Consider the following reaction: CO2 (g) + H2 (g) CO (g) + H2O (g)
Calculate the value of the equilibrium constant, Kc, for the above system, if 0.1908 moles of CO2, 0.0908 moles of H2, 0.0092 moles of CO, and 0.0092 moles of H2O vapour were present in a 2.00 L reaction vessel at equilibrium.
To calculate the value of the equilibrium constant, Kc, we need to use the formula:
Kc = ([CO]^a * [H2O]^b) / ([CO2]^c * [H2]^d)
Where [CO], [H2O], [CO2], and [H2] represent the molar concentrations of each species at equilibrium. The exponents a, b, c, and d represent the stoichiometric coefficients of each species in the balanced equation.
In this case, the balanced equation is:
CO2 (g) + H2 (g) --> CO (g) + H2O (g)
The stoichiometric coefficients for each species are: a = 1, b = 1, c = -1, d = -1.
Let's calculate the equilibrium concentrations:
[CO2] = 0.1908 moles / 2.00 L = 0.0954 M
[H2] = 0.0908 moles / 2.00 L = 0.0454 M
[CO] = 0.0092 moles / 2.00 L = 0.0046 M
[H2O] = 0.0092 moles / 2.00 L = 0.0046 M.
Now substitute these values into the formula:
Kc = ([CO]^1 * [H2O]^1) / ([CO2]^1 * [H2]^1)
= (0.0046 * 0.0046) / (0.0954 * 0.0454)
= 5.98 x 10^-4.
Therefore, the value of the equilibrium constant, Kc, for the reaction CO2 (g) + H2 (g) --> CO (g) + H2O (g) is 5.98 x 10^-4.
To calculate the value of the equilibrium constant (Kc), you need to use the concentrations of the species involved in the reaction.
In this case, you are given the number of moles of each species present in a 2.00 L reaction vessel at equilibrium. To calculate the concentrations, you need to divide the number of moles by the volume (in liters).
The initial concentration of CO2, [CO2], is calculated as follows:
[CO2] = moles of CO2 / volume of reaction vessel
= 0.1908 moles / 2.00 L
Similarly, the initial concentrations of H2, CO, and H2O are calculated as:
[H2] = 0.0908 moles / 2.00 L
[CO] = 0.0092 moles / 2.00 L
[H2O] = 0.0092 moles / 2.00 L
Since Kc is defined as the ratio of the products' concentrations to the reactants' concentrations, you need to consider the stoichiometric coefficients of each species in the balanced equation.
In this case, the stoichiometric coefficients are:
CO2 (g) + H2 (g) CO (g) + H2O (g)
1 1 1 1
Therefore, at equilibrium, the concentrations for each species are:
[CO2] = [CO2] initial - moles of CO2 reacted / volume of reaction vessel
= (0.1908 moles - 0.0092 moles) / 2.00 L
[H2] = [H2] initial - moles of H2 reacted / volume of reaction vessel
= (0.0908 moles - 0.0092 moles) / 2.00 L
[CO] = [CO] initial + moles of CO formed / volume of reaction vessel
= (0.0092 moles + 0.0092 moles) / 2.00 L
[H2O] = [H2O] initial + moles of H2O formed / volume of reaction vessel
= (0.0092 moles + 0.0092 moles) / 2.00 L
Now, you have the concentrations of all the species at equilibrium. Plug these values into the equation for Kc.
Kc = ([CO] * [H2O]) / ([CO2] * [H2])
Replace the concentration values with the calculated values and solve for Kc.
Kc = (0.0184 / 2.00) / (0.1816 / 2.00)
Finally, simplify and calculate the value of Kc.
Kc = 0.0092 / 0.0908
Therefore, the value of the equilibrium constant, Kc, for the above system is 0.101.