Free energy and equilibrium Knowledge-Based Practice

Questions

1. 1.

   When analyzing the temperature dependence of chemical equilibrium, a plot of $\ln K$ versus $1/T$ produces a straight line if $\Delta H^\circ$ and $\Delta S^\circ$ are constant over the temperature range. What quantity does the slope of this line represent?

   • A) $-\Delta H^\circ / R$
   • B) $\Delta H^\circ / R$
   • C) $\Delta S^\circ / R$
   • D) $-\Delta G^\circ / R$
2. 2.

   Under which condition is the non-standard Gibbs free energy change ($\Delta G$) of a reaction mixture equal to its standard Gibbs free energy change ($\Delta G^\circ$) at a constant temperature?

   • A) When the reaction has reached chemical equilibrium such that $Q = K$
   • B) When the standard enthalpy change equals the standard entropy change ($\Delta H^\circ = \Delta S^\circ$)
   • C) When all reactants and products are present at standard-state concentrations such that $Q = 1$
   • D) When the equilibrium constant of the reaction is equal to one ($K = 1$)
3. 3.

   A reaction mixture at constant temperature and pressure has a reaction quotient $Q$ that is greater than the equilibrium constant $K$. Which statement correctly identifies the sign of the non-standard Gibbs free energy change ($\Delta G$) and the spontaneous direction of the reaction toward equilibrium?

   • A) $\Delta G > 0$, and the reaction proceeds spontaneously in the reverse direction.
   • B) $\Delta G < 0$, and the reaction proceeds spontaneously in the forward direction.
   • C) $\Delta G > 0$, and the reaction proceeds spontaneously in the forward direction.
   • D) $\Delta G = 0$, and the reaction remains at dynamic equilibrium without net change.
4. 4.

   A reversible chemical reaction takes place at constant temperature and pressure. Which statement correctly describes the thermodynamic conditions when the system reaches dynamic chemical equilibrium?

   • A) The actual free energy change ($\Delta G$) and standard free energy change ($\Delta G^\circ$) are both equal to zero.
   • B) The total Gibbs free energy of the system reaches a maximum value, causing the actual free energy change ($\Delta G$) to vanish.
   • C) The standard free energy change ($\Delta G^\circ$) reaches zero because forward and reverse rates are equal, while $\Delta G$ remains non-zero.
   • D) The actual free energy change ($\Delta G$) is zero because the system is at a free energy minimum, whereas $\Delta G^\circ$ remains constant and is generally non-zero.
5. 5.

   For a chemical reaction at a specified temperature, which statement correctly describes the relationship between the standard Gibbs free energy change ($\Delta G^\circ$) and the equilibrium constant ($K$)?

   • A) When $\Delta G^\circ > 0$, the equilibrium constant $K$ is greater than 1, meaning products are favored at equilibrium.
   • B) When $\Delta G^\circ < 0$, the equilibrium constant $K$ is greater than 1, meaning products are favored at equilibrium.
   • C) When $\Delta G^\circ = 0$, the equilibrium constant $K$ is equal to 0, meaning no reaction occurs.
   • D) When $\Delta G^\circ < 0$, the equilibrium constant $K$ is less than 1, meaning reactants are favored at equilibrium.

Answers and step-by-step solutions appear after you finish the test.