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Writing Equilibrium Constant Expressions (Expressions for K): Homogeneous Systems
Consider the following reaction at equilibrium:
aA(g) + bB(g) ⇋ cC(g) + dD(g)
The mass-action expression, Q, for this reaction is:
At equilibrium the rate of the forward reaction is the same as the rate of the reverse reaction so that the concentration of each species remains constant, that is:
[C] = a constant
[D] = a constant
[A] = a constant
[B] = a constant
So
Q = |
[a constant]c[a constant]d [a constant]a[a constant]b |
= |
a constant |
= |
equilibrium constant |
= |
K |
The expression for the equilibrium constant, K, is the same as the mass-action expression, Q, that is:
Similarly, if all the species were present in aqueous solution, the chemical reaction could be represented as
aA(aq) + bB(aq) ⇋ cC(aq) + dD(aq)
The mass-action expression, Q, for this reaction is:
At equilibrium the rate of the forward reaction is the same as the rate of the reverse reaction so that the concentration of each species remains constant, that is:
[C] = a constant
[D] = a constant
[A] = a constant
[B] = a constant
So
Q = |
[a constant]c[a constant]d [a constant]a[a constant]b |
= |
a constant |
= |
equilibrium constant |
= |
K |
And once again, the expression for the equilibrium constant, K, is the same as the mass-action expression, Q, that is:
Writing Equilibrium Constant Expressions (Expressions for K): Heterogeneous Systems
But what happens if one of the reactants or products is a solid?
aA(aq) + bB(aq) ⇋ cC(s) + dD(aq)
The mass-action expression, Q, for this reaction is:
The concentration of the solid, C(s), is always the same! Even if the system is NOT at equilibrium, the concentration of C(s) will still not change.
The concentration of a solid is fixed by its density, that is, the amount of solid substance in a given volume is always the same at constant temperature and pressure, so the concentration of a solid is a constant.
We could then re-write the mass-action expression as:
And, at equilibrium:
Q/[C]c = a constant/a constant
= K (the equilibrium constant)
So, the expression for the equilibrium constant is:
Similarly, if one of the reactants or products is a liquid, the concentration of the liquid species does not change.
The concentration of a liquid is also fixed by its density, that is, the amount of liquid substance in a given volume at constant temperature and pressure, is always the same, so the concentration of a liquid is a constant.
So, for the reaction
aA(aq) + bB(l) ⇋ cC(aq) + dD(aq)
The mass-action expression, Q, for this reaction is:
but since [B] is always constant because B is a liquid, we can re-write the expression as:
and at equilibrium,
Q[B]b = a constant × a constant
= constant
= K (the equilibrium constant)
So the expression for the equilibrium constant, K, is