Name: predicting spontaneity with reaction quotient q
Uploaded: 2020-09-24T15:06:52.000Z
Duration: 3 min 25 s
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Free Energy Changes for Nonstandard States

The standard free energy change for a reaction can only be determined if it occurs under standard state conditions&#8212;when both the reactants and products are in their standard states. However, most chemical reactions do not occur under these conditions.
Under any conditions&#8212;standard or nonstandard&#8212;the relative amount of products and reactants present in a reaction is described by the reaction quotient, Q.
For reactions occurring in solution, Q is calculated from the ratio of the product and reactant concentrations, with each reagent concentration raised to the power of its stoichiometric coefficient. For gaseous reactions, the partial pressures of the gases can be used in place of concentrations.
The free energy change of a reaction is equal to the sum of the standard-state free energy change for the reaction, delta G naught, and RT times the natural log of Q. Here, R is the universal gas constant in joules per mole-kelvin, and T is the temperature of the reaction in kelvin.
At constant temperature, the standard-state free energy has a fixed value, but Q varies because it depends on the composition of the reaction mixture.
Consider the synthesis of ammonia gas from nitrogen and hydrogen at 298 K. Under standard conditions, which for a gas is the pure gas at 1 atm, the partial pressures of all the components are equal to 1 atm, and the magnitude of the reaction quotient equals 1.
Thus, the free energy change of the reaction is equal to the standard free energy change of the reaction, &#8722;32.8 kJ/mol, and the forward reaction is spontaneous.
Under nonstandard conditions, the components of the reaction mixture may initially have partial pressures of 1.2 atmospheres of nitrogen, 3.6 atmospheres of hydrogen, and 0.60 atmospheres of ammonia.
As before, the reaction quotient can be determined from the values for the partial pressures. Substituting for Q into the equation, the free energy for the reaction is &#8722;45.3 kJ/mol, indicating a spontaneous reaction in the forward direction.
As the forward reaction proceeds, more ammonia is produced, and the reaction composition changes.
When the reactants and products are in equilibrium, the free energy change for the reaction is zero, and the value of RT times the natural log of Q is equal and opposite in sign to the standard free energy change.
Now, if the reaction mixture contains 0.02 atmospheres of nitrogen, 0.06 atmospheres of hydrogen, and 4.8 atmospheres of ammonia, Q is much larger, and the change in free energy is 5.6 kJ/mol.
A positive free energy change indicates that the reverse reaction is energetically favorable. Thus, under these conditions, ammonia decomposes to produce nitrogen and hydrogen.

