Page 247 - Theory and Problems of BEGINNING CHEMISTRY

236 RATES AND EQUILIBRIUM [CHAP. 16

Note that the concentrations of reactants are reduced. We then merely add the columns to find the rest of the
equilibrium concentrations:
−→
A + B ←− C + D
Initial concentrations 1.50 2.50 0.00 0.00
Changes produced by reaction −0.45 −0.45 +0.45 +0.45
Equilibrium concentrations 1.05 2.05 0.45 0.45
Now that we have calculated the equilibrium concentrations, we can substitute these values into the equilibrium
constant expression:
[C][D] (0.45)(0.45)
K = = = 0.094
[A][B] (1.05)(2.05)
When the chemical equation is more complex, the equilibrium constant expression is also more complex
and the deductions about the equilibrium concentrations of reactants and products are more involved, too.

EXAMPLE 16.11. Calculate the value of the equilibrium constant for the following reaction if 1.50 mol of A and 2.50 mol
of B are placed in 1.00 L of solution and allowed to come to equilibrium. The equilibrium concentration of C is found to be
0.45 M.

−→
2A + B ←− C + D
Ans. The equilibrium constant expression for this equation is
[C][D]
K =
2
[A] [B]
2A + B ←− C + D
−→
Initial concentrations 1.50 2.50 0.00 0.00
Changes produced by reaction
Equilibrium concentrations 0.45
The changes brought about by the chemical reaction are a little different in this case. Twice as many moles per liter
of A are used up as moles per liter of C are produced. Note that the magnitudes in the middle row of this table and
the coefficients in the balanced chemical equation are in the same ratio.
−→
2A + B ←− C + D
Initial concentrations 1.50 2.50 0.00 0.00
Changes produced by reaction −0.90 −0.45 +0.45 +0.45
Equilibrium concentrations 0.45
Adding the columns gives
−→
2A + B ←− C + D
Initial concentrations 1.50 2.50 0.00 0.00
Changes produced by reaction −0.90 −0.45 +0.45 +0.45
Equilibrium concentrations 0.60 2.05 0.45 0.45
The equilibrium values are substituted into the equilibrium constant expression:

[C][D] (0.45)(0.45)
K = = = 0.27
2
2
[A] [B] (0.60) (2.05)
The next type of problem gives the initial concentrations of the reactants (and products) plus the value of
the equilibrium constant and requires calculation of one or more equilibrium concentrations. We use algebraic
quantities (such as x) to represent at least one equilibrium concentration, and we solve for the others if necessary
in terms of that quantity.