## Combining K Values in 11.39

Nathan Mariano 2G
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### Combining K Values in 11.39

Use the information in Table 11.2 to determine the value of K at 300 K for the reaction 2 BrCl(g) + H2(g) <-> Br2(g) + 2 HCl(g). When combining K values, why must you multiply?

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### Re: Combining K Values in 11.39

Suppose you have K1 for $A \rightleftharpoons B$ and K2 for $B \rightleftharpoons C$
Then by definition, $K_1 = \frac{[B]}{[A]}$ and $K_2 = \frac{[C]}{[B]}$
So if you want to know K3 for $A \rightleftharpoons C$,
which by definition is $K_3 = \frac{[C]}{[A]}$,
you can multiply K1 and K2 to get
$K_3 = K_1K_2 = \frac{[B]}{[A]}\frac{[C]}{[B]} = \frac{[B][C]}{[A][B]} = \frac{[C]}{[A]}$