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 NH2CONH2 Is the reaction spontaneous for the conditions in part (a) and/or part (b)?

Verified step by step guidance

1. Identify the reaction: NH3(g) + CO2(g) ⇌ NH2CONH2(aq).
2. Use the equation for Gibbs free energy change: \( \Delta G = \Delta G^\circ + RT \ln Q \), where \( R \) is the gas constant (8.314 J/mol·K) and \( T \) is the temperature in Kelvin.
3. Calculate the reaction quotient \( Q \) for each set of conditions. For gases, use partial pressures, and for aqueous solutions, use concentrations. \( Q = \frac{[NH2CONH2]}{P_{NH3} \times P_{CO2}} \).
4. Convert the temperature from Celsius to Kelvin: \( T = 25 + 273.15 = 298.15 \text{ K} \).
5. Substitute \( \Delta G^\circ \), \( R \), \( T \), and \( Q \) into the Gibbs free energy equation to find \( \Delta G \) for each condition. Determine spontaneity: if \( \Delta G < 0 \), the reaction is spontaneous.

Key Concepts

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. It is a crucial indicator of spontaneity; a negative ∆G indicates that a reaction can occur spontaneously, while a positive ∆G suggests non-spontaneity. The standard Gibbs free energy change (∆G°) provides a baseline for calculating ∆G under non-standard conditions using the reaction quotient.

Reaction Quotient (Q)

The reaction quotient (Q) is a dimensionless number that reflects the ratio of the concentrations of products to reactants at any point in a reaction, raised to the power of their stoichiometric coefficients. It is used to determine the direction in which a reaction will proceed to reach equilibrium. By comparing Q to the equilibrium constant (K), one can assess whether the reaction is spontaneous under given conditions, as spontaneity is influenced by the relative concentrations of reactants and products.

Temperature and Pressure Effects on Reactions

Temperature and pressure significantly influence chemical reactions, particularly in gaseous systems. Changes in temperature can affect the kinetic energy of molecules, thereby altering reaction rates and equilibria. For reactions involving gases, pressure changes can shift the position of equilibrium according to Le Chatelier's principle, impacting the Gibbs free energy and spontaneity of the reaction. Understanding these effects is essential for predicting the behavior of reactions under varying conditions.