For \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g), K_{p}=3.0 \times 10^{4}\) at 700 \(\mathrm{K} .\) In a \(2.00-\mathrm{L}\) vessel, the equilibrium mixture contains 1.17 \(\mathrm{g}\) of \(\mathrm{SO}_{3}\) and 0.105 \(\mathrm{g}\) of \(\mathrm{O}_{2} .\) How many grams of \(\mathrm{SO}_{2}\) are in the vessel?

The equilibrium constant, expressed as Kp when dealing with gases, is a crucial concept in chemical equilibrium that quantifies the relationship between the concentrations of reactants and products in a gaseous reaction at equilibrium. Given the equilibrium state of a chemical reaction, Kp is calculated using the partial pressures of the gases involved.

Kp has a fixed value at a constant temperature, which implies that at equilibrium, no matter the initial concentrations of reactants and products, the ratio of their concentrations raised to the power of their stoichiometric coefficients will always be the same. In simple terms, higher Kp values indicate a greater quantity of products relative to reactants at equilibrium, suggesting the reaction favors the product side. Conversely, a lower Kp value suggests the reaction favors the reactants. Understanding Kp is essential in predicting the direction of the reaction's shift when external conditions change, such as pressure or temperature.

Molar concentration is a way to express the concentration of a solute in a solution, defined as the number of moles of solute per liter of solution, with units typically in moles per liter (M). For gas-phase reactions, as in our chemical equilibrium example, molar concentration can also be used to describe the concentration of a gaseous compound in a mixture of gases.

It is calculated by dividing the number of moles of the compound by the volume of the gas or solution in which it is contained. Knowing the molar concentration of the reactants and products at equilibrium is essential for calculating the equilibrium constant, as these values are directly plugged into the expression for Kp or Kc (the equilibrium constant in terms of concentration). Correctly finding these concentrations is pivotal in understanding the system's balance and in predicting how it will react to external changes.

Molar mass is the mass of one mole of a substance, and it is a bridge between the macroscopic and molecular worlds, allowing chemists to count molecules by weighing. Measured in grams per mole (g/mol), it is determined by summing the atomic masses of all atoms in a molecule of the substance.

Molar mass can help us convert between the mass of a substance and the number of moles, a fundamental step in stoichiometry. For example, knowing the molar mass of SO₃ and O₂ allowed us to calculate their moles from the mass in the original exercise, a necessary step before finding their molar concentrations. Understanding molar mass is not only vital for reaction stoichiometry but also for interpreting various physical, chemical, and biological processes.

Stoichiometry is the field of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It is the roadmap that allows chemists to predict the amounts of substances consumed and produced in a given reaction.

Through stoichiometry, we can deduce how many moles of each reactant are needed to form a certain number of moles of a product and vice versa. The coefficients in a balanced chemical equation provide the necessary ratios to perform these calculations. In the context of our exercise, the stoichiometric coefficients allowed us to relate the changes in molar concentrations of SO₂, O₂, and SO₃ during the reaction. A firm grasp of stoichiometry is essential for making accurate predictions in chemistry, ranging from the laboratory to industrial processes.