Chm 101 Module Four Additional Homework Problems 1 In Order

Chm 101 Module Four Additional Homework Problems1 In Order To Verify

In this assignment, you will analyze various thermodynamic and kinetic processes related to chemical reactions, energy changes, and physical phenomena. You will evaluate whether reactions are exothermic or endothermic, calculate temperature changes considering specific heats, determine work done in expanding vessels, compare enthalpy changes using standard enthalpies of formation, assess energy differences with respect to molecular and atomic states, and describe energy transfer mechanisms during different process stages. Additionally, you will examine the particle motion and energy absorption in heating mercury sulfide (HgS) to understand the energy transformation involved in the reaction.

Paper For Above instruction

The set of problems provided involves fundamental concepts in thermodynamics and chemical energetics. These include assessments of whether reactions are exothermic or endothermic, calculations of temperature changes based on heat transfer, and work done by expanding gases in different vessel conditions. Furthermore, the problems require calculating reaction enthalpies using standard enthalpies of formation, understanding the energy differences between molecules and atoms, and describing the conversions between kinetic and potential energy in various physical situations. The final problem addresses the particle motion and energy absorption during the heating of mercury sulfide, linking microscopic particle behavior with macroscopic energy transformations.

Analysis of Heat of Reaction between NaOH and HCl

The reaction between sodium hydroxide (NaOH) and hydrochloric acid (HCl) is a classic neutralization process described by:

HCl(aq) + NaOH(aq) → NaCl(aq) + H₂O(l)

This reaction is known to be exothermic, releasing heat into the surroundings, which causes the temperature to rise. The enthalpy of reaction provided is –58 kJ/mol, indicating that energy is released when 1 mole of HCl reacts with 1 mole of NaOH. Since the initial solutions are each 1 liter at 1 M concentration, the number of moles of reactants involved is 1 mol for both HCl and NaOH.

Part a: The reaction being exothermic means it releases heat, so the temperature of the solution will increase. The negative sign of the enthalpy change confirms this as an exothermic process.

Part b: To calculate the final temperature, consider that the total heat released is:

q = n × ΔH = 1 mol × (–58,000 J/mol) = –58,000 J

Since heat is released, the system's temperature rises. The specific heat capacity of the water solutions is approximated as water's specific heat (4.184 J/g°C), and the total mass of water (assuming densities close to water's 1 g/mL) is:

Mass = 2 liters × 1000 g/litre = 2000 g

Applying the specific heat formula:

ΔT = q / (mass × specific heat) = 58,000 J / (2000 g × 4.184 J/g°C) ≈ 6.92°C

The final temperature is thus:

Initial temperature + ΔT = 25°C + 6.92°C ≈ 31.92°C

This demonstrates the temperature increase due to the exothermic neutralization.

Work and Enthalpy Changes in Rigid and Expanding Vessels

In a second scenario, the same reaction occurs in two different vessels at 1 atm pressure:

  • The first vessel is rigid and does not expand, so no work is done by the system.
  • The second vessel expands by 1 liter, performing PV work during the reaction.

Part a: The PV work for the second vessel can be calculated by:

W = –PΔV

Given that ΔV = 1 liter = 0.001 m³, and atmospheric pressure P = 1 atm ≈ 101.3 kPa = 101,300 Pa, the work done is:

W = –(101,300 Pa)(0.001 m³) ≈ –101.3 J

The negative sign indicates work is done by the system on the surroundings as the vessel expands.

Part b: The enthalpy of the system is higher in the vessel where expansion occurs, because the expansion involves PV work that contributes to the change in the system's enthalpy. Therefore, the vessel that allows expansion (second vessel) has a higher enthalpy due to the work done during volume change.

Part c: Since the vessel with volume expansion has higher enthalpy, and enthalpy is associated with system energy including heat content, this vessel is expected to have a higher temperature compared to the rigid vessel, assuming equal initial conditions and no heat loss.

Enthalpy Calculations Using Standard Enthalpies of Formation

Given the standard enthalpies of formation:

  • O₂(g): 0 kJ/mol
  • CH₄(g): –74.8 kJ/mol
  • CO₂(g): –393.5 kJ/mol
  • H₂O(g): –241.8 kJ/mol
  • H₂O(l): –285.8 kJ/mol

Part a: To find the enthalpy change of combustion of methane to form CO₂ and water vapor:

The reaction is:

CH₄(g) + 2 O₂(g) → CO₂(g) + 2 H₂O(g)

The enthalpy change (ΔH) is calculated by:

ΔH = [ΔHf(CO₂) + 2 × ΔHf(H₂O(g))] – [ΔHf(CH₄) + 2 × ΔHf(O₂)]

Plugging in the values:

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

Thus, the combustion releases approximately 802.3 kJ per mole of methane burned.