free energy changes for nonstandard states

The free energy change for a process taking place with reactants and products present under nonstandard conditions (pressures other than 1 bar; concentrations other than 1 M) is related to the standard free energy change according to this equation:
 <img alt="Phase diagram of CO2 showing transitions between solid, liquid, gas at various pressures, temperatures." src="/files/ftp_upload/11430/11430_Equation_1.png" style="height: 50px;" data-altupdatedat="1761830439000" data-alt="Eq1" />
where R is the gas constant (8.314 J/K&#183;mol), T is the absolute temperature in kelvin, and Q is the reaction quotient. This equation may be used to predict the spontaneity of a process under any given set of conditions.
Reaction Quotient (Q)
The status of a reversible reaction is conveniently assessed by evaluating its reaction quotient, Q. For a reversible reaction described by
 <img alt="Chemical reaction mechanism diagram for Michael addition with nucleophile and electrophile formation." src="/files/ftp_upload/11430/11430_Equation_2.png" style="height: 50px;" data-altupdatedat="1761830439000" data-alt="Eq1" />
the reaction quotient is derived directly from the stoichiometry of the balanced equation as
 <img alt="Chemical structure of DNA base pairs showing hydrogen bonding diagram." src="/files/ftp_upload/11430/11430_Equation_3.png" style="height: 70px;" data-altupdatedat="1761830439000" data-alt="Eq1" />
where the subscript c denotes the use of molar concentrations in the expression. The concentration-based reaction quotient, Qc, is used for condensed phase equilibria. If the reactants and products are gaseous, a reaction quotient may be similarly derived using partial pressures:
 <img alt="Chemical reaction, bromination of alkene diagram, illustrating electrophilic addition process." src="/files/ftp_upload/11430/11430_Equation_4.png" style="height: 70px;" data-altupdatedat="1761830439000" data-alt="Eq1" />
Under standard conditions, the reactant and product solution concentrations are 1 M, or the pressure of gases is 1 bar, and Q is equal to 1. Therefore, under standard conditions
 <img alt="DNA cloning process diagram with restriction enzymes, plasmid vector, and gene insertion steps." src="/files/ftp_upload/11430/11430_Equation_5.png" style="height: 50px;" data-altupdatedat="1761830439000" data-alt="Eq1" />
Under nonstandard conditions, Q must be calculated.
The numerical value of Q varies as a reaction proceeds towards equilibrium; therefore, it can serve as a useful indicator of the reaction&#8217;s status. To illustrate this point, consider the oxidation of sulfur dioxide:
 <img alt="Chemical reaction mechanism, nucleophilic substitution diagram, SN2 reaction pathway, organic chemistry." src="/files/ftp_upload/11430/11430_Equation_6.png" style="height: 50px;" data-altupdatedat="1761830439000" data-alt="Eq1" />
Consider two different experimental scenarios, one in which this reaction is initiated with a mixture of reactants only, SO2 and O2, and another that begins with only the product, SO3. For the reaction that begins with a mixture of reactants only, Q is initially equal to zero:
 <img alt="Static equilibrium diagram, &#931;Fx=0, free body analysis, physics study tool." src="/files/ftp_upload/11430/11430_Equation_7.png" style="height: 70px;" data-altupdatedat="1761830439000" data-alt="Eq1" />
As the reaction proceeds toward equilibrium in the forward direction, reactant concentrations decrease (as does the denominator of Qc), product concentration increases (as does the numerator of Qc), and the reaction quotient consequently increases. When equilibrium is achieved, the concentrations of reactants and products remain constant, as does the value of Qc.
If the reaction begins with only the product present, the value of Qc is initially undefined (immeasurably large or infinite):
 <img alt="Kirchhoff's junction rule diagram with &#931;I=0 showing current conservation at a node." src="/files/ftp_upload/11430/11430_Equation_8.png" style="height: 70px;" data-altupdatedat="1761830439000" data-alt="Eq1" />
In this case, the reaction proceeds toward equilibrium in the reverse direction. The product concentration and the numerator of Qc decrease with time, the reactant concentrations and the denominator of Qc increase, and the reaction quotient consequently decreases until it becomes constant at equilibrium.
This text is adapted from <a href="https://openstax.org/books/chemistry-2e/pages/16-4-free-energy">Openstax, Chemistry 2e, Chapter 16.4: </a><a href="https://openstax.org/books/chemistry-2e/pages/16-4-free-energy">Free Energy</a> and <a href="https://openstax.org/books/chemistry-atoms-first-2e/pages/13-2-equilibrium-constants">Openstax, Chemistry 2e, Chapter 13.2: Equilibrium Constants</a>.

The free energy change for a process taking place with reactants and products present under nonstandard conditions (pressures other than 1 bar; ...

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KEY TERMS AND CONCEPTS

predicting spontaneity with reaction quotient q

Free energy under nonstandard conditions depends on the reaction quotient, Q, and the standard free energy change. Nonstandard conditions mean that concentrations are not 1 M or pressures are not 1 bar. The relation links the gas constant R, the absolute temperature T in kelvin, and Q. It can be used to predict whether a process is spontaneous under a given set of conditions.

The reaction quotient, Q, helps show the status of a reversible reaction. It is based directly on the balanced chemical equation. For concentration data, the expression is written as Qc, and it is used for condensed phase equilibria. For gaseous reactants and products, the same idea can be written with partial pressures.

Under standard conditions, solution concentrations are 1 M and gas pressures are 1 bar, so Q equals 1. That makes the standard-state case a special reference point. Under nonstandard conditions, Q must be calculated from the current amounts of reactants and products. Its value changes as the reaction moves toward equilibrium, so it gives a useful picture of how far the system has progressed.

The oxidation of sulfur dioxide shows how Q changes in practice. If a reaction starts with only reactants such as SO2 and O2, Q is initially zero. As the reaction moves forward, reactant concentrations decrease and the product concentration increases, so Qc rises until equilibrium is reached. If the reaction starts with only product, SO3, then Qc is initially undefined because it is immeasurably large or infinite. In that case, the reaction shifts in reverse, the product concentration falls, the reactant concentrations rise, and Qc drops until it becomes constant at equilibrium.

