Name: equilibrium concentrations from an ice table
Uploaded: 2020-09-24T15:06:50.000Z
Duration: 2 min 5 s
Channel: JoVE

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North Carolina K-12 Science Standard Course of Study

9-12

Chemistry

Matter and its Interactions

PS.Chm.5.2

Calculating Equilibrium Concentrations

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 &#8722;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.

calculating equilibrium concentrations

Being able to calculate equilibrium concentrations is essential to many areas of science and technology&#8212;for example, in the formulation and dosing of pharmaceutical products. After a drug is ingested or injected, it is typically involved in several chemical equilibria that affect its ultimate concentration in the body system of interest. Knowledge of the quantitative aspects of these equilibria is required to compute a dosage amount that will solicit the desired therapeutic effect.
A more challenging type of equilibrium calculation can be one in which equilibrium concentrations are derived from initial concentrations and an equilibrium constant. For these calculations, a four-step approach is typically useful:
<ol>
	<li>Identify the direction in which the reaction will proceed to reach equilibrium.</li>
	<li>Develop an ICE table.</li>
	<li>Calculate the concentration changes and, subsequently, the equilibrium concentrations.</li>
	<li>Confirm the calculated equilibrium concentrations.</li>
</ol>
Calculation of Equilibrium Concentrations
Under certain conditions, the equilibrium constant Kc for the decomposition of PCl5(g) into PCl3(g) and Cl2(g) is 0.0211. The above procedure can be used to determine the equilibrium concentrations of PCl5, PCl3, and Cl2 in a mixture that initially contained only PCl5 at a concentration of 1.00 M.
Step 1. Determine the direction the reaction proceeds.
The balanced equation for the decomposition of PCl5 is
<img alt="Thermodynamics, entropy change formula &#916;S=qrev/T, diagram explaining energy transfer concepts." src="/files/ftp_upload/11390/11390_Equation%201.png" style="text-align: center; height: 50px;" data-altupdatedat="1754904545000" data-alt="Frictional force diagram; &#931;F=0; block on inclined plane; static equilibrium analysis; physics study." />
Because only the reactant is present initially, Qc = 0, and the reaction will proceed to the right.
Step 2. Develop an ICE table.
<table style="margin-left: auto; margin-right: auto;">
	<tbody>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;"></td>
			<td style="color: black; border: 1px solid black; text-align: center;"> PCl5 (g) </td>
			<td style="color: black; border: 1px solid black; text-align: center;"> PCl3 (g) </td>
			<td style="color: black; border: 1px solid black; text-align: center;"> Cl2 (g) </td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Initial Concentration (M)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">1.00</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0</td>
			<td style="color: black; border: 1px solid black; text-align: center;">0</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Change (M)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">&#8722;x</td>
			<td style="color: black; border: 1px solid black; text-align: center;">+x</td>
			<td style="color: black; border: 1px solid black; text-align: center;">+x</td>
		</tr>
		<tr>
			<td style="color: black; border: 1px solid black; text-align: center;">Equilibrium Concentration (M)</td>
			<td style="color: black; border: 1px solid black; text-align: center;">1.00 &#8722; x</td>
			<td style="color: black; border: 1px solid black; text-align: center;">x</td>
			<td style="color: black; border: 1px solid black; text-align: center;">x</td>
		</tr>
	</tbody>
</table>
Step 3. Solve for the change and the equilibrium concentrations.
Substituting the equilibrium concentrations into the equilibrium constant equation gives
<img alt="Chemical structure diagram, schematic of a molecular compound with multi-ring configuration." src="/files/ftp_upload/11390/11390_Equation%202.png" style="text-align: center; height: 170px;" data-altupdatedat="1754904545000" data-alt="DNA sequencing process chart; illustrates base pairing, replication, Sanger method stages, labeled diagram." />
An equation of the form ax2 + bx + c = 0 can be rearranged to solve for x:
<img alt="Equilibrium of forces diagram, &#931;F=0; illustrates static balance with vectors and forces labeled." src="/files/ftp_upload/11390/11390_Equation%203.png" style="text-align: center; height: 90px;" data-altupdatedat="1754904545000" data-alt="Static equilibrium concept; &#931;Fx=0 diagram illustrating force balance in mechanical systems." />
In this case, a = 1, b = 0.0211, and c = &#8722;0.0211. Substituting the appropriate values for a, b, and c yields:
<img alt="Static equilibrium equations, &#931;Fx=0, &#931;Fy=0, diagram with force vectors for educational use." src="/files/ftp_upload/11390/11390_Equation%204.png" style="text-align: center; height: 90px;" data-altupdatedat="1754904545000" data-alt="static equilibrium, &#931;Fx=0 equation, formula diagram; physics concept, educational use" />
The two roots of the quadratic are, therefore,
<img alt="DNA transcription process, sequence of bases diagram, genetic information flow, biological mechanisms." src="/files/ftp_upload/11390/11390_Equation%205.png" style="text-align: center; height: 50px;" data-altupdatedat="1754904545000" data-alt="Heron's formula diagram illustrating area calculation of a triangle using side lengths." />
For this scenario, only the positive root is physically meaningful (concentrations are either zero or positive), and so x = 0.135 M. The equilibrium concentrations are
<img alt="Balanced chemical equation, CaO + H&#8322;O &#8594; Ca(OH)&#8322;, exothermic reaction, chemical formula." src="/files/ftp_upload/11390/11390_Equation%206.png" style="text-align: center; height: 130px;" data-altupdatedat="1754904545000" data-alt="Stirling engine diagram showing thermodynamic cycle, gas expansion, piston motion, energy conversion." />
Step 4. Confirm the calculated equilibrium concentrations.
Substitution into the expression for Kc (to check the calculation) gives
<img alt="Lewis structure diagram, carbonatoborate anion, CO3&#8211;Bo3, bond arrangement visualization, chemistry study." src="/files/ftp_upload/11390/11390_Equation%207.png" style="text-align: center; height: 90px;" data-altupdatedat="1754904545000" data-alt="Static equilibrium; &#931;Fx=0, &#931;&#964;=0; free body diagram; beam balance; forces and torques analysis." />
The equilibrium constant calculated from the equilibrium concentrations is equal to the value of Kc given in the problem (when rounded to the proper number of significant figures).
This text has been adapted from <a href="https://openstax.org/books/chemistry-2e/pages/13-4-equilibrium-calculations">Openstax, Chemistry 2e, Section 13.4 Equilibrium Calculations</a><a href="https://openstax.org/books/chemistry-2e/pages/13-4-equilibrium-calculations">.</a>

