Question

If the equilibrium constants of the following equilibria {SO_{2(g)} +\frac{1}{2}O2 <=> SO3 and\, 2SO_{3(g)} <=> 2SO_{2(g)} +O_{2(g)}} are given by $K_1$ and $K_2$ respectively, which of the following relations is correct

• A. $K_{2}=\left(\frac{1}{K_{1}}\right)^{2}$
• B. $K_{1}=\left(\frac{1}{K_{2}}\right)^{3}$
• C. $K_{2}=\left(\frac{1}{K_{1}}\right)$
• D. $K_2 = (K_1)^2$

Answer 1

Answer: (A)

$K_{2}=\left(\frac{1}{K_{1}}\right)^{2}$

Answer 2

$SO _{2}+\frac{1}{2} O _{2} \longrightarrow SO _{3}$
$K_{1}=\frac{\left[ SO _{3}\right]}{\left[ SO _{2}\right]\left[ O _{2}\right]^{1 / 2}}$
$2 SO _{3} \longrightarrow 2 SO _{2}+ O _{2}$
$K_{2}=\frac{\left[ SO _{2}\right]^{2}\left[ O _{2}\right]}{\left[ SO _{3}\right]^{2}}$
Obviously, $K_{2}=\left(\frac{1}{K_{1}}\right)^{2}$