All questions of Thermochemistry for Chemistry Exam

Explanation:

The entropy theorem, also known as the second law of thermodynamics, states that the entropy of an isolated system can never decrease over time and will remain constant only in the case of a reversible process. This theorem is a fundamental principle in thermodynamics that has important implications for understanding the behavior of systems.

Entropy and Isolated Systems:

- An isolated system is one that does not exchange energy or matter with its surroundings. It is a closed system that is not influenced by external factors.
- Entropy is a measure of the disorder or randomness of a system. It is a state function, meaning that it depends only on the current state of the system and not on how it reached that state.
- The entropy of an isolated system can only increase or remain constant. It can never decrease.

Reversible and Irreversible Processes:

- A reversible process is one that can be reversed by an infinitesimally small change in conditions. In a reversible process, the system and its surroundings can be brought back to their original states without any net change in entropy.
- An irreversible process, on the other hand, is one that cannot be reversed without an increase in entropy. Irreversible processes are characterized by an overall increase in disorder.

Implications of the Entropy Theorem:

- The entropy theorem implies that natural processes tend to move towards a state of higher entropy or disorder. This is often referred to as the "arrow of time" or the tendency towards increasing entropy.
- This is observed in many everyday processes. For example, a drop of dye in a glass of water will gradually spread out and mix uniformly, increasing the entropy of the system.
- The entropy theorem also has implications for the efficiency of energy conversion processes. In any real process, some energy is lost as waste heat, increasing the entropy of the system and decreasing the overall efficiency.

Conclusion:

In conclusion, the entropy theorem states that the entropy of an isolated system can never decrease and will remain constant only in the case of a reversible process. This principle is a fundamental concept in thermodynamics and has important implications for understanding the behavior of systems and natural processes. It helps explain why certain processes are irreversible and why the overall entropy of the universe tends to increase over time.

The freezing temperature of liquid water at a pressure of 30 MPa is estimated to be approximately -2.2 degrees Celsius.

A

Explanation:
The change in internal energy (dU) of a system can be expressed in terms of temperature (T), entropy (S), pressure (p), and volume (V) using the first law of thermodynamics. The first law of thermodynamics states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system.

The equation for the change in internal energy (dU) is given by:

dU = Q - W

where Q is the heat added to the system and W is the work done by the system.

Key Points:
- dU represents the change in internal energy of the system.
- T represents temperature.
- S represents entropy.
- p represents pressure.
- V represents volume.

Given:
The composition of the system does not change.

Explanation:
The composition of a system refers to the types and amounts of substances present in the system. If the composition of the system does not change, it means that there is no transfer of matter into or out of the system. In other words, the number of particles and the types of particles remain constant.

When the composition of the system does not change, it implies that there is no heat added to or removed from the system, and no work is done by or on the system. Therefore, the first law of thermodynamics simplifies to:

dU = 0

Since there is no change in internal energy (dU = 0), the equation can be rearranged to:

0 = TdS - pdV

Thus, the statement "dU = TdS - pdV" is true when the composition of the system does not change. This equation is known as the fundamental equation of thermodynamics and is a mathematical representation of the first law of thermodynamics.

Conclusion:
Therefore, the correct answer is option A) true. When the composition of the system does not change, the equation dU = TdS - pdV holds true.

Explanation:

Entropy is a measure of the randomness or disorder in a system. In an isolated system, the total entropy remains constant or increases with time, according to the second law of thermodynamics. However, it is possible for the entropy to decrease locally in a small part of the system as long as the overall change in entropy of the system is positive.

Local Decrease in Entropy:
When we say that entropy may decline locally somewhere within the isolated system, it means that in a small part of the system, the entropy can decrease. This implies that the arrangement of particles or molecules within that region becomes more ordered or less random.

Increased Entropy Elsewhere:
However, the decrease in entropy in one part of the system must be balanced by an increase in entropy somewhere else within the system. This is necessary to satisfy the second law of thermodynamics, which states that the total entropy of an isolated system always increases or remains constant.

Explanation of Option C:
Option C states that the local decrease in entropy must be balanced by increased entropy somewhere within the system. This statement is correct because the overall entropy of an isolated system cannot decrease. If there is a decrease in entropy in a certain region, there must be compensatory increases in entropy elsewhere to maintain the total entropy of the system.

