Explores the law of mass action and the calculation of the equilibrium constant, K. This stack covers writing expressions for K_c (concentration) and K_p (pressure), interpreting the magnitude of K, and handling heterogeneous equilibria.
It states that for a reversible reaction at equilibrium and a constant temperature, there is a specific ratio of product concentrations to reactant concentrations that has a constant value, known as the equilibrium constant \(K\).
For the generic reaction $$ aA + bB \rightleftharpoons cC + dD $$, write the expression for the equilibrium constant, \(K_c\).
The expression is the ratio of the product concentrations to reactant concentrations, each raised to the power of their stoichiometric coefficient: $$ K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b} $$
What does a very large value of the equilibrium constant (e.g., \(K > 10^3\)) imply about the reaction?
A large \(K\) value indicates that the equilibrium lies far to the right. The concentration of products is much greater than the concentration of reactants, so the reaction is considered "product-favored."
What does a very small value of the equilibrium constant (e.g., \(K < 10^{-3}\)) imply about the reaction?
A small \(K\) value indicates that the equilibrium lies far to the left. The concentration of reactants is much greater than the concentration of products, so the reaction is "reactant-favored."
Which states of matter are excluded from the equilibrium constant expression and why?
Pure solids \((s)\) and pure liquids \((l)\) are excluded. Their concentrations (or more accurately, their activities) are considered constant and are incorporated into the value of the equilibrium constant, \(K\).
Write the \(K_c\) expression for the heterogeneous reaction: $$ Fe_2O_3(s) + 3CO(g) \rightleftharpoons 2Fe(s) + 3CO_2(g) $$
Only the gaseous components are included: $$ K_c = \frac{[CO_2]^3}{[CO]^3} $$
How is the equilibrium constant for partial pressures, \(K_p\), different from \(K_c\)?
\(K_p\) uses the partial pressures of gaseous reactants and products instead of their molar concentrations. For \(aA(g) \rightleftharpoons bB(g)\), $$ K_p = \frac{(P_B)^b}{(P_A)^a} $$.
What equation relates \(K_p\) and \(K_c\)?
$$ K_p = K_c(RT)^{\Delta n} $$ where \(R\) is the ideal gas constant, \(T\) is temperature in Kelvin, and \(\Delta n\) is the change in moles of gas.
In the equation $$ K_p = K_c(RT)^{\Delta n} $$, how do you calculate \(\Delta n\)?
\(\Delta n\) is the difference between the sum of the stoichiometric coefficients of the gaseous products and the gaseous reactants. $$ \Delta n = (moles\ of\ gas\ products) - (moles\ of\ gas\ reactants) $$
Under what condition is \(K_p = K_c\)?
\(K_p = K_c\) when \(\Delta n = 0\), meaning the number of moles of gaseous products is equal to the number of moles of gaseous reactants. The term `(RT)^0` becomes \(1\).
If a reaction's equilibrium constant is \(K\), what is the equilibrium constant (\(K'\)) for the reverse reaction?
The new equilibrium constant is the reciprocal of the original constant: `$$ K' = \frac{1}{K} $$`.
If you multiply the coefficients of a balanced chemical equation by a factor \(n\), how does the original equilibrium constant \(K\) change?
The new equilibrium constant, \(K'\), is the original constant raised to the power of \(n\). $$ K' = (K)^n $$
