Do you expect a large or small value of the equilibrium constant for a reaction with the following values of ∆G°? (a) ∆G° is positive. (b) ∆G° is negative.

Verified step by step guidance

Step 1: Understand the relationship between the standard Gibbs free energy change (∆G°) and the equilibrium constant (K) using the equation: ∆G° = -RT ln(K), where R is the universal gas constant and T is the temperature in Kelvin.

Step 2: Analyze the case when ∆G° is positive. A positive ∆G° indicates that the reaction is non-spontaneous under standard conditions, which implies that the equilibrium constant K will be less than 1, indicating a small value.

Step 3: Consider the case when ∆G° is negative. A negative ∆G° suggests that the reaction is spontaneous under standard conditions, which means the equilibrium constant K will be greater than 1, indicating a large value.

Step 4: Recall that a large equilibrium constant (K > 1) means the products are favored at equilibrium, while a small equilibrium constant (K < 1) means the reactants are favored.

Step 5: Conclude that the sign of ∆G° directly influences the magnitude of the equilibrium constant, with positive ∆G° leading to a small K and negative ∆G° leading to a large K.

Key Concepts

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

Gibbs Free Energy (∆G°)

Gibbs Free Energy (∆G°) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. A positive ∆G° indicates that a reaction is non-spontaneous under standard conditions, while a negative ∆G° suggests that the reaction is spontaneous. The sign of ∆G° is crucial for predicting the direction of a chemical reaction.

Equilibrium Constant (K)

The equilibrium constant (K) is a dimensionless value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. A large K value (K >> 1) indicates that products are favored at equilibrium, while a small K value (K << 1) suggests that reactants are favored. The relationship between K and ∆G° is fundamental in understanding reaction spontaneity.

Relationship between ∆G° and K

The relationship between Gibbs Free Energy (∆G°) and the equilibrium constant (K) is given by the equation ∆G° = -RT ln(K), where R is the universal gas constant and T is the temperature in Kelvin. This equation shows that a negative ∆G° corresponds to a large K, indicating that the reaction favors products, while a positive ∆G° corresponds to a small K, indicating that reactants are favored. Understanding this relationship is essential for predicting the behavior of chemical reactions.

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Relationship between ∆E°, ∆G°, and K

Related Practice

Textbook Question

Use the data in Appendix B to calculate ∆G for the decom-position of nitrosyl chloride at 25 °C when the partial pressures are 2.00 atm of NOCl, 1.00 * 10^-3 atm of NO, and 1.00 * 10^-3 atm of Cl2: Is the reaction spontaneous in the forward or the reverse direction under these conditions?

Textbook Question

Urea (NH2CONH2), an important nitrogen fertilizer, is produced industrially by the reaction Given that ∆G° = -13.6 kJ, calculate ∆G at 25 °C for the following sets of conditions. .(a) 10 atm NH3, 10 atm CO2, 1.0 M NH2CONH2(b) 0.10 atm NH3, 0.10 atm CO2, 1.0 M NH2CONH2Is the reaction spontaneous for the conditions in part (a) and/or part (b)?

Textbook Question

Ammonium nitrate is dangerous because it decomposes (sometimes explosively) when heated: (a) Using the data in Appendix B, show that this reaction is spontaneous at 25 °C.

Textbook Question

Use the data in Appendix B to calculate the equilibrium pressure of CO₂ in a closed 1 L vessel that contains each of the following samples:

(a) 15 g of MgCO₃ and 1.0 g of MgO at 25 °C

(b) 15 g of MgCO3 and 1.0 g of MgO at 280 °C .

Assume that ∆H° and ∆S° are independent of temperature.

Textbook Question

Consider the Haber synthesis of gaseous NH₃ (∆H°_f = -46.1 kJ/mol; ∆G°_f = -16.5 kJ/mol: (d) What are the equilibrium constants K_p and K_c for the reaction at 350 K? Assume that ∆H° and ∆S° are independent of temperature.