# Problem: At a particular temperature, K = 3.75 for the reaction SO2(g) + NO2(g) ⇌ SO3(g) + NO(g)If all four gases had initial concentrations of 0.800 M, calculate the equilibrium concentrations of the gases.

🤓 Based on our data, we think this question is relevant for Professor Orr's class at NYU.

###### FREE Expert Solution

Constructing an ICE Chart, we have: $\overline{){{\mathbf{K}}}_{{\mathbf{c}}}{\mathbf{=}}\frac{\mathbf{products}}{\mathbf{reactants}}{\mathbf{=}}\frac{\left[{\mathrm{SO}}_{3}\right]\left[\mathrm{NO}\right]}{\left[{\mathrm{SO}}_{2}\right]\left[{\mathrm{NO}}_{2}\right]}}$

Solve for x:

${\mathbf{3}}{\mathbf{.}}{\mathbf{75}}{\mathbf{=}}\frac{\left(0.800+x\right)\left(0.800+x\right)}{\mathbf{\left(}\mathbf{0}\mathbf{.}\mathbf{800}\mathbf{-}\mathbf{x}\mathbf{\right)}\mathbf{\left(}\mathbf{0}\mathbf{.}\mathbf{800}\mathbf{-}\mathbf{x}\mathbf{\right)}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}{\mathbf{3}}{\mathbf{.}}{\mathbf{75}}{\mathbf{=}}\frac{{\mathbf{\left(}\mathbf{0}\mathbf{.}\mathbf{800}\mathbf{+}\mathbf{x}\mathbf{\right)}}^{\mathbf{2}}}{{\mathbf{\left(}\mathbf{0}\mathbf{.}\mathbf{800}\mathbf{-}\mathbf{x}\mathbf{\right)}}^{\mathbf{2}}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\sqrt{\mathbf{3}\mathbf{.}\mathbf{75}}{\mathbf{=}}\sqrt{\frac{{\mathbf{\left(}\mathbf{0}\mathbf{.}\mathbf{800}\mathbf{+}\mathbf{x}\mathbf{\right)}}^{\mathbf{2}}}{{\mathbf{\left(}\mathbf{0}\mathbf{.}\mathbf{800}\mathbf{-}\mathbf{x}\mathbf{\right)}}^{\mathbf{2}}}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}{\mathbf{1}}{\mathbf{.}}{\mathbf{94}}{\mathbf{=}}\frac{\mathbf{0}\mathbf{.}\mathbf{800}\mathbf{+}\mathbf{x}}{\mathbf{0}\mathbf{.}\mathbf{800}\mathbf{-}\mathbf{x}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\left(1.94\right)\left(0.800-x\right){\mathbf{=}}{\mathbf{0}}{\mathbf{.}}{\mathbf{800}}{\mathbf{+}}{\mathbf{x}}$ ###### Problem Details

At a particular temperature, K = 3.75 for the reaction

SO2(g) + NO2(g) ⇌ SO3(g) + NO(g)

If all four gases had initial concentrations of 0.800 M, calculate the equilibrium concentrations of the gases.