The equilibrium constant \(K_c\) for a reversible reaction is expressed as the ratio of the product of the molar concentrations of the products to the product of the molar concentrations of the reactants, with each concentration raised to the power of its stoichiometric coefficient in the balanced chemical equation. For the given reaction, we need to identify the reactants, products, and their stoichiometric coefficients.
\(\text{N}_2\text{(g)} + 3\text{H}_2\text{(g)} \rightleftharpoons 2\text{NH}_3\text{(g)}\)
The general form for \(K_c\) for a reaction \(a\text{A} + b\text{B} \rightleftharpoons c\text{C} + d\text{D}\) is:
\[ K_c = \frac{[\text{C}]^c[\text{D}]^d}{[\text{A}]^a[\text{B}]^b} \]Applying this to the given reaction:
\[ K_c = \frac{[\text{NH}_3]^2}{[\text{N}_2]^1[\text{H}_2]^3} \]Which simplifies to:
\[ K_c = \frac{[\text{NH}_3]^2}{[\text{N}_2][\text{H}_2]^3} \]B) \(K_c = [\text{NH}_3]^2 / [\text{N}_2][\text{H}_2]^3\)
This option correctly represents the equilibrium constant expression, with the concentration of the product (\(\text{NH}_3\)) raised to its stoichiometric coefficient (2) in the numerator, and the concentrations of the reactants (\(\text{N}_2\) and \(\text{H}_2\)) raised to their respective stoichiometric coefficients (1 and 3) in the denominator.
The question asks for the notation used to represent the equilibrium constant for gaseous equilibria when expressed in terms of partial pressures. We need to recall the standard conventions for equilibrium constants in chemistry.
Correct Option: D) Kp is the correct notation for the equilibrium constant when expressed in terms of the partial pressures of reactants and products in a gaseous equilibrium.
The relationship between the equilibrium constants \(K_p\) (in terms of partial pressures) and \(K_c\) (in terms of molar concentrations) for a gaseous reaction is derived using the ideal gas law. This relationship depends on the change in the number of moles of gaseous products and reactants.
Consider a general reversible gaseous reaction:
\[ aA(g) + bB(g) ightleftharpoons cC(g) + dD(g) \]The equilibrium constant in terms of concentrations, \(K_c\), is given by:
\[ K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b} \]The equilibrium constant in terms of partial pressures, \(K_p\), is given by:
\[ K_p = \frac{(P_C)^c (P_D)^d}{(P_A)^a (P_B)^b} \]According to the ideal gas law, \(PV = nRT\), which can be rearranged to \(P = \frac{n}{V}RT\). Since \(\frac{n}{V}\) represents molar concentration, we can write \(P = [C]RT\), where \([C]\) is the molar concentration.
Substitute the partial pressures in terms of concentrations into the \(K_p\) expression:
\[ K_p = \frac{([C]RT)^c ([D]RT)^d}{([A]RT)^a ([B]RT)^b} \]Rearrange the terms:
\[ K_p = \frac{[C]^c [D]^d}{[A]^a [B]^b} \times \frac{(RT)^c (RT)^d}{(RT)^a (RT)^b} \]\[ K_p = K_c \times (RT)^{(c+d) - (a+b)} \]Let \(\Delta n\) be the change in the number of moles of gaseous products minus the number of moles of gaseous reactants. So, \(\Delta n = (c+d) - (a+b)\).
Therefore, the relationship becomes:
\[ K_p = K_c (RT)^{\Delta n} \]C) Kp = Kc(RT)^Δn is the correct relationship, derived directly from the definitions of \(K_p\) and \(K_c\) and the ideal gas law.
The question asks to identify what the term \(\Delta n\) represents in the relationship between the equilibrium constants \(K_p\) and \(K_c\). This relationship is fundamental in chemical equilibrium, particularly for reactions involving gases.
Correct Option: C) The difference between the number of moles of gaseous products and gaseous reactants
The relationship between the equilibrium constants \(K_p\) (in terms of partial pressures) and \(K_c\) (in terms of molar concentrations) for a gaseous reaction is given by the equation \(K_p = K_c (RT)^{\Delta n}\). The term \(\Delta n\) represents the change in the number of moles of gaseous products minus the number of moles of gaseous reactants.
The given reaction is:
\[ \text{PCl}_5(\text{g}) ightleftharpoons \text{PCl}_3(\text{g}) + \text{Cl}_2(\text{g}) \]From the balanced equation, the gaseous products are \(\text{PCl}_3(\text{g})\) and \(\text{Cl}_2(\text{g})\).
Total moles of gaseous products, \(\sum n_{\text{products}} = 1 + 1 = 2\).
From the balanced equation, the gaseous reactant is \(\text{PCl}_5(\text{g})\).
Total moles of gaseous reactants, \(\sum n_{\text{reactants}} = 1\).
The formula for \(\Delta n\) is:
\[ \Delta n = (\text{Total moles of gaseous products}) - (\text{Total moles of gaseous reactants}) \] \[ \Delta n = \sum n_{\text{products}} - \sum n_{\text{reactants}} \]Substitute the values calculated in steps 2 and 3:
\[ \Delta n = 2 - 1 \] \[ \Delta n = +1 \]Correct Option: A) +1
The question asks for the correct description of the equilibrium constant, K. We need to recall the definition and properties of the equilibrium constant in chemical reactions.
\[ aA + bB \rightleftharpoons cC + dD \]
The equilibrium constant \(K_c\) (in terms of concentrations) is given by:
\[ K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b} \]
where \([A]\), \([B]\), \([C]\), and \([D]\) are the molar concentrations of the reactants and products at equilibrium.
C) K is constant at a given temperature and is independent of the initial concentrations