Being able to calculate equilibrium concentrations is essential to many areas of science and technology&#8212;for example, in the formulation and dosing ...

Education

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Chemical Equilibrium

KEY TERMS AND CONCEPTS

equilibrium concentrations from an ice table

Equilibrium concentrations can be found from initial concentrations and an equilibrium constant. This skill matters in many areas of science and technology, including pharmaceutical product formulation and dosing. After a drug is ingested or injected, it may take part in several chemical equilibria that change its final concentration in the body system of interest. Scientists use these quantitative equilibrium relationships to help calculate a dosage that will produce the desired therapeutic effect.

A common approach is needed when equilibrium concentrations must be derived from starting values and a known Kc. The first step is to decide which way the reaction will move to reach equilibrium. Next, an ICE table is set up. ICE stands for initial, change, and equilibrium. After that, the concentration changes are solved and used to find the equilibrium concentrations. The final step is to check the answer.

The decomposition of PCl5(g) into PCl3(g) and Cl2(g) shows how this works. In the example, Kc is 0.0211, and the mixture starts with only PCl5 at 1.00 M. Because only the reactant is present at the start, Qc equals 0, so the reaction moves to the right. The ICE table gives an initial concentration of 1.00 M for PCl5 and 0 for the products, with changes of -x, +x, and +x.

Substituting the equilibrium values into the Kc expression leads to a quadratic equation. Solving it gives two roots, but only the positive root is physically meaningful because concentrations cannot be negative. In this case, x = 0.135 M. The equilibrium concentrations are then found for PCl5, PCl3, and Cl2. A final substitution into the Kc expression confirms that the calculated value matches the given equilibrium constant when rounded correctly.

