Free Energy of Dissolution - AP Chemistry

1. Calculate $\triangle G$ given $\triangle H = 10 \text{ kJ/mol}$, $T = 298 \text{ K}$, $\triangle S = 50 \text{ J/mol·K}$.

   $\triangle G = -4.9 \text{ kJ/mol}$. $\triangle G = 10000 - 298(50) = 10000 - 14900 = -4900$ J/mol.

2. Which quantity becomes zero at the dissolution equilibrium point?

   $\triangle G$. Free energy equals zero when forward and reverse rates are equal.

3. What is the primary driver of dissolution for ionic solids in water?

   Entropy increase. Breaking crystal lattice increases disorder despite ion-water interactions.

4. Calculate $\triangle G$ with $\triangle H = 20 \text{ kJ/mol}$, $T = 350 \text{ K}$, $\triangle S = 70 \text{ J/mol·K}$.

   $\triangle G = -4.5 \text{ kJ/mol}$. $\triangle G = 20000 - 350(70) = 20000 - 24500 = -4500$ J/mol.

5. Which parameter is zero for a process at equilibrium?

   $\triangle G$. At equilibrium, the free energy change equals zero.

6. Determine the spontaneity: $\triangle H = 5 \text{ kJ/mol}$, $T = 298 \text{ K}$, $\triangle S = 30 \text{ J/mol·K}$.

   Spontaneous. $\triangle G = 5000 - 298(30) = 5000 - 8940 = -3940$ J/mol, so spontaneous.

7. What is the sign of $\triangle H$ if dissolution absorbs heat?

   $\triangle H > 0$. Positive enthalpy indicates an endothermic heat-absorbing process.

8. What is indicated by a positive $\triangle G$ in dissolution?

   Non-spontaneous process. Positive free energy means the process is thermodynamically unfavorable.

9. What determines the spontaneity of a dissolution process?

   Sign of $\triangle G$. Negative $\triangle G$ means spontaneous, positive means non-spontaneous.

10. Determine the spontaneity: $\Delta H = 5 \text{ kJ/mol}$, $T = 298 \text{ K}$, $\Delta S = 30 \text{ J/mol·K}$.

    Spontaneous. $\Delta G = 5000 - 298(30) = 5000 - 8940 = -3940$ J/mol, so spontaneous.

11. What is the sign of $\triangle G$ when $\triangle H < 0$ and $\triangle S > 0$?

    $\triangle G < 0$. Both terms favor spontaneity, making $\triangle G$ always negative.

12. Calculate $\triangle G$ when $\triangle H = 15 \text{ kJ/mol}$, $T = 300 \text{ K}$, $\triangle S = 60 \text{ J/mol·K}$.

    $\triangle G = -3 \text{ kJ/mol}$. $\triangle G = 15000 - 300(60) = 15000 - 18000 = -3000$ J/mol.

13. What does a positive $\triangle S$ indicate about entropy in dissolution?

    Entropy increases. Positive $\triangle S$ means the system becomes more disordered.

14. Determine the spontaneity: $\triangle H = 5 \text{ kJ/mol}$, $T = 298 \text{ K}$, $\triangle S = 30 \text{ J/mol·K}$.

    Spontaneous. $\triangle G = 5000 - 298(30) = 5000 - 8940 = -3940$ J/mol, so spontaneous.

15. State the condition for a dissolution to be spontaneous at all temperatures.

    $\triangle H < 0$, $\triangle S > 0$. Exothermic enthalpy and positive entropy ensure spontaneity.

16. What is the sign of $\triangle G$ when dissolution is at equilibrium?

    $\triangle G = 0$. Zero free energy indicates the system has reached equilibrium.

17. Find the entropy change: $\triangle G = 10 \text{ kJ/mol}$, $\triangle H = 15 \text{ kJ/mol}$, $T = 298 \text{ K}$.

    $\triangle S = 16.78 \text{ J/mol·K}$. $\triangle S = (\triangle H - \triangle G)/T = (15000 - 10000)/298 = 16.78$ J/mol·K.

18. What does a positive $\triangle S$ indicate about entropy in dissolution?

    Entropy increases. Positive $\triangle S$ means the system becomes more disordered.

