Part 1) We're being asked to calculate the mole fraction of CO(g) in the equilibrium mixture.

*Assuming that they all have the same volume (1L):*

moles H_{2} = 0.20 mol

moles CO_{2} = 0.30 mol

moles H_{2}O = 0.55 mol

moles CO = 0.55 mol

$\overline{){\mathbf{m}}{\mathbf{o}}{\mathbf{l}}{\mathbf{e}}{\mathbf{}}{\mathbf{f}}{\mathbf{r}}{\mathbf{a}}{\mathbf{c}}{\mathbf{t}}{\mathbf{i}}{\mathbf{o}}{\mathbf{n}}{\mathbf{}}{\mathbf{\left(}}{\mathbf{X}}{\mathbf{\right)}}{\mathbf{=}}\frac{\mathbf{m}\mathbf{o}\mathbf{l}\mathbf{e}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{s}\mathbf{o}\mathbf{l}\mathbf{u}\mathbf{t}\mathbf{e}}{\mathbf{m}\mathbf{o}\mathbf{l}\mathbf{e}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{s}\mathbf{o}\mathbf{l}\mathbf{u}\mathbf{t}\mathbf{i}\mathbf{o}\mathbf{n}}}$

${\mathbf{\chi}}_{\mathbf{CO}}\mathbf{=}\frac{\mathbf{mole}\mathbf{}\mathbf{CO}}{\mathbf{total}\mathbf{}\mathbf{moles}}\phantom{\rule{0ex}{0ex}}{\mathbf{\chi}}_{\mathbf{CO}}\mathbf{=}\frac{\mathbf{0}\mathbf{.}\mathbf{55}\mathbf{}\mathbf{mol}}{\mathbf{0}\mathbf{.}\mathbf{20}\mathbf{}\mathbf{mol}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{30}\mathbf{}\mathbf{mol}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{55}\mathbf{}\mathbf{mol}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{55}\mathbf{}\mathbf{mol}}\phantom{\rule{0ex}{0ex}}{\mathbf{\chi}}_{\mathbf{CO}}\mathbf{=}\frac{\mathbf{0}\mathbf{.}\mathbf{55}\mathbf{}\overline{)\mathbf{mol}}}{\mathbf{1}\mathbf{.}\mathbf{60}\mathbf{}\overline{)\mathbf{mol}}}$

**χ**_{CO} = 0.34

Part 2) Using the equilibrium concentrations given above, calculate the value of K_{c}, the equilibrium constant for the reaction.

When H_{2}(g) is mixed with CO_{2}(g) at 2,000 K, equilibrium is achieved according to the following equation

CO_{2}(g) + H_{2}(g) ⇌ H_{2}O(g) + CO(g)

In one experiment, the following equilibrium concentrations were measured.

[H_{2}] = 0.20 mol/L

[CO_{2}] = 0.30 mol/L

[H_{2}O] = [CO] = 0.55 mol/L

What is the mole fraction of CO(g) in the equilibrium mixture?

Using the equilibrium concentrations given above, calculate the value of Kc, the equilibrium constant for the reaction.

Determine K_{p} in terms of K_{c} for this system.

When the system is cooled from 2,000 K to a lower temperature, 30.0 percent of the CO(g) is converted back to CO_{2}(g).

Calculate the value of K_{c} at this lower temperature.

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