Thermodynamics and Quantum Theory Study Guide (Chapters 6–7)

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 relevant in chemistry and physics: energy due to motion and energy due to position.

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 the energy a moving car has versus a rock held above the ground.

3. Identify which term describes energy of motion and which describes energy of position.

Try solving on your own before revealing the answer!

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 direction of energy flow affects the signs of q and w.

Key Formula:

$\Delta E = q + w$

• $q$ = heat (positive if absorbed by the system, negative if released)

• $w$ = work (positive if done on the system, negative if done by the system)

Step-by-Step Guidance

1. Recall the sign conventions: heat lost by the system ($q$) is negative, and work done by the system ($w$) is also negative.

2. Since the system is doing work and losing heat, both $q$ and $w$ should be negative in your expression.

3. Write the equation for $\Delta E$ using the correct signs for $q$ and $w$.

Try solving on your own before revealing the answer!

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:

$q = m \cdot C_s \cdot \Delta T$

• $q$ = heat absorbed or released (in Joules)

• $m$ = mass (in grams)

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

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

Step-by-Step Guidance

1. Convert the heat from kJ to J: $59.3\ \text{kJ} \times 1000 =$ (calculate this value).

2. Calculate the temperature change: $\Delta T = 398\ \text{K} - 298\ \text{K} =$ (find this value).

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

4. Plug in the values for $q$, $m$, and $\Delta T$ (but do not calculate the final value yet).

Try solving on your own before revealing the answer!

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, Enthalpy of Reaction

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: $q_{cal} = C_{cal} \cdot \Delta T$

• Relationship between moles and enthalpy: $q_{rxn} = n \cdot \Delta H_{rxn}$

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: $q_{rxn} = n \times \Delta H_{rxn}$ (remember to use the correct sign and units).

3. Set $q_{rxn}$ equal to $q_{cal}$ (since all the heat is absorbed by the calorimeter): $q_{cal} = C_{cal} \cdot \Delta T$

4. Rearrange to solve for $C_{cal}$: $C_{cal} = \frac{q_{cal}}{\Delta T}$

5. Plug in the values for $q_{cal}$ and $\Delta T$ (but do not calculate the final value yet).

Try solving on your own before revealing the answer!

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 Formulas:

• Number of moles: $n = \frac{\text{mass}}{\text{molar mass}}$

• Energy required: $q = n_{\text{rxn}} \times \Delta H_{rxn}$ (where $n_{\text{rxn}}$ is the number of reaction equivalents based on the balanced equation)

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 "reaction equivalents" this represents, based on the balanced equation (4 moles PCl3 per reaction).

3. Calculate the energy required using the mole ratio: $q = n_{\text{rxn}} \times \Delta H_{rxn}$

4. Plug in the values, but do not compute the final answer yet.

Try solving on your own before revealing the answer!