๐งช Understanding Kp and Kc: A Comprehensive Guide
Chemical equilibrium is a state where the rate of forward and reverse reactions are equal, and the concentrations of reactants and products remain constant. The equilibrium constant, denoted as either $K_c$ or $K_p$, quantifies this equilibrium. Let's break it down:
๐ Kc: Equilibrium Constant in Terms of Concentration
- โ๏ธ Definition: $K_c$ represents the ratio of products to reactants at equilibrium, where the amounts are expressed in terms of molar concentrations (moles per liter).
- ๐ Formula: For a general reversible reaction: $aA + bB \rightleftharpoons cC + dD$, the $K_c$ expression is: $K_c = \frac{{[C]^c[D]^d}}{{[A]^a[B]^b}}$, where [A], [B], [C], and [D] are the equilibrium concentrations of the reactants and products, and a, b, c, and d are their respective stoichiometric coefficients.
- ๐ก Example: Consider the reaction: $N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)$. The $K_c$ expression would be: $K_c = \frac{{[NH_3]^2}}{{[N_2][H_2]^3}}$.
๐จ Kp: Equilibrium Constant in Terms of Partial Pressures
- ๐ก๏ธ Definition: $K_p$ is similar to $K_c$, but it uses partial pressures instead of concentrations. It is used when dealing with reactions involving gases.
- ๐ข Formula: For the same general reaction $aA + bB \rightleftharpoons cC + dD$, if all components are gases, the $K_p$ expression is: $K_p = \frac{{(P_C)^c(P_D)^d}}{{(P_A)^a(P_B)^b}}$, where $P_A$, $P_B$, $P_C$, and $P_D$ are the partial pressures of the gases at equilibrium.
- โ๏ธ Example: For the reaction: $N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)$, the $K_p$ expression is: $K_p = \frac{{(P_{NH_3})^2}}{{(P_{N_2})(P_{H_2})^3}}$.
๐ค Relationship Between Kp and Kc
- ๐ Formula: $K_p$ and $K_c$ are related by the equation: $K_p = K_c(RT)^{\Delta n}$, where $R$ is the ideal gas constant (0.0821 L atm / (mol K)), $T$ is the temperature in Kelvin, and $\Delta n$ is the change in the number of moles of gas (moles of gaseous products - moles of gaseous reactants).
- ๐งฎ Calculating ฮn: In the reaction $N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)$, $\Delta n = 2 - (1 + 3) = -2$.
- ๐ก When Kp = Kc: If $\Delta n = 0$, then $K_p = K_c$ because $(RT)^0 = 1$.
โ๏ธ Writing Equilibrium Expressions: Key Steps
- โ๏ธ Identify Reactants and Products: Determine the reactants and products in the balanced chemical equation.
- ๐ Write the Ratio: Write the equilibrium expression as a ratio of products to reactants.
- โ Apply Stoichiometric Coefficients: Raise each concentration or partial pressure to the power of its stoichiometric coefficient in the balanced equation.
- โ๏ธ Include Only Gases and Aqueous Solutions: Solids and pure liquids are excluded from the equilibrium expression because their concentrations do not change during the reaction.