refer to the variations in the amounts of reactants and products in a chemical equilibrium system. These changes can affect the position of equilibrium and are central to understanding how systems respond to stresses, such as the addition or removal of substances. Recognizing how these changes impact equilibrium constants is essential for predicting the behavior of reactions under different conditions.

Equilibrium concentration: Equilibrium concentration refers to the concentrations of reactants and products in a chemical reaction when the rates of the forward and reverse reactions are equal, resulting in no net change in their amounts over time. This state is critical for understanding how substances behave under specific conditions, particularly when discussing solubility and equilibrium systems. It allows chemists to predict how changes in conditions can shift the balance of reactions, such as when a system reaches solubility limits or calculating how much of a substance will dissolve.

Equilibrium concentrations: Equilibrium concentrations refer to the concentrations of reactants and products in a chemical reaction that has reached a state of balance, where the rate of the forward reaction equals the rate of the reverse reaction. This concept is crucial for understanding how changes in conditions affect the position of equilibrium and the concentrations of substances involved. When a system is at equilibrium, the concentrations remain constant over time, even though both reactions continue to occur.

Equilibrium Constant (k): The equilibrium constant (k) is a numerical value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given chemical reaction at a specific temperature. It provides insight into the extent to which a reaction favors the formation of products or reactants, indicating whether the reaction is more product-favored or reactant-favored. A larger value of k suggests that the products are favored, while a smaller value indicates that reactants are favored.

Equilibrium constant expression: The equilibrium constant expression is a mathematical formula that relates the concentrations of reactants and products at equilibrium for a reversible chemical reaction. It allows us to quantify the ratio of the concentration of products to reactants, raised to the power of their stoichiometric coefficients. This expression is crucial for calculating equilibrium concentrations, as it provides a means to predict how far a reaction will proceed under specific conditions.

Equilibrium constant k: The equilibrium constant k is a numerical value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given chemical reaction. It provides insight into the extent of a reaction and helps predict the concentrations of substances when the system reaches equilibrium. The value of k is temperature-dependent and plays a crucial role in understanding how changes in conditions affect a reaction's position of equilibrium.

Equilibrium pressures: Equilibrium pressures refer to the partial pressures of gases in a chemical reaction at equilibrium, which remain constant over time as the rates of the forward and reverse reactions are equal. Understanding equilibrium pressures is essential for calculating equilibrium concentrations, as they are directly related to the concentration of reactants and products through the ideal gas law and the equilibrium constant expression. This concept is crucial in predicting how changes in conditions like temperature or volume affect the system's behavior.

Henderson-Hasselbalch equation: The Henderson-Hasselbalch equation is a mathematical formula used to relate the pH of a buffer solution to the concentration of its acidic and basic components. It provides a way to calculate the pH based on the ratio of the concentrations of the conjugate base and the weak acid, making it a vital tool for understanding buffer solutions and their behavior in chemical equilibria.

Henderson-Hasselbalch Equation: The Henderson-Hasselbalch equation is a mathematical formula used to calculate the pH of a buffer solution based on the concentration of its acidic and basic components. It connects the pH of a solution to the pKa of the acid and the ratio of the concentrations of the conjugate base to the acid, making it a vital tool for understanding buffer systems, acid-base titrations, and equilibrium in various chemical reactions.

Heterogeneous equilibria: Heterogeneous equilibria refer to the state of balance in a chemical reaction where the reactants and products are present in different phases, such as solids, liquids, and gases. This type of equilibrium is important because it emphasizes how the concentrations of substances in various phases impact the overall equilibrium constant and how calculations for equilibrium concentrations must account for these differences in states.

Ice table: An ice table is a structured tool used in chemistry to track the concentrations of reactants and products during a chemical equilibrium process. It helps in organizing the initial concentrations, changes that occur as the reaction progresses, and the final equilibrium concentrations, making it easier to calculate and understand the relationships between species involved in the reaction.

Ice table method: The ice table method is a systematic approach used to calculate equilibrium concentrations of reactants and products in a chemical reaction. It involves setting up an 'ICE' table, which stands for Initial, Change, and Equilibrium concentrations, allowing you to clearly organize the information and perform calculations related to the equilibrium state of the reaction.

Initial concentrations: Initial concentrations refer to the amounts of reactants and products present in a chemical system at the start of a reaction, before any changes due to the reaction itself occur. Understanding initial concentrations is crucial for determining how a system reaches equilibrium and for calculating equilibrium concentrations using various methods such as an ICE table, which organizes initial concentrations, changes in concentrations, and equilibrium concentrations.

