When 1.70 mol CO2 and 1.70 mol H2 are placed in a 0.850 L container at 395 C, the following equilibrium is achieved: CO2(g) + H2(g) = CO(g) + H2(g)

If Kc = 0.802, what are the concentrations of each substance in the equilibrium mixture?

To determine the concentrations of each substance in the equilibrium mixture, we need to use the given equilibrium constant (Kc) and the initial moles of each substance.

Let's assign variables for the initial moles of CO2, H2, CO, and H2 as follows:

CO2 initial moles = n(CO2) = 1.70 mol
H2 initial moles = n(H2) = 1.70 mol
CO initial moles = n(CO) = 0 mol (since no CO is present initially)
H2 initial moles = n(H2) = 0 mol (since no H2 is present initially)

Now, let's assign variables for the change in moles for each substance at equilibrium using the stoichiometric coefficients from the balanced equation:

Change in CO2 moles = -x
Change in H2 moles = -x
Change in CO moles = +x
Change in H2 moles = +x

Finally, let's express the equilibrium concentrations of each substance in terms of the initial moles and the changes:

CO2 equilibrium concentration = (n(CO2) - x) / V
H2 equilibrium concentration = (n(H2) - x) / V
CO equilibrium concentration = (n(CO) + x) / V
H2 equilibrium concentration = (n(H2) + x) / V

In this case, V represents the volume of the container, which is given as 0.850 L.

Now, we can substitute the given values into the equilibrium expressions to find the equilibrium concentrations:

CO2 equilibrium concentration = (1.70 - x) / 0.850
H2 equilibrium concentration = (1.70 - x) / 0.850
CO equilibrium concentration = (0 + x) / 0.850
H2 equilibrium concentration = (0 + x) / 0.850

The equilibrium constant, Kc, is defined as the ratio of the products' concentrations to the reactants' concentrations, each raised to the power of their stoichiometric coefficients. In this case, it is given as 0.802:

Kc = (CO equilibrium concentration * H2 equilibrium concentration) / (CO2 equilibrium concentration * H2 equilibrium concentration)

Substituting the equilibrium concentrations into the equation and simplifying, we have:

0.802 = (x/0.850 * x/0.850) / ((1.70 - x)/0.850 * (1.70 - x)/0.850)

To solve for x, we can cross-multiply and solve the resulting quadratic equation. Since the equation is a quadratic, there will be two possible solutions. We will need to check which one is physically realistic by substituting it back into the equilibrium concentration expressions. The valid solution will give positive equilibrium concentrations.

After obtaining the value of x, we can substitute it into the equilibrium concentration expressions to find the concentrations of each substance in the equilibrium mixture.