Problem: At 2000°C the equilibrium constant for the reaction2NO(g) ⇌ N2(g) + O2(g)is Kc = 2.4 × 103. The initial concentration of NO is 0.200 M .a) What is the equilibrium concentration of NO? b) What is the equilibrium concentration of N2? c) What is the equilibrium concentration of O2?

FREE Expert Solution

Construct an ICE chart to detemrinet the equilibrium concentration.

$\boxed{{\mathbf{K}}_{\mathbf{c}}\mathbf{=}\frac{\mathbf{products}}{\mathbf{reactants}}\mathbf{=}\frac{\left[N_2\right]\left[O_2\right]}{{\left[\mathrm{NO}\right]}^{\mathbf{2}}}}$

$\mathbf{2}\mathbf{.}\mathbf{4}\mathbf{\times }{\mathbf{10}}^{\mathbf{3}}\mathbf{=}\frac{\left(x\right)\left(x\right)}{\mathbf{0}\mathbf{.}\mathbf{200}\mathbf{-}\mathbf{2}\mathbf{x}}$

$\frac{\mathbf{i}\mathbf{ni}\mathbf{t}\mathbf{i}\mathbf{a}\mathbf{l}\mathbf{ }\mathbf{\left[}\mathbf{N}\mathbf{O}\mathbf{\right]}}{{\mathbf{K}}_{\mathbf{c}}}\mathbf{=}\frac{\mathbf{0}\mathbf{.}\mathbf{200}}{\mathbf{2}\mathbf{.}\mathbf{4}\mathbf{\times }{\mathbf{10}}^{\mathbf{3}}}\mathbf{<}\mathbf{<}\mathbf{<}\mathbf{500}\mathbf{;}\mathbf{ }\mathit{x}\mathbf{ }\mathit{i}\mathit{s}\mathbf{ }\mathit{r}\mathit{e}\mathit{t}\mathit{a}\mathit{i}\mathit{n}\mathit{e}\mathit{d}\mathbf{ }\mathit{i}\mathit{n}\mathbf{ }\mathit{t}\mathit{h}\mathit{e}\mathbf{ }\mathit{d}\mathit{e}\mathit{n}\mathit{o}\mathit{m}\mathit{i}\mathit{n}\mathit{a}\mathit{t}\mathit{o}\mathit{r}$

$[2.4\times {10}^3=\frac{x^2}{\cancel{0.200-2x}}]\cancel{\left[0.200-2x\right]}$

$$\begin{gathered} \mathbf{(}\mathbf{2}\mathbf{.}\mathbf{4}\mathbf{\times }{\mathbf{10}}^{\mathbf{3}}\mathbf{)}\mathbf{(}\mathbf{0}\mathbf{.}\mathbf{200}\mathbf{-}\mathbf{2}\mathbf{x}\mathbf{)}\mathbf{=}{\mathbf{x}}^{\mathbf{2}} \\ \mathbf{480}\mathbf{-}\mathbf{4800}\mathbf{x}\mathbf{=}{\mathbf{x}}^{\mathbf{2}} \\ {\mathbf{x}}^{\mathbf{2}}\mathbf{+}\mathbf{4800}\mathbf{x}\mathbf{-}\mathbf{480}\mathbf{=}\mathbf{0} \end{gathered}$$