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Given that the equilibrium constant for the reaction $2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g)$ has a value of 278 at a particular temperature. What is the value of the equilibrium constant for the following reaction at the same temperature? $SO_3(g) \rightleftharpoons SO_2(g) + \frac{1}{2}O_2(g)$
A
$1.3\times10^{-5}$
B
$1.8\times10^{-3}$
C
$3.6\times10^{-3}$
D
$6.0\times10^{-2}$
Detailed Solution
$2SO_2 + O_2 \rightleftharpoons 2SO_3$; $K = 278$
Reversing the reaction gives $\frac{1}{K}$; halving it gives the square root.
$SO_3 \rightleftharpoons SO_2 + \frac{1}{2}O_2$; $K' = \sqrt{\frac{1}{K}} = \sqrt{\frac{1}{278}}$
$K' = 5.99\times10^{-2} \approx 6.0\times10^{-2}$
Reversing the reaction gives $\frac{1}{K}$; halving it gives the square root.
$SO_3 \rightleftharpoons SO_2 + \frac{1}{2}O_2$; $K' = \sqrt{\frac{1}{K}} = \sqrt{\frac{1}{278}}$
$K' = 5.99\times10^{-2} \approx 6.0\times10^{-2}$