Name: finding kc from equilibrium data
Uploaded: 2020-09-24T15:06:50.000Z
Duration: 2 min 46 s
Channel: JoVE

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Calculating the Equilibrium Constant

The equilibrium constant, Kc, can be determined by substituting the corresponding values into the equilibrium constant expression if the concentrations of all the reactants and products at equilibrium are known.
A gaseous mixture of sulfur dioxide and oxygen at 530 &#176;C is allowed to react according to the reaction shown. At equilibrium, the mixture contains 0.10 molar of sulfur dioxide, 0.15 molar of oxygen, and 10.88 molar of sulfur trioxide. 
By substituting the values into the equilibrium expression, the Kc equals 7.9 &#215; 104. 
The Kc can also be calculated as long as the initial concentration of all of the components and the equilibrium concentration of at least one compound is known.
The unknown equilibrium concentrations can then be calculated using the reaction stoichiometry. An ICE table is used to organize the information for the initial, change, and equilibrium concentrations of the reaction.
When a reaction mixture containing 0.11 molar nitrogen and 0.36 molar hydrogen is allowed to reach equilibrium at 500 &#176;C, it produces 0.020 molar ammonia at equilibrium. To calculate the Kc, the equilibrium concentrations of the nitrogen and hydrogen need to be determined.
The stoichiometry of the reaction shows that 1 mole of nitrogen gas and 3 moles of hydrogen gas are required to produce 2 moles of ammonia gas.
The change, x, when multiplied by the coefficients of the reactants and products, denotes the concentration of the reactants consumed and the concentration of the product produced to reach equilibrium. 
Since 2x equals 0.020, x equals 0.010. The equilibrium concentration of nitrogen and hydrogen can then be determined by subtracting the respective concentration change from their initial concentration which equals 0.10 and 0.33 molar, respectively.
Substituting equilibrium concentrations in the Kc expression, the Kc equals 0.11.
The Kp for reactions involving gases can be calculated using an ICE table and the equilibrium expression written with partial pressures.