Example:
For example, consider a container divided into two compartments by a partition. Initially, the particles are evenly distributed in both compartments, resulting in a high level of randomness or entropy. If the partition is removed, the particles will spread out and become more uniformly distributed throughout the container. This leads to an increase in the overall entropy of the system.

However, during the removal of the partition, there may be a temporary decrease in entropy in the region where the partition was located. This is because the particles in that region become more ordered as they move away from the partition. But this temporary decrease in entropy is balanced by the increase in entropy in the rest of the system, resulting in an overall increase in entropy.

Therefore, option C is the correct answer as it accurately explains that a local decrease in entropy within an isolated system must be balanced by increased entropy elsewhere within the system.

**Explanation:**

**Entropy in an Isolated System:**

Entropy is a measure of the disorder or randomness in a system. In an isolated system, the total entropy remains constant unless there is an exchange of energy or matter with the surroundings.

**Change in Entropy:**

According to the second law of thermodynamics, the total entropy of an isolated system tends to increase over time. This means that the system becomes more disordered or random as time passes. Therefore, the entropy of an isolated system continuously increases.

**Equilibrium State:**

At the state of equilibrium, the system has reached a state of maximum entropy. This means that the system is in the most disordered or random state possible. In this state, there is no further tendency for the entropy to increase. Therefore, the entropy at the state of equilibrium is at its maximum value.

**Answer Explanation:**

Based on the above information, we can conclude that the correct answer is option B: "increases, maximum." The entropy of an isolated system continuously increases over time and reaches its maximum value at the state of equilibrium.

Other options can be ruled out:

- Option A: "decreases, minimum" is incorrect because entropy in an isolated system does not decrease over time. It either remains constant or increases.
- Option C: "increases, minimum" is incorrect because the entropy at the state of equilibrium is at its maximum value, not minimum.
- Option D: "decreases, maximum" is incorrect because the entropy of an isolated system does not decrease over time. It either remains constant or increases.

In summary, the entropy of an isolated system continuously increases and reaches its maximum value at the state of equilibrium.

Phase Change of the First Order

- A phase change of the first order refers to a transition between two phases of matter where both phases coexist at equilibrium.
- This type of phase change satisfies the following requirements:

Changes of Volume and Entropy

- During a first-order phase change, there are changes in volume and entropy. This is because the arrangement of molecules or atoms changes between the two phases, leading to a difference in density and disorder.
- For example, during the melting of ice to water, there is a change in volume as the solid structure breaks down into a less ordered liquid phase.

First-Order Derivative of Gibbs Function

- Another requirement satisfied by a phase change of the first order is that the first-order derivative of the Gibbs function changes discontinuously.
- The Gibbs function is a thermodynamic potential that combines enthalpy, entropy, and volume. In a first-order phase transition, there is a sudden change in the slope of the Gibbs function, indicating a discontinuity.

Conclusion

- In conclusion, a phase change of the first order satisfies both the requirements mentioned - changes in volume and entropy, as well as a discontinuous change in the first-order derivative of the Gibbs function.

The equation for Gibbs energy, also known as Gibbs free energy, is a fundamental equation used in thermodynamics to determine the spontaneity of a chemical reaction. It relates the change in Gibbs energy (∆G) to the enthalpy change (∆H), the entropy change (∆S), and the temperature (T) of the system. The equation is as follows:

∆G = ∆H - T∆S

This equation can be used for both the elements hydrogen (H) and fluorine (F). Let's explore why this is the case.

Explanation:
1. Gibbs Energy Equation:
The Gibbs energy equation is a mathematical representation of the second law of thermodynamics, which states that for a spontaneous process, the total entropy of the universe increases. It is given by the equation:

∆G = ∆H - T∆S

where:
- ∆G is the change in Gibbs energy
- ∆H is the change in enthalpy
- ∆S is the change in entropy
- T is the temperature in Kelvin

2. Application to Hydrogen (H):
When considering the element hydrogen (H), the Gibbs energy equation can be applied to determine the spontaneity of various hydrogen-related reactions. For example, the equation can be used to calculate the Gibbs energy change for the reaction of hydrogen gas with oxygen gas to form water:

2H₂(g) + O₂(g) -> 2H₂O(l)

By calculating the enthalpy change (∆H) and entropy change (∆S) for this reaction and substituting the values into the Gibbs energy equation, we can determine whether the reaction is spontaneous at a given temperature.

