The equilibrium constant \(K_{\mathrm{c}}\) for the reaction $$\mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}(g)$$ is 4.2 at \(1650^{\circ} \mathrm{C}\). Initially \(0.80 \mathrm{~mol} \mathrm{H}_{2}\) and \(0.80 \mathrm{~mol}\) \(\mathrm{CO}_{2}\) are injected into a 5.0 - \(\mathrm{L}\) flask. Calculate the concentration of each species at equilibrium.

Understanding chemical equilibrium is a pivotal concept in chemistry, essential for grasping how reactions proceed and reach a state of balance. It occurs when a system's forward reaction (reactants turning into products) and reverse reaction (products re-forming into reactants) proceed at the same rate. As a result, the concentrations of all reactants and products remain constant over time, meaning they do not show any noticeable change despite the continuous occurrence of both reactions.

In the provided exercise, chemical equilibrium is achieved in the reaction involving hydrogen, carbon dioxide, water, and carbon monoxide gases. When a system reaches equilibrium, it's crucial to note that the process doesn't halt; both the forward and reverse reactions are ongoing, just at a rate that doesn't change the overall quantities of reactants and products.

To measure this dynamic balance, chemists use the equilibrium constant, denoted as K_c in the case of concentrations, which provides a ratio reflecting the relationship between the concentrations of products and reactants at equilibrium.

One effective tool for solving equilibrium problems is the ICE Table, which stands for Initial, Change, and Equilibrium. This is a practical method for organizing what's known and what needs to be determined about the reactants and products in a chemical reaction. It's like a ledger that keeps track of where the reaction starts, how it changes, and where it eventually balances out.

In our exercise, the ICE Table is used to track the initial moles of hydrogen and carbon dioxide, both set at 0.8 mole. Since no products were present initially, their moles are counted as zero. As the reaction proceeds, we document the change for each substance: losing 'x' moles of reactants and gaining 'x' moles of products. This simple accounting allows us to express the final equilibrium concentrations in terms of 'x', which is our unknown value representing the extent of the reaction at equilibrium.

Using an ICE Table effectively simplifies complicated equilibrium calculations by providing a systematic approach to determine concentration changes throughout the reaction.

Equilibrium expressions are mathematical representations that relate the concentrations of the products and reactants at equilibrium for a chemical reaction. These expressions are based on the law of mass action which states that for a reversible reaction at equilibrium and at a constant temperature, a certain ratio of the concentrations of reactants and products is constant, known as the equilibrium constant (K).

In this particular exercise, the equilibrium expression is given by the formula:
\[K_c = \frac{[H_{2}O][CO]}{[H_{2}][CO_{2}]}\]
The square brackets indicate the molar concentrations of each species at equilibrium. The expression for the equilibrium constant, K_c, demonstrates that its value is determined by the concentration of the products raised to the power of their coefficients and divided by the concentration of the reactants raised to the power of their coefficients as shown in a balanced chemical equation.

To find the equilibrium concentrations, we substitute the expressions from the ICE Table into the equilibrium constant formula and solve for 'x'. Once 'x' is known, we can then determine the concentrations of all species at equilibrium. Properly setting up and calculating equilibrium expressions is critical in predicting the behavior of a chemical system under various conditions.