A mixture consisting of \(1.000 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) and \(1.000 \mathrm{~mol} \mathrm{CO}(\mathrm{g})\) is placed in a \(10.00-\mathrm{L}\) reaction vessel at \(800 \mathrm{~K}\). At equilibrium, \(0.665 \mathrm{~mol} \mathrm{CO}_{2}(\mathrm{~g})\) is present as a result of the reaction \(\mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})=\) \(\mathrm{CO}_{2}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g})\). What are (a) the equilibrium concentrations for all substances and (b) the value of \(K_{e}\) ?

A chemical reaction involves the transformation of reactants into products. This process occurs when reactant molecules collide with sufficient energy to overcome the activation energy barrier, leading to a rearrangement of atoms to form new substances. In our example, the chemical reaction under study is a combination of carbon monoxide (CO) and water vapor (H₂O) to produce carbon dioxide (CO₂) and hydrogen gas (H₂).

This transformation honors the law of conservation of mass, meaning that the number of atoms of each element remains the same before and after the reaction. To visualize this concept, picture a dance floor where dance partners (atoms) switch partners (bonds) without leaving the dance (reactor). This particular dance is orchestrated so that each dancer (atom) ends up with a new partner (molecule) in a 1:1 ratio, following the stoichiometry of the reaction.

In the realm of chemistry, when a reaction reaches a stage where the rate of the forward reaction equals the rate of the reverse reaction, it is said to be at equilibrium. The equilibrium constant, symbolized by K_c, is a numerical value that quantifies the ratio of concentrations of products to reactants at this state, each raised to the power of their stoichiometric coefficients.

Picture the balance scale; the equilibrium constant is like the scale's reading, illustrating whether the reaction favors products, reactants, or is balanced. A larger K_c suggests products are favored, indicating a 'heavier' side with more products, while a smaller K_c implies the scale tips towards the reactants, suggesting their dominance at equilibrium.

The art of stoichiometry lies in the quantitative relationship between reactants and products in a chemical reaction. It's like a recipe that dictates the exact proportions of ingredients needed and the amount of product formed.

In our scenario, the stoichiometry of the reaction is 1:1:1:1, signifying for every mole of CO and H₂O that reacts, one mole of CO₂ and H₂ will form. Furthermore, when 0.665 mol of CO₂ is produced, an equal amount of H₂ forms while the same quantity of CO and H₂O is consumed. This stoichiometric relationship is crucial for calculating the changes in concentrations and is a fundamental concept in understanding chemical reactions.

The equilibrium concentrations refer to the amounts of reactants and products present when the chemical reaction has reached equilibrium. These concentrations can be calculated systematically, often starting with initial concentrations and then adjusting based on the reaction stoichiometry and changes in moles of substances as the reaction progresses.

In the given exercise, we applied stoichiometry to find the changes in concentrations from initial to equilibrium. Like a bookkeeper, we 'debited' the consumed reactants and 'credited' the formed products to their respective 'accounts' to tally the equilibrium 'balance'. The concentration of each substance at equilibrium represents its 'final balance', which plays a pivotal role in calculating the equilibrium constant.