Equilibrium Concentrations from an ICE Table

equilibrium-concentrations-from-an-ice-table

the equilibrium constant

Chemical Equilibrium and Kc Rules

Chemical equilibrium and the equilibrium constant Kc describe how reactants and products are balanced in a reaction. In the oxidation of sulfur dioxide, a mixture that starts with reactants only has no product at first. As the reaction moves forward toward equilibrium, reactant concentrations decrease and product concentration increases. When equilibrium is reached, the concentrations of both stay constant. A reaction can also begin with only products present. In that case, the reaction moves...

le chatelier's principle: changing concentration

le-chatelier-s-principle-changing-concentration

Shifting Equilibrium by Changing Concentration

Chemical equilibrium is a dynamic balance. At equilibrium, the forward and reverse reactions happen at equal rates. If the system is stressed in a way that changes one rate more than the other, it is no longer at equilibrium and will shift until balance is restored. This behavior is described by Le Châtelier’s principle. Changes in concentration are a major stress on an equilibrium system. Reaction rates depend mainly on concentration and temperature. For that reason, changing the amount of a...

homogeneous equilibria for gaseous reactions

homogeneous-equilibria-for-gaseous-reactions

Relating Kc and Kp in Gas Equilibria

Gas-phase equilibrium can be written using either concentration or pressure. The equilibrium constant may be shown as Kc, which uses molar concentration, or as Kp, which uses partial pressure of the reactants and products. The link between Kc and Kp comes from the ideal gas equation and the definition of molarity. Molarity is the number of moles divided by volume. In the ideal gas equation, P stands for partial pressure, V for volume, n for number of moles, R for the gas constant, and T for...

calculating the equilibrium constant

Finding Kc from Equilibrium Data

The equilibrium constant, Kc, can be found from the equilibrium concentrations of reactants and products. When those concentrations are known, the calculation is straightforward. The values are placed into the Kc expression for the reaction. One example uses nitrogen dioxide and dinitrogen tetroxide. When 0.10 mol NO2 is added to a 1.0-L flask at 25 °C, the concentrations change until equilibrium is reached. At equilibrium, [NO2] is 0.016 M and [N2O4] is 0.042 M, and these values are used to...

reaction quotient

Using Q to Track Equilibrium Changes

Reaction quotient Q helps track how far a reversible reaction has moved toward equilibrium. For a balanced reaction such as m A + n B ⇌ x C + y D, Q comes directly from the stoichiometric coefficients in the equation. When concentrations are used, the expression is written as Qc. For gases, a similar form uses partial pressures. These expressions use relative concentration and pressure values, not absolute values. That means reaction quotients are dimensionless and have no units. As a reaction...

Equilibrium concentrations can be found from initial concentrations and an equilibrium constant. This skill matters in many areas of science and technology, including pharmaceutical product formulation and dosing. After a drug is ingested or injected, it may take part in several chemical equilibria that change its final concentration in the body system of interest. Scientists use these quantitative equilibrium relationships to help calculate a dosage that will produce the desired therapeutic...

dynamic equilibrium

Chemical Equilibrium in Reversible Reactions

Chemical equilibrium in reversible reactions happens when a reaction moves in both directions at the same time. A reversible reaction uses a double arrow to show that products can turn back into reactants. At equilibrium, the concentrations of reactants and products stay constant over time because the forward and reverse reaction rates are equal. The video uses the reversible decomposition of colorless dinitrogen tetroxide to brown nitrogen dioxide as an example. At time zero, there is finite...

le chatelier's principle: changing volume (pressure)

le-chatelier-s-principle-changing-volume-pressure

Gas Equilibrium Under Volume Changes

Gas-phase equilibrium can shift when the volume of the system changes. In these reactions, a change in pressure changes concentration because the partial pressure of an ideal gas is proportional to its molar concentration. That means pressure changes affect equilibrium in the same way as concentration changes. When the volume of a gas mixture changes, the concentrations of reactants and products change together. Since every gas in the equilibrium occupies the same space, the same volume change...

le chatelier's principle: changing temperature

le-chatelier-s-principle-changing-temperature

Le Chatelier's Principle in Heating and Cooling

Le Chatelier's principle helps explain how chemical equilibrium responds to heating and cooling. A system at equilibrium will shift to restore balance after a temperature change, but the equilibrium constant, K, will not stay the same. Instead, the mixture reaches a new equilibrium with a different composition. This temperature effect is different from a concentration change, which shifts equilibrium without changing K. To understand why temperature matters, the reaction can be written with...

the small x assumption

Estimating Equilibrium with Small Changes

A small equilibrium constant can make equilibrium calculations easier. In these reactions, the equilibrium position favors the reactants. When the initial reactant concentration is high and the Kc value is small, the change in concentration may be negligible. In that case, the equilibrium concentration is close to the initial concentration. This idea helps simplify weak acid and weak base problems. Chemists can assume that some equilibrium concentrations are equal to the initial concentrations.

key terms and concepts

Learn how to find equilibrium concentrations with an ICE table, use Kc, and check answers with a PCl5 decomposition example for high school chemistry.

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Equilibrium Concentrations from an ICE Table

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