The equilibrium constant is given for two of the reactions below. Determine the value of the missing equilibrium constant.

A(g) + B(g) ? AB(g) Kc = 0.24

AB(g) + A(g) ? A2B(g) Kc = 3.8

2 A(g) + B(g) ? A2B(g) Kc = ?

A. 4.0

B. 0.91

C. 3.6

D. 16

E. 0.63

B. 091

Explanation:

When we add these two equilbria, the equilibrium constant for the resultant equilibrium is the product of the first two.

Notice that when we add the first two reactions in this question, we obtain the equilibrium for which we are seeking its equilibrium constant. Therefore,

A(g) + B(g) ? AB(g)           Kc₁ = [AB] / [A][B]          

                             +

AB(g) + A(g) ? A2B(g)       Kc₂ = [A₂B] /[ AB][A]

   2 A(g) + B(g)  ⇄ A₂B(g)    Kc₃ = [A₂B] / [A]²[B]

Kc₁Kc₂ =  [AB] / [A][B]  x  [A₂B] / [AB][A] =  [A₂B] / [A]²[B]

Thus,

Kc₃ = 0.24 x 3.8 = 0.91

This procedure is not limited to two reaction, it could done for more than two, as long as the desired equilibrium is the desired one.

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most historians agree that gabriel mouton, the vicar of st. paul’s church in lyons, france, is the “founding father” of the metric system. he proposed a decimal system of measurement in 1670. mouton based it on the length of one minute of arc of a great circle of the earth (now called a nautical mile, 1852 meters). he also proposed the swing-length of a pendulum with a frequency of one beat per second as the unit of length (about 25 cm). a pendulum beating with this length would have been fairly easy to produce, thus facilitating the widespread distribution of uniform standards. over the years, his work was revised, improved, and extended by a number of french scientists.

the political sponsor of weights and measures reform in the french revolutionary national assembly was the bishop of autun, better known as talleyrand. under his auspices, the french academy appointed several committees to carry out the work of developing a usable system of weights and measures for france. one of the committees recommended a decimalized measurement system based upon a length equal to one ten-millionth of the length of a quadrant of the earth’s meridian (i.e., one ten-millionth of the distance between the equator and the north pole).