91Ó°ÊÓ

For a general reaction: \[aA + bB \rightleftharpoons cC + dD\] \(K_C\) is the equilibrium constant in terms of concentrations, and it relates the concentrations of reactants and products at equilibrium: \[ K_C = \frac{[C]^c[D]^d}{[A]^a[B]^b} \] On the other hand, \(K_P\) is the equilibrium constant in terms of partial pressures and relates the partial pressures of reactants and products at equilibrium: \[ K_P = \frac{(P_C)^c(P_D)^d}{(P_A)^a(P_B)^b} \] The relationship between Kc and Kp is given by: \[ K_P = K_C \times (\frac{RT}{P})^{\Delta n} \] Where: - R: Ideal gas constant - T: Temperature in Kelvin - P: Total pressure - \(\Delta n\): Change in the number of moles of gas during the reaction (\(n_\text{final} - n_\text{initial}\)) For the given reaction: \[2A(g) + B(g) \rightleftharpoons A_{2}B(g)\] The change in the number of gas moles is: \[ \Delta n = 1 - (2 + 1) = -2 \] Thus: \[ K_p = K_c \times (\frac{RT}{P})^{-2} \] In general, this equation indicates that Kc and Kp have a numerical relationship, but they are not always exactly the same.

The equilibrium constant Kc is expressed in terms of concentrations, which are typically measured in mol/L. It is dimensionless when the given reaction has balanced stoichiometry, but in general, it can have units derived from the stoichiometric coefficients (\(a\), \(b\), \(c\), and \(d\)). Therefore, Kc may or may not have units. On the other hand, Kp is expressed in terms of partial pressures, typically measured in atm or bar. Thus, Kp will always have units derived from the pressure units (\(a\), \(b\), \(c\), and \(d\)). So, it is possible to differentiate Kc from Kp by comparing the units used to express the equilibrium constant.

When we increase the pressure for a reaction at constant temperature, the reaction tends to shift in the direction that reduces the pressure (Le Chatelier's principle). This can be achieved by moving towards the side with fewer gas moles. For the given reaction: \[2A(g) + B(g) \rightleftharpoons A_{2}B(g)\] The relationship between Kp and Kc is given by: \[ K_p = K_c \times (\frac{RT}{P})^{\Delta n} \] In this case, since \(\Delta n\) is negative, increasing the pressure will make the \((\frac{RT}{P})^{\Delta n}\) term larger, causing Kp to increase. Since Kc and Kp are related, Kc will also increase as the total pressure of the system is increased. #Conclusion# (a) False: Kc and Kp are numerically related, but they are not always the same. (b) True: Units can differentiate between Kc and Kp. (c) True: For the given equilibrium, the value of Kc increases with increasing pressure.