# Relationship between free energy and the equilibrium constant

• chazgurl4life
In summary, the conversation discusses the relationship between free energy and the equilibrium constant, as represented by the equation ΔGo = -RT ln K. The conversation also mentions the temperature dependence of Kb for NH3(aq), with specific values found at different temperatures. It is noted that over moderate temperature ranges, both deltaSo and deltaHo can be considered approximately temperature independent. The conversation then discusses the plotting of information to estimate deltaSo and deltaHo for a reaction, with the equation lnKb = deltaH/R - deltaS/r being mentioned. However, it is pointed out that this equation is not correct and the relationship between ΔG_0~,~~ΔH_0~ and ΔS_0~ is still unclear.
chazgurl4life
The relationship between free energy and the equilibrium constant is

Go = -RT ln K

By measuring the pH at various temperatures, the Kb for NH3(aq) was found to be temperature dependent, yielding the following values:

temperature (K) Kb
283 1.34 X 10-5
293 1.42 X 10-5
303 1.50 X 10-5

Over moderate temperature ranges (ranges less than 100 K degrees) both deltaSo and deltaHo can be considered approximately temperature independent. By plotting the available information appropriately, obtain estimates for deltaSo and delayHo for the reaction:

ok so i figured out that my y=mx+b equation should loook lik:

lnKb=delta H/R(gas constnt) - delta S/r

bbut what is my x-axis and y axis?

1. This question belongs in the Coursework & Homework section of the forums. Henceforth, please post such questions there (and use a more descriptive title).

2.
ok so i figured out that my y=mx+b equation should loook lik:

lnKb=delta H/R(gas constnt) - delta S/r
That's not right. What is the relationship between $\Delta G_0~,~~\Delta H_0$ and $\Delta S_0$ ?

Last edited:

I would like to provide a response to the content by explaining the relationship between free energy and the equilibrium constant and how it relates to the given information about the temperature-dependent Kb for NH3(aq).

Firstly, the equation provided (Go = -RT ln K) shows the direct relationship between free energy (Go) and the equilibrium constant (K). This equation is known as the Gibbs-Helmholtz equation and it states that the change in free energy (Go) is directly proportional to the natural logarithm of the equilibrium constant (ln K) at a given temperature (T).

In the given information, the Kb values for NH3(aq) were found to be temperature dependent, meaning that the equilibrium constant changes with temperature. This is because temperature affects the enthalpy (Ho) and entropy (So) of the reaction, which in turn affects the free energy change of the reaction.

To estimate Ho and So for the reaction, we can rearrange the Gibbs-Helmholtz equation to solve for Ho and So:

Ho = Go + RTln K
So = -Rln K

Using the given data, we can plot a graph of ln K versus 1/T (where T is the temperature in Kelvin) and the slope of this graph will give us -Ho/R, while the y-intercept will give us So/R. This is because at different temperatures, the equilibrium constant (K) will have different values, but the slope and intercept remain constant.

Therefore, by plotting the ln K values for NH3(aq) at different temperatures and using the slope and intercept to calculate Ho and So, we can estimate the values of these thermodynamic parameters for the reaction.

In conclusion, the relationship between free energy and the equilibrium constant is important in understanding the temperature dependence of chemical reactions. By using the Gibbs-Helmholtz equation and the given information, we can estimate the enthalpy and entropy changes of a reaction and gain a better understanding of its thermodynamic properties.

## 1. How is free energy related to the equilibrium constant?

The equilibrium constant (K) is a measure of the ratio of product concentrations to reactant concentrations at equilibrium. It is related to the change in free energy (ΔG) by the equation ΔG = -RTlnK, where R is the gas constant and T is the temperature in Kelvin. This means that the larger the equilibrium constant, the more negative the change in free energy, indicating a more favorable reaction.

## 2. What is the significance of the relationship between free energy and the equilibrium constant?

The relationship between free energy and the equilibrium constant provides important information about the spontaneity and direction of a chemical reaction. A negative ΔG and a large equilibrium constant indicate a spontaneous reaction that favors the formation of products, while a positive ΔG and a small equilibrium constant suggest a non-spontaneous reaction that favors the formation of reactants.

## 3. How does temperature affect the relationship between free energy and the equilibrium constant?

Temperature has a significant impact on the equilibrium constant and the associated free energy change. As temperature increases, the equilibrium constant also increases, making the reaction more favorable. This is because higher temperatures increase the kinetic energy of molecules, allowing them to overcome activation energy barriers and reach equilibrium faster.

## 4. Can the equilibrium constant be used to predict the direction of a reaction?

Yes, the equilibrium constant can be used to predict the direction of a reaction. If the equilibrium constant is greater than 1, the reaction will proceed in the forward direction, while a value less than 1 indicates that the reaction will favor the reverse direction. A value of 1 suggests that the reaction is at equilibrium.

## 5. How is the relationship between free energy and the equilibrium constant applied in practical applications?

The relationship between free energy and the equilibrium constant is used in various fields, such as biochemistry, chemical engineering, and environmental science. It is used to determine the feasibility and direction of chemical reactions, as well as to optimize reaction conditions for industrial processes. It also plays a crucial role in understanding and predicting biochemical reactions in living systems.

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