Thermochemistry — Hard Practice Quiz

A Chemistry cheat sheet for Thermochemistry — every key formula with its symbols defined — plus a hard-level practice quiz to test recall.

Formulas & key concepts

Kinetic Energy: Energy of motion of an object.

$$E_k = \frac{1}{2}mv^2$$

Where: m = mass, v = velocity

Change in Internal Energy: Difference between final and initial energy states.

$$\Delta E = E_{\text{final}} - E_{\text{initial}}$$

First Law of Thermodynamics: Energy change equals heat plus work.

$$\Delta E = q + w$$

Where: q = heat, w = work

Work Done by Gas: Work done by an expanding gas at constant pressure.

$$w = -P\Delta V$$

Where: P = pressure, ΔV = volume change

Enthalpy Change: At constant pressure, enthalpy change equals heat transferred.

$$\Delta H = \Delta E + P\Delta V = q_P$$

Where: q<sub>P</sub> = heat at constant pressure

Specific Heat: Heat capacity per gram of substance.

$$C_s = \frac{q}{m \times \Delta T}$$

Where: q = heat, m = mass, ΔT = temperature change

Heat Calculation: Quantity of heat absorbed or released.

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

Where: C<sub>s</sub> = specific heat, m = mass, ΔT = temperature change

Standard Enthalpy of Reaction: Calculate reaction enthalpy from formation enthalpies.

$$\Delta H^\circ_{rxn} = \sum n \Delta H^\circ_f(\text{products}) - \sum m \Delta H^\circ_f(\text{reactants})$$

Where: n, m = stoichiometric coefficients

<table style="width:100%; border-collapse: collapse; font-size: 0.9em;"> <tr style="border-bottom: 1px solid #ccc;"><th>Substance</th><th>Specific Heat (J/g·K)</th></tr> <tr><td>Water (H<sub>2</sub>O(l))</td><td>4.18</td></tr> <tr><td>Methane (CH<sub>4</sub>(g))</td><td>2.20</td></tr> <tr><td>Nitrogen (N<sub>2</sub>(g))</td><td>1.04</td></tr> <tr><td>Aluminum (Al(s))</td><td>0.90</td></tr> <tr><td>Carbon dioxide (CO<sub>2</sub>(g))</td><td>0.84</td></tr> <tr><td>Calcium carbonate (CaCO<sub>3</sub>(s))</td><td>0.82</td></tr> <tr><td>Iron (Fe(s))</td><td>0.45</td></tr> <tr><td>Mercury (Hg(l))</td><td>0.14</td></tr> </table>

$$\text{Specific Heats of Substances}$$

<table style="width:100%; border-collapse: collapse; font-size: 0.85em;"> <tr style="border-bottom: 1px solid #ccc;"><th>Substance</th><th>ΔH°<sub>f</sub> (kJ/mol)</th></tr> <tr><td>Water (H<sub>2</sub>O(l))</td><td>-285.8</td></tr> <tr><td>Water vapor (H<sub>2</sub>O(g))</td><td>-241.8</td></tr> <tr><td>Carbon dioxide (CO<sub>2</sub>(g))</td><td>-393.5</td></tr> <tr><td>Methane (CH<sub>4</sub>(g))</td><td>-74.80</td></tr> <tr><td>Ammonia (NH<sub>3</sub>(g))</td><td>-46.19</td></tr> <tr><td>Sodium chloride (NaCl(s))</td><td>-410.9</td></tr> <tr><td>Calcium carbonate (CaCO<sub>3</sub>(s))</td><td>-1207.1</td></tr> <tr><td>Glucose (C<sub>6</sub>H<sub>12</sub>O<sub>6</sub>(s))</td><td>-1273</td></tr> <tr><td>Ethanol (C<sub>2</sub>H<sub>5</sub>OH(l))</td><td>-277.7</td></tr> <tr><td>Acetylene (C<sub>2</sub>H<sub>2</sub>(g))</td><td>226.7</td></tr> <tr><td>Benzene (C<sub>6</sub>H<sub>6</sub>(l))</td><td>49.0</td></tr> </table> <p style="font-size: 0.85em; margin-top: 5px;"><em>Note: ΔH°<sub>f</sub> for elements in standard state = 0</em></p>

$$\text{Standard Enthalpies of Formation}$$

Practice quiz

  1. A gas in a piston-cylinder assembly absorbs $150 \text{ J}$ of heat and expands, doing $75 \text{ J}$ of work on the surroundings. If the gas initially had a kinetic energy of $200 \text{ J}$ and its mass remains constant, what is its final kinetic energy? Assume all internal energy change manifests as kinetic energy change for this simplified scenario.

    • $125 \text{ J}$
    • $200 \text{ J}$
    • $275 \text{ J}$
    • $350 \text{ J}$

    Answer: $275 \text{ J}$

  2. $50.0 \text{ g}$ of liquid water at $25.0^{\circ}\text{C}$ is heated to $75.0^{\circ}\text{C}$ at constant atmospheric pressure. Given the specific heat of water is $4.18 \text{ J/g} \cdot \text{K}$, what is the enthalpy change for this process?

