CHM 101 Module Four Additional Homework Problems 1 In 962283

CHM 101 Module Four Additional Homework Problems 1. In Order to Verify

Analyze a series of chemical thermodynamics problems involving reaction enthalpy, work, and enthalpy of formation. The tasks include calculating temperature change during an acid-base neutralization, determining work done by expanding and rigid vessels, and computing enthalpy changes for methane combustion with different water phases, using provided data and concepts such as specific heat, pressure-volume work, and standard enthalpies of formation.

Paper For Above instruction

Understanding the thermochemistry principles underlying chemical reactions is essential for chemists to predict and quantify energy changes during reactions. The problems provided offer practical applications of concepts such as enthalpy, heat transfer, work, and the significance of physical states in thermodynamic calculations. This paper explores these topics in detail, illustrating calculations and conceptual explanations based on the specific problems provided.

Problem 1: Heat of Reaction in an Acid-Base Neutralization

In the first problem, a chemist mixes 1 liter each of 1 M NaOH and 1 M HCl at an initial temperature of 25°C. The specific heat of water is given as 4.184 J/g°C, and the enthalpy of the reaction (neutralization) is –58 kJ/mol, indicating an exothermic process.

Part (a) asks whether the reaction is exothermic or endothermic. Since the enthalpy change is negative, it signifies the release of heat during the reaction, making it exothermic. Consequently, the temperature of the solution will increase due to heat release.

Part (b) requires calculating the final temperature assuming no heat transfer to the surroundings and considering only water’s specific heat capacity. To do this, first, determine the total mass of the water involved: 1 liter each of NaOH and HCl, with water’s density approximately 1 g/mL, results in roughly 1000 g + 1000 g = 2000 g of water. The moles of each reactant are 1 mol for NaOH and HCl respectively, leading to 1 mol of neutralization product.

The heat released (q) from the neutralization is: q = ΔH × molar amount = (–58,000 J/mol) × 1 mol = –58,000 J. The negative sign indicates heat is released into the water, warming it. Applying the heat equation: q = m × c × ΔT, where m is the mass of water, c is specific heat, and ΔT is the temperature change:

ΔT = q / (m × c) = 58,000 J / (2000 g × 4.184 J/g°C) ≈ 6.93°C.

Adding this temperature increase to the initial 25°C yields a final temperature of approximately 31.93°C. Thus, the reaction heats the solution by about 7°C, confirming its exothermic nature.

Problem 2: Work Done in Expanding and Rigid Vessels, and Enthalpy Changes

This problem compares two vessels containing the same chemical reaction, initially at atmospheric pressure. One vessel is rigid, unable to expand, while the other expands by 1 liter to maintain constant pressure at 1 atm. The focus is on calculating work, enthalpy, and temperature differences resulting from these dynamics.

(a) The work done (W) by the system is given by PV work, W = –PΔV. For the expanding vessel, ΔV = 1 liter = 0.001 m³ (since 1 liter = 0.001 m³). At 1 atm, P = 101.325 kPa. Therefore, W = –(101.325 kPa)(0.001 m³) = –0.1013 kJ. The negative sign indicates work done by the system as it expands.

In the rigid vessel, ΔV = 0, so no PV work is done (W = 0). The expansion vessel performs approximately 0.1013 kJ of work on the surroundings during the expansion.

(b) The enthalpy (H) for each state depends on the PV work and internal energy. Since the second vessel performs work during expansion, it gains additional energy compared to the rigid vessel, which cannot perform work. The system's enthalpy generally increases with work done on the surroundings. Thus, the vessel that expands (second vessel) has a higher enthalpy after the reaction compared to the rigid vessel.

(c) Thermodynamically, the temperature of the content in the vessel that performs work during expansion is likely higher because the energy input associated with expansion contributes to increasing internal energy and, consequently, temperature. Conversely, the rigid vessel, which cannot perform work and does not change volume, may have a slightly lower temperature as less energy is available to raise the temperature.

Problem 3: Enthalpy of Formation and Combustion of Methane

The third problem utilizes standard enthalpies of formation to calculate the enthalpy change during methane combustion, considering whether water is gaseous or liquid as product.

Using the enthalpy of formation data, the combustion of methane to form CO₂ and water involves the following reaction:

CH₄(g) + 2 O₂(g) → CO₂(g) + 2 H₂O

In the first scenario, where water forms as a gas, the change in enthalpy (ΔH) is calculated by:

ΔH = [ΔH°f (CO₂) + 2 × ΔH°f (H₂O, g)] – [ΔH°f (CH₄) + 2 × ΔH°f (O₂)]

Substituting the values:

ΔH = [(–393.5) + 2 × (–241.8)] – [ (–74.8) + 2 × 0 ] = (–393.5 – 483.6) – (–74.8) = –877.1 + 74.8 = –802.3 kJ/mol

This indicates the combustion releases 802.3 kJ per mole of methane when forming gaseous water.

In the second scenario, with water as a liquid, the calculation adjusts the enthalpy of formation for water to –285.8 kJ/mol:

ΔH = [–393.5 + 2 × (–285.8)] – [–74.8 + 0] = (–393.5 – 571.6) – (–74.8) = –965.1 + 74.8 = –890.3 kJ/mol

The more negative value reflects a greater heat release when water is in liquid form. This difference largely results from the enthalpy of condensation, which releases additional energy during condensation from vapor to liquid.

These calculations highlight that the physical state of reaction products significantly impacts the total enthalpy change, emphasizing the importance of phase considerations in thermodynamic calculations. The energy released during condensation contributes an additional exothermic effect, evident in the more negative ΔH when forming liquid water.

Conclusion

The examination of these thermodynamic problems demonstrates critical principles such as energy release in exothermic reactions, the role of pressure-volume work, and the influence of product phases on enthalpy changes. Accurate calculations require careful consideration of the system's initial conditions, physical states, and the proper application of thermodynamic equations. Such analyses are foundational in chemical thermodynamics, informing areas from process design to energy management in chemical manufacturing.

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