Derivation of the Equilibrium Constant

In summary, the conversation is discussing the derivation of the equilibrium constant from Gibbs free energy. The first question is about the equation \Sigmav_{j}A_{j}=0 and its relation to the number of atoms. The expert clarifies that it is a mass conservation equation and the products are assumed to be negative. The second question is about the range of the sum, with the expert explaining that it sums for all j, not just up to n.
  • #1
gsingh2011
115
1
I'm trying to understand this: http://en.wikipedia.org/wiki/Equilibrium_constant#Derivation_from_Gibbs_Free_Energy
And there are few steps that I don't get. My first question is probably a stupid one, but where does the [tex]\Sigma[/tex]v[tex]_{j}[/tex]A[tex]_{j}[/tex]=0 come from? What exactly is it summing up, the number of atoms? Are you assuming that the products side is negative? (Because I don't see how else you would get zero) And why does it only go up to n?

I'll ask my other questions after I get some replies because it's possible I'll figure them out after I read the replies.
 
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  • #2
gsingh2011 said:
where does the [tex]\Sigma[/tex]v[tex]_{j}[/tex]A[tex]_{j}[/tex]=0 come from? What exactly is it summing up, the number of atoms? Are you assuming that the products side is negative? (Because I don't see how else you would get zero) And why does it only go up to n?

My guess is it is just a mass conservation, and yes, products are negative.
 
  • #3
Borek said:
My guess is it is just a mass conservation, and yes, products are negative.

Ok, but why does it only sum up to n? The first equation in the derivation shows the first product being n but then shows more products after that. If it was mass conservation, wouldn't it have to sum passed n?
 
  • #4
Where does it sum only to n? It sums for all j.
 
  • #5


First of all, there are no stupid questions in science. It's important to ask for clarification when something is not clear, so don't hesitate to ask.

Now, to answer your first question, the \Sigmav_{j}A_{j}=0 comes from the fact that in a chemical reaction, the total number of atoms on both sides of the equation must be equal. This is known as the law of conservation of mass. Therefore, the sum of the stoichiometric coefficients (\Sigmav_{j}) multiplied by the number of atoms of each element (A_{j}) must be equal to zero. This equation is used to ensure that the number of atoms on the reactant side is equal to the number of atoms on the product side.

To answer your second question, the equation only goes up to n because it represents a general chemical reaction with n number of reactants and products. Therefore, the sum of the stoichiometric coefficients and the number of atoms is only relevant up to n.

I hope this helps clarify the derivation of the equilibrium constant. If you have any other questions, please feel free to ask.
 

1. What is the equilibrium constant and why is it important?

The equilibrium constant (Keq) is a ratio of the concentrations of products to reactants at equilibrium in a chemical reaction. It is important because it allows us to quantitatively understand the direction and extent of a reaction at equilibrium.

2. How is the equilibrium constant derived?

The equilibrium constant can be derived using the law of mass action, which states that the rate of a chemical reaction is proportional to the concentrations of the reactants. By setting up an equilibrium expression and manipulating it algebraically, we can obtain an equation for Keq.

3. What factors affect the value of the equilibrium constant?

The value of the equilibrium constant is affected by temperature, pressure, and the initial concentrations of reactants and products. It is also dependent on the stoichiometry of the reaction, meaning the coefficients of the reactants and products in the balanced chemical equation.

4. How is the equilibrium constant used in chemical calculations?

The equilibrium constant is used to calculate the concentrations of reactants and products at equilibrium, as well as to predict the direction of a reaction. It can also be used to determine the equilibrium constant for a reverse reaction or for a reaction that is the sum of two or more reactions.

5. What is the relationship between the equilibrium constant and the reaction quotient?

The reaction quotient (Q) is similar to the equilibrium constant, except it is calculated using the initial concentrations of reactants and products instead of the equilibrium concentrations. The relationship between Keq and Q allows us to determine if a reaction is at equilibrium (Q = Keq) or if it will shift to reach equilibrium (Q ≠ Keq).

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