Quiz on chemical and phase equilibrium for ME students

Absolutely! Preparing for an exam can be tough, but with a focused review and some practice, you'll be well on your way to mastering chemical and phase equilibrium. Let's get you ready!

Quick Study Guide: Chemical and Phase Equilibrium

• Equilibrium Defined: A state where macroscopic properties (temperature, pressure, composition) remain constant over time. It's a dynamic process at the microscopic level. For Mechanical Engineers, understanding equilibrium is crucial for designing and analyzing systems like power cycles, refrigeration, and chemical reactors.
• Chemical Equilibrium:
  • Equilibrium Constant ($K_p$, $K_c$): Relates the concentrations or partial pressures of products to reactants at equilibrium. For a reversible reaction $aA + bB \rightleftharpoons cC + dD$, $K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$ and $K_p = \frac{P_C^c P_D^d}{P_A^a P_B^b}$. Note $K_p = K_c(RT)^{\Delta n}$, where $\Delta n$ is the change in moles of gas.
  • Gibbs Free Energy ($\Delta G$): The criterion for spontaneity and equilibrium. At constant temperature and pressure, a system reaches equilibrium when $\Delta G = 0$. The standard Gibbs Free Energy change is related to the equilibrium constant by $\Delta G^0 = -RT \ln K$.
  • Le Chatelier's Principle: "When a system at equilibrium is subjected to a change (stress), it will adjust itself to counteract the change and restore a new equilibrium." Changes include concentration, pressure (for gases), and temperature.
• Phase Equilibrium:
  • Gibbs Phase Rule: $F = C - P + 2$. This rule predicts the number of independent intensive variables ($F$, degrees of freedom) that can be varied for a system at equilibrium, where $C$ is the number of components and $P$ is the number of phases.
  • Clapeyron Equation: Describes the relationship between pressure, temperature, and enthalpy change during a phase transition (e.g., solid-liquid, liquid-vapor). $ \frac{dP}{dT} = \frac{\Delta h}{T\Delta v} $.
  • Clausius-Clapeyron Equation: An approximation of the Clapeyron equation for liquid-vapor phase transitions, assuming ideal gas behavior for the vapor and negligible liquid volume. $ \ln\left(\frac{P_2}{P_1}\right) = -\frac{\Delta h_{vap}}{R}\left(\frac{1}{T_2} - \frac{1}{T_1}\right) $.
  • Phase Diagrams: Graphical representations (e.g., P-T, P-v, T-v) showing the conditions under which different phases of a substance can exist at equilibrium. Key points include the triple point (all three phases coexist) and critical point (above which distinct liquid and gas phases cease to exist).
  • Fugacity and Activity: Concepts used to extend equilibrium calculations to non-ideal systems, analogous to pressure for real gases and concentration for real solutions, respectively.

Practice Quiz

1. For a pure substance, if you are at the triple point, how many independent intensive properties can be varied while maintaining equilibrium between all three phases?

1. A. 0
2. B. 1
3. C. 2
4. D. 3

2. Consider the exothermic reaction $N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)$. According to Le Chatelier's Principle, which action would shift the equilibrium towards the formation of more $NH_3$?

1. A. Increasing the temperature
2. B. Decreasing the pressure
3. C. Removing $N_2$ from the system
4. D. Adding an inert gas at constant volume

3. The Clapeyron equation, $ \frac{dP}{dT} = \frac{\Delta h}{T\Delta v} $, is fundamental for understanding:

1. A. The effect of pressure on reaction rates.
2. B. The relationship between pressure and temperature along phase equilibrium lines.
3. C. The change in specific volume with temperature at constant pressure.
4. D. The variation of enthalpy with pressure at constant temperature.

4. For a chemical reaction, if the standard Gibbs Free Energy change ($\Delta G^0$) is negative, what does this imply about the equilibrium constant ($K$)?

1. A. $K < 1$
2. B. $K = 1$
3. C. $K > 1$
4. D. $K = 0$

5. Which of the following statements is true about the critical point on a P-T diagram for a pure substance?

1. A. It is the point where solid, liquid, and gas phases coexist.
2. B. Above this point, the distinction between liquid and gas phases disappears.
3. C. It is the highest temperature at which the substance can exist as a liquid.
4. D. It represents the point where the substance has its lowest enthalpy.

6. A system consisting of water (liquid) and water vapor (gas) at equilibrium has how many degrees of freedom ($F$)?

1. A. 0
2. B. 1
3. C. 2
4. D. 3

7. The Clausius-Clapeyron equation is derived from the Clapeyron equation under which key assumption(s)?

1. A. The enthalpy of vaporization is temperature-dependent.
2. B. The volume of the liquid phase is significant compared to the vapor phase.
3. C. The vapor phase behaves as an ideal gas and the liquid volume is negligible.
4. D. Both the liquid and vapor phases behave as ideal gases.