Write a chemical equation for an equilibrium system that...

Write a chemical equation for an equilibrium system that would lead to the following expressions (a-d) for $K$. (a) $K=\frac{\left(P_{\mathrm{CO}_{2}}\right)^{3}\left(P_{\mathrm{H}_{2} \mathrm{O}}\right)^{4}}{\left(P_{\mathrm{C}_{3} \mathrm{H}_{8}}\right)\left(P_{\mathrm{O}_{2}}\right)^{5}}$ (b) $K=\frac{P_{\mathrm{C}_{10} \mathrm{H}_{12}}}{\left(P_{\mathrm{C}_{5} \mathrm{H}_{6}}\right)^{2}}$ (c) $K=\frac{\left[\mathrm{PO}_{4}^{3-}\right]\left[\mathrm{H}^{+}\right]^{3}}{\left[\mathrm{H}_{3} \mathrm{PO}_{4}\right]}$ (d) $K=\frac{\left(P_{\mathrm{CO}_{2}}\right)\left(P_{\mathrm{H}_{2} \mathrm{O}}\right)}{\left[\mathrm{CO}_{3}^{2-}\right]\left[\mathrm{H}^{+}\right]^{2}}$

Write a chemical equation for an equilibrium system that would lead to the following expressions (a-d) for $K$.
(a) $K=\frac{\left(P_{\mathrm{CO}_{2}}\right)^{3}\left(P_{\mathrm{H}_{2} \mathrm{O}}\right)^{4}}{\left(P_{\mathrm{C}_{3} \mathrm{H}_{8}}\right)\left(P_{\mathrm{O}_{2}}\right)^{5}}$
(b) $K=\frac{P_{\mathrm{C}_{10} \mathrm{H}_{12}}}{\left(P_{\mathrm{C}_{5} \mathrm{H}_{6}}\right)^{2}}$
(c) $K=\frac{\left[\mathrm{PO}_{4}^{3-}\right]\left[\mathrm{H}^{+}\right]^{3}}{\left[\mathrm{H}_{3} \mathrm{PO}_{4}\right]}$
(d) $K=\frac{\left(P_{\mathrm{CO}_{2}}\right)\left(P_{\mathrm{H}_{2} \mathrm{O}}\right)}{\left[\mathrm{CO}_{3}^{2-}\right]\left[\mathrm{H}^{+}\right]^{2}}$

Key Concepts

Reaction Stoichiometry

Reaction stoichiometry involves the quantitative relationship between reactants and products in a balanced chemical equation. The stoichiometric coefficients not only ensure that the mass and atoms are conserved but also appear as exponents in the equilibrium constant expression, directly affecting the value of K by representing the relative amounts of each substance involved in the reaction.

Chemical Equilibrium

Chemical equilibrium refers to the state in a reversible reaction when the rates of the forward and reverse reactions become equal, resulting in no net change in the concentrations or pressures of the reactants and products. This concept is central to understanding how reactions behave over time and how conditions such as temperature and pressure can affect the balance between the reacting species.

Equilibrium Constant

The equilibrium constant (K) is a numerical value that characterizes the ratio of the concentration or pressure of products to reactants at equilibrium, each raised to the power of their stoichiometric coefficients from the balanced chemical equation. It provides insight into the position of equilibrium, indicating whether the products or reactants are favored in the system under given conditions.

Partial Pressures vs. Concentrations

For reactions involving gases, equilibrium constants can be expressed in terms of partial pressures (Kp), while for reactions in solution, concentrations (Kc) are used. This distinction is important because it relates to how the physical state of the substances influences the derivation and application of the equilibrium constant, reflecting differences in how gaseous and solute species interact in their respective environments.

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