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Ch.15 - Chemical Equilibrium
Chapter 15, Problem 41a

Indicate whether each of the following statements about the reaction quotient Q is true or false: (a) The expression for 𝑄𝑐 looks the same as the expression for 𝐾𝑐.

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Understand that both the reaction quotient \( Q_c \) and the equilibrium constant \( K_c \) are calculated using the same expression, which is the ratio of the concentrations of the products to the reactants, each raised to the power of their stoichiometric coefficients.
Recognize that the difference between \( Q_c \) and \( K_c \) lies in the state of the reaction: \( Q_c \) is calculated at any point in time, while \( K_c \) is specifically at equilibrium.
Write the general expression for \( Q_c \) for a reaction: \( aA + bB \rightleftharpoons cC + dD \), where \( Q_c = \frac{[C]^c[D]^d}{[A]^a[B]^b} \).
Note that the expression for \( K_c \) is identical to that of \( Q_c \), \( K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b} \), but it is evaluated when the system is at equilibrium.
Conclude that the statement is true because the mathematical expressions for \( Q_c \) and \( K_c \) are indeed the same, differing only in the conditions under which they are evaluated.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Reaction Quotient (Q)

The reaction quotient, denoted as Q, is a measure of the relative concentrations of products and reactants in a chemical reaction at any point in time. It is calculated using the same expression as the equilibrium constant (K), but it can be evaluated at any set of concentrations, not just at equilibrium. Q helps determine the direction in which a reaction will proceed to reach equilibrium.
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Reaction Quotient Q

Equilibrium Constant (K)

The equilibrium constant, represented as K, quantifies the ratio of the concentrations of products to reactants at equilibrium for a reversible reaction. It is a specific value that remains constant at a given temperature and is derived from the balanced chemical equation. K provides insight into the extent of a reaction and whether products or reactants are favored at equilibrium.
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Equilibrium Constant K

Comparison of Q and K

The relationship between Q and K is crucial for predicting the behavior of a reaction. If Q < K, the reaction will proceed in the forward direction to produce more products; if Q > K, the reaction will shift backward to form more reactants. When Q equals K, the system is at equilibrium, and no net change occurs. Understanding this comparison is essential for analyzing dynamic chemical systems.
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Comparing Q to K Example
Related Practice
Textbook Question

The equilibrium 2 NO(𝑔) + Cl2(𝑔) β‡Œ 2 NOCl(𝑔) is established at 500.0 K. An equilibrium mixture of the three gases has partial pressures of 0.095 atm, 0.171 atm, and 0.28 atm for NO, Cl2, and NOCl, respectively. (b) If the vessel has a volume of 5.00 L, calculate Kc at this temperature.

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Textbook Question

Phosphorus trichloride gas and chlorine gas react to form phosphorus pentachloride gas: PCl3(𝑔) + Cl2(𝑔) β‡Œ PCl5(𝑔). A 7.5-L gas vessel is charged with a mixture of PCl3(𝑔) and Cl2(𝑔), which is allowed to equilibrate at 450 K. At equilibrium the partial pressures of the three gases are 𝑃PCl3 = 0.124 atm, 𝑃Cl2 = 0.157 atm, and 𝑃PCl5 = 1.30 atm. (a) What is the value of 𝐾𝑝 at this temperature?

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Textbook Question

A mixture of 0.2000 mol of CO2, 0.1000 mol of H2, and 0.1600 mol of H2O is placed in a 2.000-L vessel. The following equilibrium is established at 500 K: CO2(𝑔) + H2(𝑔) β‡Œ CO(𝑔) + H2O (𝑔) (d) Calculate 𝐾𝑐 for the reaction.

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Textbook Question

Indicate whether each of the following statements about the reaction quotient Q is true or false: (b) If 𝑄𝑐 < 𝐾𝑐, the reaction needs to proceed to the right to reach equilibrium.

Textbook Question

At 100Β°C, the equilibrium constant for the reaction COCl2(𝑔) β‡Œ CO(𝑔) + Cl2(𝑔) has the value 𝐾𝑐 = 2.19Γ—10βˆ’10. Are the following mixtures of COCl2, CO, and Cl2 at 100Β°C at equilibrium? If not, indicate the direction that the reaction must proceed to achieve equilibrium. (a) [COCl2] = 2.00Γ—10βˆ’3 𝑀, [CO] = 3.3Γ—10βˆ’6 𝑀, [Cl2] = 6.62Γ—10βˆ’6𝑀

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Textbook Question

At 900 K, the following reaction has 𝐾𝑝 = 0.345: 2 SO2(𝑔) + O2(𝑔) β‡Œ 2 SO3(𝑔) In an equilibrium mixture the partial pressures of SO2 and O2 are 0.135 atm and 0.455 atm, respectively. What is the equilibrium partial pressure of SO3 in the mixture?

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