In gas reactions, it's important to understand the connection between two values called equilibrium constants: ( K_p ) and ( K_c ). These help us figure out what happens when the amounts of substances in a reaction change.

So, what do these constants mean?

• ( K_c ): This is the equilibrium constant that uses concentrations, which tell us how much of each substance is present in a solution (measured in molarity, ( M )).

• ( K_p ): This is the equilibrium constant that uses partial pressures (measured in atm, which is a way to measure gas pressure).

There is a relationship between these two constants, described by this equation:

$K_p = K_c (RT)^{\Delta n}$

Let's break this down:

• ( R ): This is a constant value (0.08206 ( L \cdot atm/(K \cdot mol) )), which helps with gas calculations.

• ( T ): This stands for temperature but must be in Kelvin.

• ( \Delta n ): This is the change in the number of gas moles. You find it by subtracting the number of moles of reactants from the number of moles of products.

How Changes in Concentration Affect ( K_c ) and ( K_p )

1. Effect on ( K_c ):

   • If you change the amounts of reactants or products, it doesn’t change ( K_c ). It might shift the balance of the reaction. According to a rule called Le Chatelier's principle, if you add more of a reactant, the reaction will move to the right to produce more products. Still, the value of ( K_c ) stays the same when things settle down.

2. Effect on ( K_p ):

   • Just like ( K_c ), changing how much reactant or product is present doesn’t change ( K_p ). But how much ( K_p ) changes depends on the temperature. For example, in a reaction that releases heat (called exothermic), if you increase the temperature, ( K_p ) goes down. For reactions that absorb heat (called endothermic), increasing the temperature actually raises ( K_p ).

Looking at Statistics

• Equilibrium Shift Statistics: We can measure how much the balance of a reaction changes when we change concentrations. If you double the concentration of all reactants, it will significantly change the balance, but ( K_c ) won’t change.

• Example: Let’s look at a simple reaction:

  $A(g) \rightleftharpoons B(g), \Delta n = 1 - 1 = 0$

  In this case, since the number of moles stays the same, it follows that ( K_p = K_c ), no matter how much of A or B is there at the start.

To sum it up, while the concentrations of substances can change how a reaction balances out, the values of ( K_c ) and ( K_p ) do not change at a given temperature. This shows that these constants are steady and not affected by how much of each substance is present.