3. Application to Fluorine (F):
Similarly, the Gibbs energy equation can be applied to the element fluorine (F) and its related reactions. For instance, the reaction of fluorine gas with hydrogen gas to form hydrogen fluoride can be analyzed using the Gibbs energy equation:

F₂(g) + H₂(g) -> 2HF(g)

By calculating the appropriate enthalpy change (∆H) and entropy change (∆S) for this reaction and substituting the values into the Gibbs energy equation, we can determine the spontaneity of the reaction under specific temperature conditions.

4. Conclusion:
In conclusion, the equation for Gibbs energy (∆G = ∆H - T∆S) can be used for both hydrogen (H) and fluorine (F). This equation allows us to determine the spontaneity of chemical reactions involving these elements by considering the enthalpy change, entropy change, and temperature. By applying the Gibbs energy equation, we can gain insights into the thermodynamic feasibility of reactions involving hydrogen and fluorine.

The molal chemical potential is given by the equation:

μ = μ° + RT ln(γX)

where:
- μ is the molal chemical potential
- μ° is the standard molal chemical potential
- R is the gas constant (8.314 J/mol·K)
- T is the temperature in Kelvin
- γ is the activity coefficient
- X is the molality of the solute.

(T1+T2)/2

Trouton's rule states that the entropy change of vaporization for a pure substance is approximately the same for all substances, regardless of their chemical nature. This means that the entropy change of vaporization is constant and does not vary significantly between different substances.

The given relation for vapour pressure p in kPa at temperature T is:

p = 101.325 exp (88/R)(1-Tb/T)

Let's break down the equation and understand each component:

1. p: This represents the vapour pressure at temperature T. Vapour pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature.

2. 101.325: This is a constant factor and represents the atmospheric pressure in kilopascals (kPa). It is used as a reference value.

3. exp: This is the exponential function, also known as the "base e" function. In this equation, it is used to calculate the exponential value.

4. 88/R: This term represents a constant value (88) divided by the ideal gas constant (R). The ideal gas constant is a fundamental constant in chemistry and is equal to 8.314 J/(mol·K) or 0.0821 L·atm/(mol·K). The value of R depends on the units used in the equation.

5. (1-Tb/T): This term represents the ratio of the boiling temperature (Tb) to the temperature (T) at which we want to calculate the vapour pressure. It is subtracted from 1 to obtain the ratio of the difference between the boiling temperature and the given temperature to the boiling temperature.

Now, let's analyze the options given:

a) p = 101.325 exp (88/R)(1 T/T
b) p = 101.325 exp (88/R)(1 Tb/T
c) p = 101.325 exp (88/R)(1-T/Tb
d) p = 101.325 exp (88/R)(1-Tb/T) [Correct Option]

The correct option is (d) because it correctly represents the given relation for vapour pressure. The boiling temperature (Tb) is in the denominator of the fraction, and it is subtracted from the given temperature (T). This is consistent with the equation p = 101.325 exp (88/R)(1-Tb/T).

Option (a) is incorrect because it is missing the closing bracket after T/T.

Option (b) is incorrect because it is missing the closing bracket after Tb/T.

Option (c) is incorrect because the term (1-T/Tb) is in the wrong order. It should be (1-Tb/T).

Therefore, the correct answer is option (d), p = 101.325 exp (88/R)(1-Tb/T), as it accurately represents the given relation for vapour pressure.

B) SdP - VdT

Understanding Nernst's Contribution
The Nernst equation is pivotal in thermodynamics and electrochemistry, particularly in defining the relationship between temperature and entropy. It is closely associated with the Third Law of Thermodynamics.
What is the Third Law of Thermodynamics?
- The Third Law states that as the temperature of a perfect crystal approaches absolute zero, the entropy approaches a constant minimum.
- This implies that at absolute zero, a perfect crystal would have zero entropy, meaning there is only one way to arrange the particles.
Nernst's Theorem
- Nernst formulated what is often referred to as the Nernst Heat Theorem, which is a key aspect of the Third Law of Thermodynamics.
- This theorem essentially states that the entropy change of a system approaches zero as the temperature approaches absolute zero.
Significance of Nernst’s Law
- Nernst's contributions help in understanding how entropy behaves at low temperatures.
- This understanding has implications for various fields, including cryogenics and quantum mechanics.
Conclusion
Nernst’s expression and the formulation of his law solidify his association with the Third Law of Thermodynamics. Therefore, the correct answer to the question is option 'C', emphasizing Nernst’s significant role in elucidating the behavior of entropy at low temperatures.

