An equilibrium mixture at 1000 K contains an equilibrium...

An equilibrium mixture at 1000 K contains an equilibrium mixter $0.276\ \mathrm{mol}\ \mathrm{H}_{2}, 0.276 \mathrm{mol}\ \mathrm{CO}_{2}, 0.224\ \mathrm{mol}\ \mathrm{CO},$ and $0.224\ \mathrm{mol}\ \mathrm{H}_{2} \mathrm{O}$ $$\mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})$$ (a) Show that for this reaction, $K_{\mathrm{c}}$ is independent of the reaction volume, $V$ (b) Determine the value of $K_{\mathrm{c}}$ and $K_{\mathrm{p}}$

An equilibrium mixture at 1000 K contains an equilibrium mixter $0.276\ \mathrm{mol}\ \mathrm{H}_{2}, 0.276 \mathrm{mol}\ \mathrm{CO}_{2}, 0.224\ \mathrm{mol}\ \mathrm{CO},$ and $0.224\ \mathrm{mol}\ \mathrm{H}_{2} \mathrm{O}$
$$\mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})$$
(a) Show that for this reaction, $K_{\mathrm{c}}$ is independent of the reaction volume, $V$
(b) Determine the value of $K_{\mathrm{c}}$ and $K_{\mathrm{p}}$

Key Concepts

Volume Independence of Kc

The independence of Kc from the reaction volume arises because when concentrations (moles per unit volume) are substituted into the equilibrium expression, any dependence on the volume cancels out due to the balanced stoichiometry of the reaction. This means that while changes in volume affect individual concentrations, the ratio specified by Kc remains unchanged for a given temperature.

Equilibrium Constant (Kc and Kp)

The equilibrium constant, denoted as Kc for concentrations and Kp for partial pressures, quantifies the ratio of the concentration or fugacity of products to reactants at equilibrium according to the stoichiometric coefficients. It is specific to a given reaction at a particular temperature and provides important information about the position of equilibrium and the extent to which a reaction proceeds.

Relationship between Kc and Kp

The relationship between the equilibrium constants Kc and Kp is given by the equation Kp = Kc (RT)^(?n), where R is the universal gas constant, T is the temperature in Kelvin, and ?n is the difference in moles of gaseous products and reactants. This relation allows conversion between concentration-based and pressure-based equilibrium constants, reflecting the impact of the number of gas moles on the equilibrium state.

Chemical Equilibrium

Chemical equilibrium refers to the state in a reversible chemical reaction where the rate of the forward reaction equals the rate of the reverse reaction, leading to constant concentrations of all reactants and products over time. This balance is achieved even though both reactions continue to occur and is a foundational concept for analyzing chemical reactions under equilibrium conditions.

Law of Mass Action

The law of mass action states that at equilibrium, the ratio of the product of the concentrations of the products to the product of the concentrations of the reactants, each raised to the power of their respective stoichiometric coefficients, is constant. This principle is used to derive the expression for the equilibrium constant (Kc) and is crucial in understanding how reaction conditions affect equilibrium composition.

Transcript

Please give Ace some feedback