Problem 20 - Chemistry: The Central Science in SI Units, Global Edition

Question

Which of the following statements are true and which are false? (a) For the reaction \(2 \mathrm{~A}(g)+\mathrm{B}(g) \rightleftharpoons \mathrm{A}_{2} \mathrm{~B}(g) K_{c}\) and \(K_{p}\) are numerically the same. (b) It is possible to distinguish \(K_{c}\) from \(K_{p}\) by comparing the units used to express the equilibrium constant. \((\mathbf{c})\) For the equilibrium in (a), the value of \(K_{c}\) increases with increasing pressure.

Step-by-Step Solution

Answer

Statement (a) is false, as Kc and Kp are not numerically the same for the given reaction since \(\Delta n \neq 0\). Statement (b) is true, as Kc and Kp can be distinguished by their units. Statement (c) is false, as the value of Kc is not directly affected by changes in pressure but only by changes in temperature.

Step 1: a) Comparing Kc and Kp for the given reaction

For the given reaction, we have: \[2A(g) + B(g) \rightleftharpoons A_2B(g)\] Kc and Kp are related by the following equation: \[K_p = K_c(RT)^{\Delta n}\] where R is the gas constant, T is the temperature in Kelvin, and \(\Delta n\) is the change in the number of moles of gas in the balanced equation (products minus reactants). In this reaction, \(\Delta n = (1) - (2+1) = -2\). Since \(\Delta n\) is not equal to 0, Kc and Kp will not be numerically the same. Therefore, statement (a) is false.

Step 2: b) Distinguishing Kc and Kp by their units

Kc and Kp are equilibrium constants that have different units. Kc is generally expressed in terms of concentrations (moles per liter, M) while Kp is expressed in terms of partial pressures (atmospheres, atm). It is indeed possible to distinguish between Kc and Kp by comparing the units used to express the equilibrium constant. Statement (b) is true.

Step 3: c) Effect of increasing pressure on the value of Kc

For the given reaction, the value of Kc is not directly affected by changes in pressure. Kc can only be affected by changes in temperature. The position of equilibrium, however, can be affected by changes in pressure due to Le Chatelier's principle. In the given reaction, increasing pressure would shift the equilibrium towards the side with fewer moles of gas (the right side) in order to alleviate the increased pressure. This means that the amount of A2B would increase, while the amount of A and B would decrease. This change affects the ratio of concentrations at equilibrium, but the constant Kc itself would remain unchanged. So, statement (c) is false.

Key Concepts

Equilibrium Constant (Kc and Kp)

The equilibrium constant is a significant concept when studying reaction equilibrium. There are two types of equilibrium constants depending on how the equilibrium is expressed: \(K_c\) and \(K_p\).

\(K_c\) is used when the equilibrium is expressed in terms of concentrations. It's calculated with concentration values, given in moles per liter (M).
On the other hand, \(K_p\) is applied when partial pressures are used, which are typically measured in atmospheres (atm).

Both \(K_c\) and \(K_p\) are related through the equation:
\[ K_p = K_c (RT)^{\Delta n} \]
Here, \(R\) is the ideal gas constant, \(T\) is the temperature in Kelvin, and \(\Delta n\) is the difference in moles of gas between products and reactants.

This relationship is crucial in determining whether \(K_c\) and \(K_p\) will have the same numerical value. If \(\Delta n = 0\), then \(K_c = K_p\). However, if \(\Delta n eq 0\), then they differ.

Understanding this helps clarify why, in some reactions, \(K_c\) and \(K_p\) are equivalent, and in others, they are not.

Le Chatelier's Principle

Le Chatelier's Principle is a foundational concept in understanding how equilibria respond to changes in their environment. It states that if a system at equilibrium is disturbed by an external change, such as pressure, temperature, or concentration, the system will adjust itself to partially counteract the effect of the change and attain a new equilibrium.

For example, consider a gaseous reaction where increasing the pressure would shift the equilibrium towards the side with fewer moles of gas. This shift happens because the system attempts to reduce the stress of increased pressure by favoring the formation of fewer gas molecules.

• Higher pressure => shifts towards fewer moles of gas
• Increased temperature => shifts depending on endothermic or exothermic nature of the reaction
• Increased concentration of one species => shifts the equilibrium to consume the added species

Le Chatelier's Principle is handy for predicting how external changes will affect the direction of equilibrium shifts, but it should not be confused with changes in the equilibrium constant, \(K_c\), which remains constant unless temperature is altered.

Reaction Stoichiometry

Reaction stoichiometry is crucial for understanding chemical reactions' balance and proportions. It focuses on the quantities of reactants and products in a chemical equation.

Using stoichiometry, we can determine how much of each substance is involved in a reaction. This involves using mole ratios derived from the balanced chemical equation, which provide insights into the quantitative relationship between reactants and products.

For example, in the reaction \(2A(g) + B(g) \rightleftharpoons A_2B(g)\), stoichiometry lets us calculate the change in moles of each substance when the reaction reaches equilibrium. Here, the balanced equation shows that two moles of \(A\) and one mole of \(B\) react to form one mole of \(A_2B\).

This stoichiometric relationship helps in determining the equilibrium concentrations and is vital in calculating the equilibrium constant \(K_c\) or \(K_p\), where the stoichiometric coefficients become the powers to which concentration or pressure terms are raised in the expression for the equilibrium constant.