Le Chatelier's Principle: Le Chatelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium shifts to counteract the change and re-establish equilibrium. This principle is crucial for understanding how changes in concentration, temperature, and pressure affect chemical systems and their equilibria.

Molarity (m): Molarity is a way to express the concentration of a solution, defined as the number of moles of solute per liter of solution. This measurement is essential when calculating equilibrium concentrations because it helps to quantify how much of a substance is present in a given volume, allowing for comparisons and predictions of chemical behavior in reactions at equilibrium.

Multiple equilibria systems: Multiple equilibria systems refer to situations in chemical reactions where more than one equilibrium state can exist, depending on the concentrations of reactants and products. These systems highlight how different factors can lead to different distributions of chemical species at equilibrium, illustrating the dynamic nature of chemical reactions. Understanding these systems is crucial for calculating equilibrium concentrations accurately, as they emphasize the role of initial conditions and changes in concentration on the final equilibrium state.

Pressure: Pressure is defined as the force exerted per unit area on a surface, commonly measured in units such as atmospheres (atm), pascals (Pa), or mmHg. It plays a crucial role in influencing chemical reactions, state changes, and equilibria by affecting how particles collide and interact, which can ultimately drive the direction of chemical processes and affect their thermodynamic properties.

Reaction quotient q: The reaction quotient, denoted as q, is a mathematical expression that relates the concentrations of the reactants and products in a chemical reaction at any point in time. It serves as a tool to determine the direction in which a reaction will proceed to reach equilibrium, comparing the current state of the system to its equilibrium state. By evaluating q, one can predict whether reactants will convert to products or vice versa, providing insight into how far a reaction has progressed.

Reversible Reactions: Reversible reactions are chemical processes in which the reactants can be converted into products and, under certain conditions, the products can be converted back into reactants. This dynamic process allows for an ongoing exchange between reactants and products, which is essential in understanding how systems reach equilibrium and how equilibrium constants can be applied to quantify the concentrations of various species at that state.

Reversible reactions: Reversible reactions are chemical processes that can proceed in both the forward and reverse directions, allowing the reactants to form products and the products to convert back into reactants. This dynamic balance is essential for understanding how systems respond to changes and maintain equilibrium. The concept of reversible reactions is critical when discussing factors that affect equilibrium and calculating concentrations of substances at equilibrium.

Shift to the left: A shift to the left refers to the movement of a chemical equilibrium towards the reactants' side, indicating an increase in the concentrations of reactants and a decrease in the concentrations of products. This phenomenon can occur due to changes in concentration, temperature, or pressure, affecting how the equilibrium position responds to those changes. Understanding this shift is essential for calculating equilibrium concentrations and predicting the direction of a reaction's progression.

Shift to the right: A shift to the right in a chemical equilibrium signifies an increase in the concentration of products relative to reactants, leading to a higher product formation. This shift occurs when factors such as changes in concentration, temperature, or pressure favor the forward reaction, thus altering the equilibrium position. Understanding this concept is crucial for calculating equilibrium concentrations and predicting the outcomes of chemical reactions.

Solubility Product Constant (Ksp): The solubility product constant, Ksp, is an equilibrium constant that reflects the solubility of a sparingly soluble ionic compound in water. It is calculated from the concentrations of the ions in a saturated solution at a specific temperature and is crucial for understanding how much of a compound can dissolve in a solution before reaching saturation.

Temperature: Temperature is a measure of the average kinetic energy of particles in a substance, which directly influences how substances interact and react with one another. It plays a crucial role in determining reaction rates, the spontaneity of reactions, equilibrium positions, and the behavior of acids and bases.

Van 't Hoff Equation: The van 't Hoff equation is a mathematical relationship that connects the change in the equilibrium constant of a reaction to the change in temperature. It shows how the equilibrium position shifts with temperature changes and helps in understanding how various factors affect the concentrations of reactants and products at equilibrium.

Van 't Hoff equation: The van 't Hoff equation relates the change in the equilibrium constant of a reaction to the change in temperature, highlighting the temperature dependence of chemical equilibria. This equation is crucial for understanding how variations in temperature can affect the concentrations of reactants and products at equilibrium, offering insights into the thermodynamic properties of reactions.

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Practice QuizGlossary

Practice Quiz Glossary

2.3 Calculating equilibrium concentrations

Equilibrium Concentrations and Pressures

Calculations with equilibrium constant

Top images from around the web for Calculations with equilibrium constant

Top images from around the web for Calculations with equilibrium constant

ICE table method

Multiple equilibria systems

Equilibrium in acid-base reactions

Key Terms to Review (35)

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AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.

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