**Explanation:**

During phase transitions such as vaporization, melting, and sublimation, certain properties of the substance change. Let's examine each of these phase transitions and their effects on pressure, temperature, volume, and entropy:

**Vaporization:**

Vaporization is the process of converting a liquid into a gas. During this phase transition:

- Pressure and temperature can vary depending on the conditions, but they are not constant. For example, in an open system, the pressure may change due to the evaporation of the liquid.
- Volume increases significantly as the liquid expands into a gas phase.
- Entropy increases as the substance transitions from a more ordered state (liquid) to a more disordered state (gas). This is because gas molecules have more freedom of movement compared to liquid molecules.

**Melting:**

Melting is the process of converting a solid into a liquid. During this phase transition:

- Pressure and temperature can vary depending on the conditions, but they are not constant. For example, the melting point of a substance is the temperature at which it changes from a solid to a liquid, and this temperature can vary depending on pressure.
- Volume generally increases as the solid expands upon melting. However, there are exceptions where the volume decreases upon melting, such as in the case of water between 0°C and 4°C.
- Entropy generally increases as the substance transitions from a more ordered state (solid) to a more disordered state (liquid). This is because the movement of particles in a liquid is more random compared to a solid.

**Sublimation:**

Sublimation is the process of converting a solid directly into a gas without going through the liquid phase. During this phase transition:

- Pressure and temperature can vary depending on the conditions, but they are not constant. For example, the sublimation point of a substance is the temperature at which it changes from a solid to a gas, and this temperature can vary depending on pressure.
- Volume increases significantly as the solid expands into a gas phase.
- Entropy increases as the substance transitions from a more ordered state (solid) to a more disordered state (gas). This is because gas molecules have more freedom of movement compared to solid molecules.

Therefore, the correct answer is option 'C' - both pressure and temperature do not remain constant during phase transitions, but volume and entropy do change.

**Explanation:**

The principle of entropy is a fundamental concept in thermodynamics that relates to the dispersal of energy and the tendency of a system to move towards a state of greater disorder. It is often described as a measure of the "randomness" or "disorder" of a system.

**a) Transfer of heat through a finite temperature difference:**

When heat is transferred between two objects that are at different temperatures, it flows from the hotter object to the colder object until they reach thermal equilibrium. This process can be described in terms of entropy because the heat transfer tends to increase the overall randomness or disorder of the system. As heat flows, the energy becomes more evenly distributed, increasing the entropy of the system.

**b) Mixing of two fluids:**

When two fluids are mixed, their particles become more randomly arranged, leading to an increase in disorder or randomness. This mixing process is accompanied by an increase in entropy because the energy becomes more dispersed and distributed among the particles. Therefore, the mixing of two fluids can be regarded as applying the principle of entropy.

**c) Maximum temperature attainable from two finite bodies:**

The maximum temperature that can be attained by two finite bodies is determined by the second law of thermodynamics, which is closely related to the principle of entropy. According to the second law, heat flows spontaneously from a hotter object to a colder object, and it is not possible to transfer heat from a colder object to a hotter object without the input of external energy. This limitation is due to the increase in entropy that occurs when heat flows from a hotter body to a colder body. Therefore, the concept of maximum temperature attainable from two finite bodies is based on the principle of entropy.

**d) All of the mentioned:**

All of the mentioned situations - transfer of heat through a finite temperature difference, mixing of two fluids, and the maximum temperature attainable from two finite bodies - involve processes that are related to the principle of entropy. In each case, there is an increase in disorder or randomness, leading to an increase in the entropy of the system. Therefore, option 'D' is correct as all of the mentioned situations can be regarded as applying the principle of entropy.

This equation is not complete. The complete equation for Gibbs energy is given by:

dG = Vdp - SdT + μdn

where:
- dG is the change in Gibbs energy
- V is the volume
- p is the pressure
- S is the entropy
- T is the temperature
- μ is the chemical potential
- n is the number of moles of substance present.