calculating the equilibrium constant

The equilibrium constant for a reaction is calculated from the equilibrium concentrations (or pressures) of its reactants and products. If these concentrations are known, the calculation simply involves their substitution into the Kc expression.
For example, gaseous nitrogen dioxide forms dinitrogen tetroxide according to this equation:
<img alt="DNA structure diagram with deoxyribose, phosphate, adenine, illustrating genetic information coding." src="/files/ftp_upload/11388/11388_Equation_1.png" style="text-align: center; height: 50px;" data-altupdatedat="1761830439000" data-alt="Eq1" />
When 0.10 mol NO2 is added to a 1.0-L flask at 25 &#176;C, the concentration changes so that at equilibrium, [NO2] = 0.016 M and [N2O4] = 0.042 M. The value of the equilibrium constant for the reaction can be calculated as follows:
<img alt="Chemical structure diagram of tetrodotoxin molecule (C11H17N3O8), neurotoxin study." src="/files/ftp_upload/11388/11388_Equation_2.png" style="text-align: center; height: 90px;" data-altupdatedat="1761830439000" data-alt="Eq2" />
A slightly more challenging example is provided next, in which the reaction stoichiometry is used to derive equilibrium concentrations from the information provided. The basic strategy of this computation is helpful for many types of equilibrium computations and relies on the use of terms for the reactant and product concentrations initially present, for how they change as the reaction proceeds, and for what they are when the system reaches equilibrium. The acronym ICE is commonly used to refer to this mathematical approach, and the concentration terms are usually gathered in a tabular format called an ICE table.
Calculation of an Equilibrium Constant
Iodine molecules react reversibly with iodide ions to produce triiodide ions.
<img alt="Chemical reaction diagram, SN1 mechanism, tertiary alkyl halide, nucleophilic substitution process." src="/files/ftp_upload/11388/11388_Equation_3.png" style="text-align: center; height: 50px;" data-altupdatedat="1761830439000" data-alt="Eq3" />
If a solution with the concentrations of I2 and I&#8722; both equal to 1.000 &#215; 10&#8722;3 M before reaction gives an equilibrium concentration of I2 of 6.61 &#215; 10&#8722;4 M, what is the equilibrium constant for the reaction?
To calculate the equilibrium constants, equilibrium concentrations are needed for all the reactants and products:
<img alt="DNA replication process diagram with enzymes like DNA polymerase and helicase." src="/files/ftp_upload/11388/11388_Equation_4.png" style="text-align: center; height: 90px;" data-altupdatedat="1761830439000" data-alt="Eq4" />
The initial concentrations of the reactants and the equilibrium concentration of the product are provided. This information can be used to derive terms for the equilibrium concentrations of the reactants, presenting all the information in 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;"> I2 (aq) </td>
			<td style="color: black; border: 1px solid black; text-align: center;">I&#8722; (aq) </td>
			<td style="color: black; border: 1px solid black; text-align: center;"> I3&#8722; (aq) </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;">1.000 &#215; 10&#8722;3</td>
			<td style="color: black; border: 1px solid black; text-align: center;">1.000 &#215; 10&#8722;3</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;">&#8722;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;"> 1.000 &#215; 10&#8722;3 &#8722; x </td>
			<td style="color: black; border: 1px solid black; text-align: center;"> 1.000 &#215; 10-3 &#8722; x </td>
			<td style="color: black; border: 1px solid black; text-align: center;">x</td>
		</tr>
	</tbody>
</table>
At equilibrium the concentration of I2 is 6.61 &#215; 10&#8722;4 M so that
<img alt="Optical labels for fluorescence imaging; diagram of static quenching mechanism and absorption." src="/files/ftp_upload/11388/11388_Equation_5.png" style="text-align: center; height: 90px;" data-altupdatedat="1761830439000" data-alt="Eq5" />
The ICE table may now be updated with numerical values for all its concentrations:
<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;">I2 (aq) </td>
			<td style="color: black; border: 1px solid black; text-align: center;">I&#8722; (aq) </td>
			<td style="color: black; border: 1px solid black; text-align: center;">I3&#8722; (aq)</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;"> 1.000 &#215; 10&#8722;3 </td>
			<td style="color: black; border: 1px solid black; text-align: center;"> 1.000 &#215; 10&#8722;3 </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;3.39 &#215; 10&#8722;4 </td>
			<td style="color: black; border: 1px solid black; text-align: center;"> &#8722;3.39 &#215; 10&#8722;4 </td>
			<td style="color: black; border: 1px solid black; text-align: center;"> +3.39 &#215; 10-4 </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;"> 6.61 &#215; 10&#8722;4 </td>
			<td style="color: black; border: 1px solid black; text-align: center;"> 6.61 &#215; 10&#8722;4 </td>
			<td style="color: black; border: 1px solid black; text-align: center;"> 3.39 &#215; 10&#8722;4 </td>
		</tr>
	</tbody>
</table>
Finally, the equilibrium concentrations can be substituted into the Kc expression and solved:
<img alt="Bernoulli's equation, energy conservation in fluid dynamics; fluid flow diagram, pressure analysis." src="/files/ftp_upload/11388/11388_Equation_6.png" style="text-align: center; height: 90px;" data-altupdatedat="1761830439000" data-alt="Eq6" />
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>.

The equilibrium constant for a reaction is calculated from the equilibrium concentrations (or pressures) of its reactants and products. If these ...

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Chemical Equilibrium

KEY TERMS AND CONCEPTS

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 calculate the equilibrium constant for the reaction.

A more advanced example uses reaction stoichiometry to find equilibrium concentrations from the information given. This method is useful for many equilibrium calculations. It tracks the amount present at the start, how it changes as the reaction proceeds, and the amount present at equilibrium. The acronym ICE is used for this approach, and the values are often organized in an ICE table.

The iodine example shows how this works. I2 reacts reversibly with iodide ions to form triiodide ions. If a solution starts with 1.000 × 10^-3 M I2 and 1.000 × 10^-3 M I−, and the equilibrium concentration of I2 is 6.61 × 10^-4 M, the equilibrium constant can be found for the reaction.

To do this, the initial concentrations of the reactants and the equilibrium concentration of the product are used to build an ICE table. The table shows I2, I−, and I3− with initial, change, and equilibrium entries. From the given equilibrium value for I2, the other concentrations can be calculated, including 6.61 × 10^-4 M for I2 and I− and 3.39 × 10^-4 M for I3−.

Once the equilibrium concentrations are known, they are substituted into the Kc expression and solved. This same strategy links the ICE table to the final equilibrium constant. It is a practical way to handle equilibrium problems in chemistry.

Finding Kc from Equilibrium Data

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...

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...

calculating equilibrium concentrations

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...

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

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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

Use equilibrium concentrations and ICE tables to find Kc in chemistry. See how nitrogen dioxide and iodine examples connect data to the equilibrium constant.

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Finding Kc from Equilibrium Data

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