# Relationship between Free energy change and Equilibrium constant (K)

• Jef123
In summary, when solving for the equilibrium constant K, the relationship between the vapor pressure of each molecular compound in a reaction is that the inverse of the coefficient of the gas in the chemical equation is equal to K. This means that to solve for the vapor pressure of a specific gas, you would need to know the value of K and the other gases in the equation. If there are multiple gases, more information would be needed to solve for the vapor pressure of water.
Jef123
1. I have a question regarding the equation ΔG° = -RT lnK. When solving for the equilibrium constant K, what is the relationship between the vapor pressure of each molecular compound in a reaction?

ΔG° = Free energy change
R = Universal gas constant
T = Temperature
K = equilibrium constant
*K can be solved for in concentration or pressure or solubility

2. Meaning, for the reaction aA(s) + bB(g) --> cC(g) + dD(g) where the lower case coefficients are the number of moles and the upper case coefficients are the molecular compounds. Assuming I solved for ΔG at a specific temperature and then solved for K If I wanted to find the the vapor pressure or the concentration of bB how would I relate the value of the equilibrium constant K to solve for B?

My thought is that 1/Bb = K. Is this correct?

There is a specific applied problem from where my question is derived, so if anyone would like me to post it to clarify areas where I may not be explicit enough, I can.

C and D are gases as well, so they are part of K as well.

Hard to say what you are expected to do not knowing the problem, but typically you should find C and D from the stoichiometry (for example using ICE table).

Here's the problem:

A humidity sensor consists of a cardboard square that is colored blue in dry weather and red in humid weather. The color change is due to the reaction:

CoCl2(s) + 6 H2O(g) ⇌ [Co(H2O)6]Cl2(s)

For this reaction at 25 °C, ΔH° = -352 kJ/mol and ΔS° = -899 J/(K mol). Assuming that ΔH and ΔS are independent of temperature, what is the vapor pressure of water (in mm Hg) at equilibrium for the above reaction at 35 °C on a hot summer day?

I used the equation ΔG° = ΔH° - TΔS° at T = 35°C = 308.15 K. So, ΔG = -74973.15 J

Then, I used ΔG° = - RTlnK and solved for K at T = 308.15 Kelvin. Thus, K = 5.5 x 1012 atm.

This is where I am confused and had to look up the solution: 1/(H2O)6 = 5.5 x 1012. They then solved for H2O

I think I actually just understood what they did. wow. So if there was more than one gas in the equation then I would need more information to solve for the pressure of water because there would be more than one variable?

Jef123 said:
So if there was more than one gas in the equation then I would need more information to solve for the pressure of water because there would be more than one variable?

Yes.

I can provide some clarification on the relationship between free energy change (ΔG°) and equilibrium constant (K). The equation ΔG° = -RT lnK is known as the Gibbs free energy equation and it describes the relationship between the free energy change of a reaction (ΔG°) and the equilibrium constant (K). This equation is derived from thermodynamics and is used to predict the direction and extent of a chemical reaction at a given temperature.

The equilibrium constant (K) is a measure of the ratio of products to reactants at equilibrium. It is a dimensionless quantity and can be expressed in terms of concentrations, pressures, or solubility. The value of K tells us whether the reaction favors the products (K>1) or the reactants (K<1) at equilibrium.

Now, regarding the relationship between the vapor pressure of each molecular compound in a reaction and the equilibrium constant (K), it is important to note that the equilibrium constant is a function of temperature and does not depend on the physical state of the reactants and products. In other words, the equilibrium constant will be the same regardless of whether the reactants and products are in the gas phase, liquid phase, or solid phase.

In the specific reaction you mentioned, aA(s) + bB(g) --> cC(g) + dD(g), the equilibrium constant (K) is given by K = ([C]^c[D]^d)/([A]^a^b), where the brackets represent the concentrations of the respective species. If you want to solve for the vapor pressure of B, you can use the ideal gas law (PV = nRT) to relate the concentration of B to its vapor pressure. However, you cannot simply say that 1/Bb = K. The value of K will depend on the concentrations of all the species involved in the reaction, not just B.

In summary, the equilibrium constant (K) is not directly related to the vapor pressure of a specific species in a reaction. It is a measure of the overall equilibrium state of the reaction and is determined by the concentrations of all the species involved. I hope this helps clarify your question. If you have a specific applied problem that you would like to share, I would be happy to provide further explanation.

## What is the relationship between free energy change and equilibrium constant (K)?

The relationship between free energy change (ΔG) and equilibrium constant (K) is given by the equation ΔG = -RTlnK, where R is the gas constant and T is the temperature in Kelvin. This equation is known as the Gibbs-Helmholtz equation and it shows that the free energy change is directly proportional to the logarithm of the equilibrium constant.

## How does the value of ΔG affect the value of K?

The value of ΔG affects the value of K because the two are directly related through the equation ΔG = -RTlnK. A negative ΔG (exergonic reaction) will result in a positive value for lnK, indicating a large value for K and a reaction that strongly favors the products. On the other hand, a positive ΔG (endergonic reaction) will result in a negative value for lnK, indicating a small value for K and a reaction that strongly favors the reactants.

## What is the significance of the equilibrium constant (K)?

The equilibrium constant (K) is a measure of the relative concentrations of reactants and products at equilibrium for a given chemical reaction. It is a constant value at a specific temperature and pressure, and it provides information about the direction and extent of a chemical reaction. A large value of K indicates that the products are favored at equilibrium, while a small value of K indicates that the reactants are favored.

## How does temperature affect the relationship between ΔG and K?

The relationship between ΔG and K is affected by temperature through the gas constant (R) and the temperature in Kelvin (T) in the equation ΔG = -RTlnK. A change in temperature will alter the value of lnK, which in turn affects the value of ΔG. Generally, an increase in temperature will result in a larger value for K, indicating that the products are favored at higher temperatures.

## Can the equilibrium constant (K) be used to predict the direction of a reaction?

Yes, the equilibrium constant (K) can be used to predict the direction of a reaction. A large value of K indicates that the products are favored, while a small value of K indicates that the reactants are favored. Therefore, if the initial concentrations of reactants and products are known, the value of K can be used to determine which direction the reaction will proceed in order to reach equilibrium.

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