Name: gas equilibrium under volume changes
Uploaded: 2020-09-24T15:06:51.000Z
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Le Chatelier's Principle: Changing Volume (Pressure)

Le Ch&#226;telier&#8217;s principle can be used to predict how a system at equilibrium would respond to the stress of a change in volume or pressure.
The volume of a gas is inversely proportional to its pressure; therefore, for a system at equilibrium, a decrease in volume increases the pressure and disturbs the equilibrium. In response, the equilibrium position will shift in a direction to minimize the stress.
The ideal gas law states that the pressure of a gas is directly proportional to the number of moles. Thus, the direction of the shift needed to restore equilibrium is dependent on the number of moles of gas particles on either side of the reaction.
As more moles of gas results in a higher pressure, an increase in pressure shifts the equilibrium position to the side with fewer moles to lower the pressure. Likewise, a decrease in pressure shifts the equilibrium position to the side with more moles of gas.
Consider a chemical equilibrium, where one mole of gaseous phosphorus pentachloride decomposes into one mole of phosphorus trichloride and one mole of chlorine gas&#8212;two total moles of product.
If the piston is pushed down, the volume of the equilibrium system decreases, increasing the pressure. This disturbs the equilibrium and results in Q greater than K. Thus, the equilibrium position shifts towards the reactants, with fewer moles of gas particles, in order to lower the pressure and restore equilibrium.
Conversely, pulling the piston up increases the volume and decreases the pressure. In this case, Q becomes smaller than K. In order to raise the pressure, the equilibrium position shifts towards the products, the side with the most moles of gas, and restores equilibrium.
Increasing the pressure by adding an inert gas to an equilibrium mixture at constant volume, does not affect the equilibrium because the partial pressures of the gaseous reactants and products remain unchanged.
For equilibrium systems with equal numbers of moles of gaseous reactants and products, such as the reaction between iodine gas and chlorine gas to produce iodine monochloride, a change in the volume of the system will have no effect on the equilibrium.

le chatelier's principle: changing volume (pressure)

For gas-phase equilibria, changes in the concentrations of reactants and products can occur with altered volume and pressure. The partial pressure, P, of an ideal gas is proportional to its molar concentration, M.
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So changes in the partial pressures of any reactant or product are essentially changes in concentrations; therefore, these changes yield the same effects on equilibria. Aside from adding or removing reactants or products, the pressures (concentrations) of species in a gas-phase equilibrium can also be changed by changing the volume occupied by the system. Since all species of a gas-phase equilibrium occupy the same volume, a given change in volume will cause the same change in concentration for both reactants and products. In order to discern what shift, if any, this type of stress will induce, the stoichiometry of the reaction must be considered.
At equilibrium, the reaction N2 (g) + O2 (g) &#8652; 2 NO (g) is described by the reaction quotient
<img alt="Chromatography process, diagram of distillation setup, liquid separation, chemical analysis." src="/files/ftp_upload/11392/11392_Equation%202.png" style="text-align: center; height: 70px;" data-altupdatedat="1761830439000" data-alt="Eq2" />
If the volume occupied by an equilibrium mixture of these species is decreased by a factor of 3, the partial pressures of all three species will be increased by a factor of 3:
<img alt="Kirchhoff's law circuit diagram with resistors, voltage sources; static equilibrium analysis." src="/files/ftp_upload/11392/11392_Equation%203.png" style="text-align: center; height: 70px;" data-altupdatedat="1761830439000" data-alt="Eq3" />
And so, changing the volume of this gas-phase equilibrium mixture does not result in a shift of the equilibrium.
A similar treatment of a different system, 2 SO2 (g) + O2 (g) &#8652; 2 SO3 (g), however, yields a different result:
<img alt="Chemical equilibrium graph; Le Chatelier&#8217;s principle; reaction quotient shifts; system response." src="/files/ftp_upload/11392/11392_Equation%204.png" style="text-align: center; height: 200px;" data-altupdatedat="1761830439000" data-alt="Eq4" />
In this case, the change in volume results in a reaction quotient smaller than the equilibrium constant, and so the equilibrium will shift right.
These results illustrate the relationship between the stoichiometry of a gas-phase equilibrium and the effect of a volume-induced pressure (concentration) change. If the total molar amounts of reactants and products are equal, as in the first example, a change in volume does not shift the equilibrium. If the molar amounts of reactants and products are different, a change in volume will shift the equilibrium in a direction that better &#8220;accommodates&#8221; the volume change. In the second example, three moles of reactant (SO2 and O2) yield two moles of product (SO3), and so decreasing the system volume causes the equilibrium to shift right since the forward reaction produces less gas (2 mol) than the reverse reaction (3 mol). Conversely, increasing the volume of this equilibrium system would result in a shift towards reactants.
This text has been adapted from <a href="https://openstax.org/books/chemistry-2e/pages/13-3-shifting-equilibria-le-chateliers-principle">Openstax, Chemistry 2e, Section 13.3 Shifting Equilibria: LeChatelier&#8217;s Principle</a>.

For gas-phase equilibria, changes in the concentrations of reactants and products can occur with altered volume and pressure. The partial pressure, P, of ...

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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 affects each species in the same way. To predict whether the equilibrium shifts, you must look at the reaction stoichiometry.

For the equilibrium N2(g) + O2(g) ⇌ 2 NO(g), decreasing the volume by a factor of 3 increases the partial pressures of all three gases by a factor of 3. In this case, the reaction quotient still matches the equilibrium position, so the equilibrium does not shift. The total moles of reactants and products are equal, and that is why the volume change has no effect.

A different result appears for 2 SO2(g) + O2(g) ⇌ 2 SO3(g). Here, decreasing the volume makes the reaction quotient smaller than the equilibrium constant, so the equilibrium shifts right. Three moles of reactant form two moles of product, so the forward reaction makes less gas. Increasing the volume would shift this system toward the reactants.

Gas Equilibrium Under Volume Changes

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

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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

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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...

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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...

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Equilibrium Concentrations from an ICE Table

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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...

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

Learn how changing volume changes pressure and concentration in gas-phase equilibrium, and why stoichiometry decides whether the system shifts left or right.

Gas Equilibrium Under Volume Changes | JoVE K12

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Gas Equilibrium Under Volume Changes

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