    • $5.23 \text{ kJ}$
    • $10.45 \text{ kJ}$
    • $20.90 \text{ kJ}$
    • $2.09 \text{ kJ}$

    Answer: $10.45 \text{ kJ}$

  3. A system undergoes a process where its internal energy decreases by $100 \text{ J}$. If the system expands against a constant external pressure of $2.0 \text{ atm}$ and its volume changes from $1.0 \text{ L}$ to $3.0 \text{ L}$, how much heat was exchanged with the surroundings? (Note: $1 \text{ L} \cdot \text{atm} = 101.3 \text{ J}$)

    • $-505.2 \text{ J}$
    • $-305.2 \text{ J}$
    • $305.2 \text{ J}$
    • $505.2 \text{ J}$

    Answer: $305.2 \text{ J}$

  4. Consider the combustion of methane: $\text{CH}_4(\text{g}) + 2\text{O}_2(\text{g}) \rightarrow \text{CO}_2(\text{g}) + 2\text{H}_2\text{O}(\text{l})$. If $16.0 \text{ g}$ of methane is completely combusted, and all the heat released is absorbed by $1.00 \text{ kg}$ of water initially at $20.0^{\circ}\text{C}$, what will be the final temperature of the water? (Assume no heat loss to surroundings. Use molar mass of $\text{CH}_4 = 16.04 \text{ g/mol}$)

    • $20.0^{\circ}\text{C}$
    • $106.2^{\circ}\text{C}$
    • $232.4^{\circ}\text{C}$
    • $444.8^{\circ}\text{C}$

    Answer: $232.4^{\circ}\text{C}$

  5. For a chemical reaction occurring at constant temperature, under what conditions would the change in enthalpy ($\Delta H$) be approximately equal to the change in internal energy ($\Delta E$)?

    • When the reaction involves only solids and liquids.
    • When the reaction is carried out in an open container.
    • When the system does a large amount of work on the surroundings.
    • When the heat absorbed by the system is zero.

    Answer: When the reaction involves only solids and liquids.

  6. A substance of mass $m$ and specific heat $C_s$ absorbs heat $q$. If its initial temperature is $T_i$, derive an expression for its final temperature $T_f$.

    • $T_f = T_i - \frac{q}{C_s \times m}$
    • $T_f = \frac{q}{C_s \times m} - T_i$
    • $T_f = T_i + \frac{q}{C_s \times m}$
    • $T_f = q \times C_s \times m + T_i$

    Answer: $T_f = T_i + \frac{q}{C_s \times m}$

  7. An object has an initial kinetic energy $E_k$. If its mass is reduced to one-third ($\frac{1}{3}$) of its original value and its velocity is doubled, what is its new kinetic energy in terms of $E_k$?

    • $\frac{1}{3}E_k$
    • $\frac{2}{3}E_k$
    • $\frac{4}{3}E_k$
    • $\frac{8}{3}E_k$

    Answer: $\frac{4}{3}E_k$

  8. Calculate the change in internal energy ($\Delta E$) for the combustion of $1.00 \text{ mol}$ of acetylene ($\text{C}_2\text{H}_2(\text{g})$) at $25^{\circ}\text{C}$ and $1.00 \text{ atm}$ pressure, given the reaction: $2\text{C}_2\text{H}_2(\text{g}) + 5\text{O}_2(\text{g}) \rightarrow 4\text{CO}_2(\text{g}) + 2\text{H}_2\text{O}(\text{l})$. Assume ideal gas behavior and $R = 8.314 \text{ J/mol} \cdot \text{K}$.

    • $-1303.2 \text{ kJ}$
    • $-1299.5 \text{ kJ}$
    • $-1295.8 \text{ kJ}$
    • $-1292.1 \text{ kJ}$

    Answer: $-1295.8 \text{ kJ}$

  9. A $100.0 \text{ g}$ piece of iron (specific heat $0.45 \text{ J/g} \cdot \text{K}$) at $150.0^{\circ}\text{C}$ is dropped into $200.0 \text{ g}$ of water (specific heat $4.18 \text{ J/g} \cdot \text{K}$) at $20.0^{\circ}\text{C}$ in an insulated container. What is the final temperature of the system?

    • $20.0^{\circ}\text{C}$
    • $26.6^{\circ}\text{C}$
    • $35.1^{\circ}\text{C}$
    • $42.3^{\circ}\text{C}$

    Answer: $26.6^{\circ}\text{C}$

  10. A chemical reaction occurs in a closed system at constant pressure. The system releases $50 \text{ kJ}$ of heat to the surroundings and does $10 \text{ kJ}$ of work on the surroundings. Which of the following statements is true regarding the change in internal energy ($\Delta E$) and enthalpy ($\Delta H$) for the system?

    • $\Delta E = -60 \text{ kJ}$ and $\Delta H = -50 \text{ kJ}$
    • $\Delta E = -40 \text{ kJ}$ and $\Delta H = -50 \text{ kJ}$
    • $\Delta E = -60 \text{ kJ}$ and $\Delta H = -60 \text{ kJ}$
    • $\Delta E = -50 \text{ kJ}$ and $\Delta H = -40 \text{ kJ}$

    Answer: $\Delta E = -60 \text{ kJ}$ and $\Delta H = -50 \text{ kJ}$

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