Thermodynamics and Quantum Theory Study Guide – Step-by-Step Guidance

Q1. Name the energy that is associated with the position and the energy that is associated with the motion of an object, respectively.

Background

Topic: Types of Energy (Kinetic and Potential)

This question tests your understanding of the two main forms of energy in physics and chemistry: energy due to position and energy due to motion.

Key Terms:

• Kinetic Energy (KE): Energy associated with the motion of an object.

• Potential Energy (PE): Energy associated with the position or arrangement of an object.

Step-by-Step Guidance

1. Recall that energy can be classified based on whether it is due to movement or position.

2. Think about what type of energy an object has when it is moving versus when it is held at a certain height or in a certain configuration.

3. Match the correct term (kinetic or potential) to each description.

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Q2. In terms of heat (q) and work (w), represent the change in energy ΔE of the system that is doing work on the surroundings, as well as losing heat to the surroundings.

Background

Topic: First Law of Thermodynamics

This question tests your understanding of how energy changes in a system are related to heat and work, and how the signs of q and w are assigned.

Key Formula:

$\Delta E = q + w$

• $q$ = heat absorbed or released by the system

• $w$ = work done on or by the system

Step-by-Step Guidance

1. Recall the sign conventions: heat lost by the system ($q < 0$), work done by the system ($w < 0$).

2. Substitute the appropriate signs for $q$ and $w$ into the formula for $\Delta E$.

3. Write the expression for $\Delta E$ using these values.

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Q3. Determine the specific heat capacity of an alloy that requires 59.3 kJ to raise the temperature of 150.0 g alloy from 298 K to 398 K.

Background

Topic: Calorimetry and Specific Heat

This question tests your ability to use the relationship between heat, mass, temperature change, and specific heat capacity to solve for the specific heat of a substance.

Key Formula:

$q = m c_s \Delta T$

• $q$ = heat absorbed (in J or kJ)

• $m$ = mass (in g)

• $c_s$ = specific heat capacity (in J/g·K)

• $\Delta T$ = change in temperature (in K)

Step-by-Step Guidance

1. Convert the heat absorbed from kJ to J if necessary (1 kJ = 1000 J).

2. Calculate the temperature change: $\Delta T = T_{final} - T_{initial}$.

3. Rearrange the formula to solve for $c_s$: $c_s = \frac{q}{m \Delta T}$.

4. Plug in the values for $q$, $m$, and $\Delta T$ (be sure all units are consistent).

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Q4. A 21.8 g sample of ethanol (C2H5OH) is burned in a bomb calorimeter, according to the following reaction. If the temperature rises from 25.0 to 62.3°C, determine the heat capacity of the calorimeter. The molar mass of ethanol is 46.07 g/mol. Remember the mole ratio to ΔH°rxn relationship.

C2H5OH(l) + 3 O2(g) → 2 CO2(g) + 3 H2O(g) ΔH°rxn = -1235 kJ

Background

Topic: Calorimetry – Bomb Calorimeter

This question tests your ability to relate the heat released by a reaction to the temperature change in a calorimeter and to use stoichiometry to connect mass, moles, and energy.

Key Formulas:

• Heat absorbed by calorimeter: $q_{cal} = C_{cal} \Delta T$

• Energy released by reaction: $q_{rxn} = n \times \Delta H_{rxn}$

• In a bomb calorimeter: $q_{rxn} = -q_{cal}$

Step-by-Step Guidance

1. Calculate the number of moles of ethanol burned: $n = \frac{\text{mass}}{\text{molar mass}}$.

2. Calculate the heat released by the reaction: $q_{rxn} = n \times \Delta H_{rxn}$ (be careful with the sign).

3. Set $q_{rxn} = -q_{cal}$ and solve for $C_{cal}$ using the temperature change.

4. Plug in the values for $q_{rxn}$ and $\Delta T$ to solve for $C_{cal}$.

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Q5. How much energy is required to decompose 612 g of PCl3, according to the reaction below? The molar mass of PCl3 is 137.32 g/mol and may be useful.

4 PCl3(g) → P4(s) + 6 Cl2(g) ΔH°rxn = +1207 kJ

Background

Topic: Stoichiometry and Enthalpy Calculations

This question tests your ability to use stoichiometry to relate mass to moles and then to energy using the enthalpy change of a reaction.

Key Steps and Formulas:

• Convert mass to moles: $n = \frac{\text{mass}}{\text{molar mass}}$

• Use the mole ratio from the balanced equation to relate moles of PCl3 to energy change.

• Calculate the energy required: $\text{Energy} = n_{PCl_3} \times \frac{\Delta H_{rxn}}{4}$

Step-by-Step Guidance

1. Calculate the number of moles of PCl3: $n = \frac{612\ \text{g}}{137.32\ \text{g/mol}}$.

2. Determine how many moles of reaction this represents (since 4 moles of PCl3 decompose per reaction as written).

3. Multiply the number of "reaction equivalents" by the enthalpy change per reaction ($+1207$ kJ per 4 moles PCl3).

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