Predicting Spontaneity with Reaction Quotient Q

predicting-spontaneity-with-reaction-quotient-q

spontaneity

Spontaneous Change in Matter and Energy

Spontaneous change in matter and energy happens naturally under certain conditions. A nonspontaneous process will not occur unless it is driven by a continual input of energy from an outside source. Under a given set of conditions, processes also tend to move in one direction rather than the other. Water flows downhill on its own, so that is a spontaneous process. Water flowing uphill needs a pump, so that is nonspontaneous. Iron in the earth’s atmosphere will corrode, but rust does not turn...

entropy

Entropy in Matter and Energy Changes

Entropy describes how energy and matter are spread through a system. It is a thermodynamic state function, so it can change when a physical or chemical change occurs. When entropy increases, disorder increases. When entropy decreases, disorder decreases. A change in entropy is written as ΔS = Sf - Si. The concept is also linked to microstates, which are the specific arrangements of the locations and energies of all atoms or molecules in a system. Boltzmann’s relation, S = k ln W, connects...

second law of thermodynamics

Entropy and Spontaneous Change

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third law of thermodynamics

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standard entropy change for a reaction

Calculating Entropy Change from Tables

Entropy is a state function, so the standard entropy change of a chemical reaction can be found from standard molar entropy values in a table. The reaction entropy, written as ΔS°rxn, is calculated by subtracting the total entropy of the reactants from the total entropy of the products. The balanced equation matters because the stoichiometric coefficients set how many moles of each substance are included. A table of standard entropies gives values in J/mol·K for substances such as graphite,...

gibbs free energy

Predicting Spontaneity with Gibbs Energy

Gibbs free energy helps predict whether a process is spontaneous under constant temperature and pressure. It is a thermodynamic property based on the system’s enthalpy and entropy. Chemists also call it free energy, and it is a state function. The idea was introduced in the late nineteenth century by American mathematician Josiah Willard Gibbs. Unlike the second law approach, it uses system properties only. That makes it a useful shortcut when tracking both the system and the surroundings is...

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Temperature and Spontaneous Processes

Temperature can change whether a process is spontaneous. In chemistry, spontaneity means a process can happen on its own under a given set of conditions. Phase changes are one clear example, and some chemical reactions also change spontaneity as temperature changes. The relationship uses free energy change, enthalpy change, and entropy change. Entropy is a measure of disorder in the system. The key equation shows that the sign of free energy depends on the signs of enthalpy and entropy, and in...

calculating standard free energy changes

Using Formation Data to Find Free Energy

Standard free energy change is the free energy change for a reaction under standard conditions of 1 bar pressure and 298 K. Free energy is a state function, so its value depends only on the starting and ending states of the system. That makes it possible to calculate standard free energy changes from tabulated thermodynamic data. One common method uses standard enthalpy and entropy values to find standard free energy change, ΔG°. Another method uses standard free energies of formation, ΔGf°,...

Free energy under nonstandard conditions depends on the reaction quotient, Q, and the standard free energy change. Nonstandard conditions mean that concentrations are not 1 M or pressures are not 1 bar. The relation links the gas constant R, the absolute temperature T in kelvin, and Q. It can be used to predict whether a process is spontaneous under a given set of conditions. The reaction quotient, Q, helps show the status of a reversible reaction. It is based directly on the balanced chemical...

free energy and equilibrium

Predicting Reaction Direction with Free Energy

Free energy and equilibrium help predict which way a chemical reaction will move. A negative value of ΔG means the forward reaction is favored. A positive value means the reverse reaction is favored. When ΔGrxn is zero, the forward and reverse driving forces are equal, and the system is at equilibrium. The reaction quotient, Q, helps show whether a reaction must move forward or backward to reach equilibrium. Q is the numerical value of the mass action expression for the system. If Q is less...

key terms and concepts

Learn how reaction quotient Q and standard free energy change predict spontaneity under nonstandard conditions, using concentration, pressure, and equilibrium examples.

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Predicting Spontaneity with Reaction Quotient Q

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