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General Chemistry Principles, Patterns, and Applications, 2011

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Note the Pattern<br />

To determine K for a reaction that is the sum of two or more reactions, add the reactions but multiply the<br />

equilibrium constants.<br />

E X A M P L E 7<br />

The following reactions occur at 1200°C:<br />

1. CO( g) + 3H2( g) CH 4( g) + H2O( g) K1= 9.17 ´10 - 2<br />

CH 4( g) + 2H2S( g) CS2( g) + 4H2( g) K2 = 3.3´104 Calculate the equilibrium<br />

constant for the following reaction at the same temperature.<br />

1. CO g<br />

( ) + 2H2S( g) CS2( g) + H2O( g) + H2( g) K3 = ?<br />

Given: two balanced equilibrium equations, values of K, <strong>and</strong> an equilibrium equation for the overall<br />

reaction<br />

Asked for: equilibrium constant for the overall reaction<br />

Strategy:<br />

Arrange the equations so that their sum produces the overall equation. If an equation had to be reversed,<br />

invert the value of K for that equation. Calculate K for the overall equation by multiplying the equilibrium<br />

constants for the individual equations.<br />

Solution:<br />

The key to solving this problem is to recognize that reaction 3 is the sum of reactions 1 <strong>and</strong> 2:<br />

CO g<br />

( ) + 3H 2( g)CH 4( g) + 2H 2S( g)CO( g) + 2H 2S( g) CH 4( g) + H 2O( g)<br />

CS2( g) + 3H 2( g) + H 2( g) CS2( g) + H 2O( g) + H 2( g)<br />

for K 1 <strong>and</strong> K 2 are given, so it is straightforward to calculate K 3:<br />

K 3 = K 1 K 2 = (9.17 × 10 −2 )(3.3 × 10 4 ) = 3.03 × 10 3<br />

The values<br />

Exercise<br />

In the first of two steps in the industrial synthesis of sulfuric acid, elemental sulfur reacts with oxygen to<br />

produce sulfur dioxide. In the second step, sulfur dioxide reacts with additional oxygen to form sulfur<br />

trioxide. The reaction for each step is shown, as is the value of the corresponding equilibrium constant at<br />

25°C. Calculate the equilibrium constant for the overall reaction at this same temperature.<br />

Saylor URL: http://www.saylor.org/books<br />

Saylor.org<br />

1369

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