# What is K_2...for 2CO(g) + O_2(g) rightleftharpoons 2CO_2(g)?

## Given....$2 C O \left(g\right) + {O}_{2} \left(g\right) r i g h t \le f t h a r p \infty n s 2 C {O}_{2} \left(g\right)$ ....for which ${K}_{1} = 6$...what is ${K}_{2}$ for the reaction... $2 C O \left(g\right) + {O}_{2} \left(g\right) r i g h t \le f t h a r p \infty n s 2 C {O}_{2} \left(g\right)$?: $A .$ ${K}_{2} = 36$; $B .$ ${K}_{2} = 6$; $C .$ $\text{unknown}$; $D .$ $2.50$?

May 9, 2017

$\text{Option D}$

#### Explanation:

For $2 C O \left(g\right) + {O}_{2} \left(g\right) \rightarrow 2 C {O}_{2} \left(g\right)$

We have ${K}_{c 1} = 6 = \frac{{\left[C {O}_{2}\right]}^{2}}{\left[{O}_{2}\right] {\left[C O\right]}^{2}}$

But for...........

$C O \left(g\right) + \frac{1}{2} {O}_{2} \left(g\right) \rightarrow C {O}_{2} \left(g\right)$

We have ${K}_{c 2} = \frac{\left[C {O}_{2} \left(g\right)\right]}{\left[C O\right] {\left[{O}_{2}\right]}^{\frac{1}{2}}}$

But ${K}_{c 2} = \sqrt{\frac{{\left[C {O}_{2}\right]}^{2}}{\left[{O}_{2}\right] {\left[C O\right]}^{2}}} = \sqrt{{K}_{\text{c1}}} = \sqrt{6} = 2.45$, close enuff to $D .$