19. What is the relationship between $\triangle H$ and $\triangle S$ in spontaneous dissolution?

    $\triangle H < T\triangle S$. For spontaneity, the entropy term must overcome unfavorable enthalpy.

20. What is the unit of Gibbs free energy change?

    Joules (J) or kilojoules (kJ). Energy units for thermodynamic quantities in the SI system.

21. State the effect on $\triangle G$ if both $\triangle H$ and $\triangle S$ are positive.

    Depends on $T$. Sign depends on whether $T\triangle S$ is greater or less than $\triangle H$.

22. Which factor affects the sign of $\triangle G$ at constant pressure and temperature?

    Enthalpy and entropy. Both enthalpy and entropy contributions determine free energy sign.

23. What effect does increased pressure have on gas solubility in liquids?

    Increases solubility. Henry's law: gas solubility is directly proportional to pressure.

24. Identify the factor that primarily affects $\triangle S$ in dissolution.

    Molecular disorder. Dissolution typically increases randomness as molecules spread out.

25. What does a negative $\triangle S$ for dissolution indicate?

    Entropy decreases. Negative entropy change indicates decreased molecular disorder.

26. Identify the formula for entropy change.

    $\triangle S = \frac{\triangle H - \triangle G}{T}$. Rearranged form of the Gibbs free energy equation.

27. What does a positive $\triangle S$ indicate about entropy in dissolution?

    Entropy increases. Positive $\triangle S$ means the system becomes more disordered.

28. Which parameter is affected by both enthalpy and entropy in dissolution?

    Gibbs free energy ($\triangle G$). Free energy depends on both $\triangle H$ and $T\triangle S$ terms.

29. Calculate $\triangle H$ given $\triangle G = -3 \text{ kJ/mol}$, $T = 310 \text{ K}$, $\triangle S = 80 \text{ J/mol·K}$.

    $\triangle H = 21.8 \text{ kJ/mol}$. $\triangle H = \triangle G + T\triangle S = -3000 + 310(80) = 21800$ J/mol.

30. What type of process occurs when $\triangle G > 0$?

    Non-spontaneous process. Positive free energy indicates thermodynamically unfavorable conditions.

31. What is the significance of $\triangle G = 0$ in dissolution?

    Equilibrium state. Zero free energy indicates the system is at thermodynamic equilibrium.

32. Calculate the enthalpy change: $\Delta G = -5 \text{ kJ/mol}$, $T = 298 \text{ K}$, $\Delta S = 20 \text{ J/mol·K}$.

    $\Delta H = 1.96 \text{ kJ/mol}$. $\Delta H = \Delta G + T \Delta S = -5000 + 298(20) = 1960$ J/mol.

33. Determine the spontaneity: $\triangle H = 5 \text{ kJ/mol}$, $T = 298 \text{ K}$, $\triangle S = 30 \text{ J/mol·K}$.

    Spontaneous. $\triangle G = 5000 - 298(30) = 5000 - 8940 = -3940$ J/mol, so spontaneous.

34. What is the effect of increasing temperature on an exothermic dissolution?

    Decreases solubility. Le Chatelier's principle: heat addition shifts equilibrium away from products.

35. Which variable increases the dissolution rate in endothermic reactions?

    Temperature. Higher kinetic energy from temperature increases dissolution rate.

36. How does the dissolution of a gas in a liquid typically affect $\Delta S$?

    $\Delta S$ decreases. Gas molecules become more ordered when dissolved in liquid.

37. What is the formula for Gibbs free energy change?

    $\triangle G = \triangle H - T\triangle S$. Fundamental thermodynamic equation relating free energy to enthalpy and entropy.

38. In dissolution, what does a negative $\triangle H$ imply?

    Exothermic process. Negative enthalpy means heat is released to the surroundings.

39. State the sign of $\triangle G$ for a spontaneous dissolution.

    $\triangle G < 0$. Negative free energy indicates a thermodynamically favorable process.

40. Identify the type of dissolution with $\triangle S > 0$ and $\triangle H < 0$.

    Spontaneous dissolution. Both favorable enthalpy and entropy make $\triangle G$ negative at all temperatures.

41. Identify the term for the heat change during dissolution.

    Enthalpy change ($\triangle H$). Enthalpy measures the heat absorbed or released during the process.

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