For A Phase Change, $\Delta H^0 = -44 \, \text{kJ/mol}$ And $\Delta S^0 = -0.12 \, \text{kJ/(K} \cdot \text{mol)}$. What Are $\Delta G$ And The Spontaneity Of The Phase Change At 350 K?A. $\Delta G = -2.0 \,
Introduction
In thermodynamics, a phase change is a process where a substance transforms from one state to another, such as from solid to liquid or from liquid to gas. The spontaneity of a phase change is determined by the change in Gibbs free energy (ΔG). In this article, we will explore the calculation of ΔG and the spontaneity of a phase change at a given temperature.
The Gibbs Free Energy Equation
The Gibbs free energy equation is given by:
ΔG = ΔH - TΔS
where ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy.
Given Values
We are given the following values:
- ΔH^0 = -44 kJ/mol (change in enthalpy)
- ΔS^0 = -0.12 kJ/(K·mol) (change in entropy)
- T = 350 K (temperature)
Calculating ΔG
To calculate ΔG, we need to substitute the given values into the Gibbs free energy equation:
ΔG = ΔH - TΔS ΔG = -44 kJ/mol - (350 K)(-0.12 kJ/(K·mol)) ΔG = -44 kJ/mol + 42 kJ/mol ΔG = -2 kJ/mol
Interpretation of ΔG
A negative value of ΔG indicates that the phase change is spontaneous. In this case, ΔG = -2 kJ/mol, which means that the phase change is spontaneous.
Spontaneity of the Phase Change
The spontaneity of a phase change is determined by the sign of ΔG. If ΔG is negative, the phase change is spontaneous. If ΔG is positive, the phase change is non-spontaneous.
In this case, ΔG = -2 kJ/mol, which means that the phase change is spontaneous.
Conclusion
In conclusion, we have calculated the change in Gibbs free energy (ΔG) and determined the spontaneity of a phase change at a given temperature. The results show that the phase change is spontaneous at 350 K.
References
- Atkins, P. W., & de Paula, J. (2010). Physical chemistry. Oxford University Press.
- Chang, R. (2010). Physical chemistry for the life sciences. Cambridge University Press.
Appendix
Derivation of the Gibbs Free Energy Equation
The Gibbs free energy equation is derived from the first law of thermodynamics and the second law of thermodynamics.
The first law of thermodynamics states that energy cannot be created or destroyed, only converted from one form to another. Mathematically, this is expressed as:
ΔE = Q - W
where ΔE is the change in energy, Q is the heat added to the system, and W is the work done by the system.
The second law of thermodynamics states that the total entropy of a closed system will always increase over time. Mathematically, this is expressed as:
ΔS = ΔQ / T
where ΔS is the change in entropy, ΔQ is the heat added to the system, and T is the temperature.
Combining the first and second laws of thermodynamics, we get:
ΔG = ΔH - TΔS
where ΔG is the change in Gibbs free energy, ΔH is the change in enthalpy, T is the temperature, and ΔS is the change in entropy.
Units of Measurement
The units of measurement for the Gibbs free energy equation are:
- ΔG: kJ/mol
- ΔH: kJ/mol
- T: K
- ΔS: kJ/(K·mol)
Q: What is the Gibbs free energy equation?
A: The Gibbs free energy equation is a mathematical expression that relates the change in Gibbs free energy (ΔG) to the change in enthalpy (ΔH), temperature (T), and change in entropy (ΔS). It is given by:
ΔG = ΔH - TΔS
Q: What is the significance of the Gibbs free energy equation?
A: The Gibbs free energy equation is a fundamental concept in thermodynamics that helps us understand the spontaneity of a process. A negative value of ΔG indicates that the process is spontaneous, while a positive value indicates that the process is non-spontaneous.
Q: How do I calculate the Gibbs free energy?
A: To calculate the Gibbs free energy, you need to know the change in enthalpy (ΔH), temperature (T), and change in entropy (ΔS). You can then use the Gibbs free energy equation to calculate ΔG.
Q: What are the units of measurement for the Gibbs free energy equation?
A: The units of measurement for the Gibbs free energy equation are:
- ΔG: kJ/mol
- ΔH: kJ/mol
- T: K
- ΔS: kJ/(K·mol)
Q: What is the relationship between ΔG and the spontaneity of a process?
A: A negative value of ΔG indicates that the process is spontaneous, while a positive value indicates that the process is non-spontaneous.
Q: Can I use the Gibbs free energy equation to predict the spontaneity of a process?
A: Yes, you can use the Gibbs free energy equation to predict the spontaneity of a process. However, you need to know the values of ΔH, T, and ΔS to calculate ΔG.
Q: What are some common applications of the Gibbs free energy equation?
A: The Gibbs free energy equation has many applications in chemistry, physics, and engineering. Some common applications include:
- Predicting the spontaneity of chemical reactions
- Calculating the equilibrium constant of a reaction
- Understanding the thermodynamics of phase changes
- Designing and optimizing chemical processes
Q: Can I use the Gibbs free energy equation to calculate the equilibrium constant of a reaction?
A: Yes, you can use the Gibbs free energy equation to calculate the equilibrium constant of a reaction. The equilibrium constant (K) is related to ΔG by the following equation:
ΔG = -RT ln(K)
where R is the gas constant and T is the temperature.
Q: What are some common mistakes to avoid when using the Gibbs free energy equation?
A: Some common mistakes to avoid when using the Gibbs free energy equation include:
- Using incorrect units of measurement
- Failing to account for the temperature dependence of ΔH and ΔS
- Ignoring the non-ideal behavior of gases and liquids
- Failing to consider the effects of pressure and volume on the system
Q: Can I use the Gibbs free energy equation to calculate the entropy of a system?
A: Yes, you can use the Gibbs free energy equation to calculate the entropy of a system. The entropy (S) is related to ΔG by the following equation:
ΔG = ΔH - TΔS
Rearranging this equation, we get:
ΔS = (ΔH - ΔG) / T
This equation can be used to calculate the entropy of a system if you know the values of ΔH, ΔG, and T.