For the chemical reactions shown below, write an expression for the equilibrium constant in terms of the partial pressures of the reactants and products. 1\. \(\mathrm{PCl}_{5}(g) \rightleftarrows \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g)\) 2\. \(2 \mathrm{NOCl}(g) \rightleftarrows 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g)\) 3\. \(\mathrm{PCl}_{3}(g)+3 \mathrm{NH}_{3}(g) \rightleftarrows \mathrm{P}\left(\mathrm{NH}_{2}\right) 3(g)+3 \mathrm{HCl}(g)\)

Understanding the concept of chemical equilibrium is crucial for mastering chemistry. It refers to the state of a reversible chemical reaction where the rate of the forward reaction equals the rate of the reverse reaction. As a result, the concentrations—or in the case of gases, the partial pressures—of reactants and products remain constant over time.

At equilibrium, it's important to note that the reactants are not completely converted into products; instead, both reactants and products are present in a ratio that does not change. This dynamic balance is where no net change is observed, which can be misleading because reactions at the molecular level are still occurring. The equilibrium constant expression quantitatively defines the concentrations of the reactants and products in this balanced state.

The concept of partial pressures is often used when dealing with chemical reactions involving gases. The partial pressure of a gas in a mixture is the pressure the gas would exert if it occupied the entire volume of the mixture by itself. Dalton's Law states that the total pressure of a mixture of gases is equal to the sum of their partial pressures.

When writing the equilibrium constant expression for reactions with gaseous components, the partial pressures of the reactants and products are used. This reflects the fact that gases mix thoroughly and react according to their partial pressures in a given volume. It's also a demonstration of how the gaseous state conforms to the ideal gas law under many conditions.

Reaction coefficients play a defining role in writing equilibrium expressions. These coefficients are the numbers placed before the chemical formulas in a balanced equation and signify the ratio in which molecules react or are produced. In the context of equilibrium, these coefficients become the exponents for the partial pressures (or concentrations) of the respective reactants and products.

For instance, a reaction coefficient of 2 in front of a reactant means that two moles of that substance are involved in the reaction, and this will be reflected in the equilibrium expression by squaring the partial pressure of that reactant. Such precise quantification is essential for accurate calculations and predictions about the behavior of the reaction at equilibrium.

A balanced chemical equation is the foundation for any quantitative analysis in chemistry. It is arrived at by ensuring that the number of atoms of each element is the same on both the reactant and product sides of an equation. This balance is a requirement from the Law of Conservation of Mass, which states that matter is neither created nor destroyed in a chemical reaction.

In order to write the equilibrium constant expression correctly, it is essential to start with a fully balanced chemical equation. The coefficients from this equation directly influence the powers to which the partial pressures are raised in the equilibrium expression. Remember that getting this step right is critical for understanding the stoichiometry of the reaction and for making correct calculations based on that reaction's equilibrium state.