Relationship between free energy and the equilibrium constant

[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?

 

[Gokul43201]

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 $\Delta S_0$ ?

 

[Blueshift5]

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.