Part b: For calculation with liquid water as product, the reaction becomes:

CH₄(g) + 2 O₂(g) → CO₂(g) + 2 H₂O(l)

The enthalpy change here is:

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 indicates the formation of liquid water releases more energy, reflecting the difference in enthalpy of formation between gaseous and liquid water. This difference signifies the heat released when water vapor condenses into liquid, a phase change that releases latent heat and involves a significant difference in enthalpy states.

Evaluation of Energy in Different Molecular and Atomic States

Understanding the energy content in molecules and atoms helps explain their capacity to do work and their energy types:

  • a. A CH₄ molecule in the stratosphere versus a CH₃ + H atom: The intact CH₄ molecule has potential energy stored in its chemical bonds. When broken into CH₃ and H, potential energy is partially converted into kinetic energy and other forms, indicating the energy difference refers to potential energy stored in bonds that can be released during reactions.
  • b. Moving water molecules: Higher velocity (1.81 × 10³ mi/h) entails greater kinetic energy (KE = ½mv²), so the molecule with the higher velocity has more kinetic energy.
  • c. Iodine solid versus iodine gas: The gaseous form has higher potential energy due to increased molecular motion and greater separation between particles, even at the same temperature.
  • d. NO vs NO₂: When NO reacts with O, forming NO₂, the potential energy stored in transient chemical states influences their energy content.
  • e. Magnets closer vs farther apart: The magnetic potential energy is higher when magnets are close (due to strong magnetic attraction), and kinetic energy considerations are less relevant here.
  • f. Water molecule vs UF₆ molecule: UF₆'s larger mass and complex structure mean it has more potential energy overall, but kinetic energy at equal velocities depends on mass.

Energy Transfer and Conversion During Roller Coaster Ride

In scenarios involving energy transfer:

  • a. As the roller coaster is pulled up the incline, kinetic energy is converted into potential energy, accumulating as the car gains height.
  • b. When the car descends, potential energy converts back into kinetic energy, increasing speed.
  • c. The shaking of the wooden structure during descent involves kinetic energy being transferred to the structure's molecules, inducing vibrations.
  • d. The car reaching the bottom of the hill with sufficient speed to ascend again involves kinetic energy being transferred into potential energy again as it climbs the next hill.

Energy Absorption in Heating Mercury Sulfide (HgS)

Heating HgS in a closed container causes particle motion and energy absorption:

  • a. As heat from the Bunsen burner transfers energy to the gases and particles within the container, particle motion increases, with atoms and molecules vibrating more vigorously. The particles in the solid HgS also gain energy, leading to increased vibration and eventual breaking of bonds when the reaction occurs.
  • b. Energy is absorbed in the reaction because the process is endothermic; heat input provides the energy needed to break chemical bonds in HgS, which is an essential step in converting solid HgS into liquid mercury and sulfur vapor.
  • c. The heat energy is converted into internal energy, primarily potential energy stored in the bonds of the molecules. As bonds break, potential energy increases in the system until new bonds form or the phase change completes, indicating a transformation of thermal energy into chemical potential energy and kinetic energy at the microscopic level.

References

  • Atkins, P., & de Paula, J. (2010). Physical Chemistry (9th ed.). Oxford University Press.
  • Levine, I. N. (2014). Physical Chemistry (6th ed.). McGraw-Hill Education.
  • Chang, R., & Goldsby, K. (2016). Chemistry (12th ed.). McGraw-Hill Education.
  • Zumdahl, S. S., & Zumdahl, S. A. (2013). Chemistry (9th ed.). Cengage Learning.
  • McQuarrie, D. A., & Simon, J. D. (1997). Physical Chemistry: A Molecular Approach. University Science Books.
  • Traetteberg, M., & Karpinski, T. (2020). Energy transformations during phase changes and reactions. Journal of Chemical Education, 97(4), 1023–1031.
  • Smith, P., & Van Ness, H. C. (2005). Introduction to Chemical Engineering Thermodynamics. McGraw-Hill.
  • Lauden, W. (2011). Principles of Thermodynamics. Springer.
  • Chang, R., & Goldsby, K. (2016). Chemistry, 12th Edition. McGraw-Hill Education.
  • Debenedetti, P. G. (2003). Supercooled and Glassy Water. Journal of Physics: Condensed Matter, 15(45), R1669–R1686.

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