Thermochemistry — Practice Quiz

A Chemistry cheat sheet for Thermochemistry — every key formula with its symbols defined — plus a medium-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 $2.0 \text{ kg}$ object is moving at a velocity of $5.0 \text{ m/s}$. What is its kinetic energy?

    • $10 \text{ J}$
    • $25 \text{ J}$
    • $50 \text{ J}$
    • $100 \text{ J}$

    Answer: $25 \text{ J}$

  2. A system absorbs $150 \text{ J}$ of heat from its surroundings and performs $50 \text{ J}$ of work on the surroundings. What is the change in the internal energy of the system?

    • $-200 \text{ J}$
    • $-100 \text{ J}$
    • $100 \text{ J}$
    • $200 \text{ J}$

    Answer: $100 \text{ J}$

  3. A gas expands from an initial volume of $2.0 \text{ L}$ to a final volume of $5.0 \text{ L}$ against a constant external pressure of $1.5 \text{ atm}$. Calculate the work done by the gas in Joules. (Given: $1 \text{ L} \cdot \text{atm} = 101.3 \text{ J}$)

    • $-4.5 \text{ J}$
    • $-456 \text{ J}$
    • $4.5 \text{ J}$
    • $456 \text{ J}$

    Answer: $-456 \text{ J}$

  4. How much heat is required to raise the temperature of $100.0 \text{ g}$ of liquid water from $25.0^\circ \text{C}$ to $75.0^\circ \text{C}$? Use the provided specific heat table.

    • $418 \text{ J}$
    • $2090 \text{ J}$
    • $20900 \text{ J}$
    • $41800 \text{ J}$

    Answer: $20900 \text{ J}$

  5. A $50.0 \text{ g}$ sample of an unknown metal absorbs $1125 \text{ J}$ of heat when its temperature increases from $20.0^\circ \text{C}$ to $70.0^\circ \text{C}$. What is the specific heat capacity of the metal?

    • $0.225 \text{ J/g} \cdot \text{K}$
    • $0.45 \text{ J/g} \cdot \text{K}$
    • $0.90 \text{ J/g} \cdot \text{K}$
    • $1.125 \text{ J/g} \cdot \text{K}$

    Answer: $0.45 \text{ J/g} \cdot \text{K}$

  6. For a process occurring at constant pressure, which of the following correctly describes the relationship between the enthalpy change ($\Delta H$) and the internal energy change ($\Delta E$)?

    • $\Delta H = \Delta E$
    • $\Delta H = \Delta E - P\Delta V$
    • $\Delta H = \Delta E + P\Delta V$
    • $\Delta H = P\Delta V - \Delta E$

    Answer: $\Delta H = \Delta E + P\Delta V$

  7. Calculate the standard enthalpy of reaction ($\Delta H^\circ_{rxn}$) for the combustion of methane: $\text{CH}_4(\text{g}) + 2\text{O}_2(\text{g}) \rightarrow \text{CO}_2(\text{g}) + 2\text{H}_2\text{O}(\text{l})$. Use the provided standard enthalpies of formation table.

    • $-890.3 \text{ kJ/mol}$
    • $-802.3 \text{ kJ/mol}$
    • $-74.80 \text{ kJ/mol}$
    • $890.3 \text{ kJ/mol}$

    Answer: $-890.3 \text{ kJ/mol}$

  8. Under what condition is the change in internal energy ($\Delta E$) approximately equal to the change in enthalpy ($\Delta H$) for a chemical reaction?

    • When the reaction is endothermic.
    • When the reaction is exothermic.
    • When there is no significant change in volume ($\Delta V \approx 0$).
    • When the pressure is extremely high.

    Answer: When there is no significant change in volume ($\Delta V \approx 0$).

  9. Based on the provided table of specific heats, which substance requires the most heat to raise the temperature of a $1 \text{ g}$ sample by $1 \text{ K}$?

    • Aluminum ($\text{Al}(\text{s})$)
    • Iron ($\text{Fe}(\text{s})$)
    • Water ($\text{H}_2\text{O}(\text{l})$)
    • Methane ($\text{CH}_4(\text{g})$)

    Answer: Water ($\text{H}_2\text{O}(\text{l})$)

  10. If the velocity of an object is doubled while its mass remains constant, how does its kinetic energy change?

    • It remains the same.
    • It doubles.
    • It triples.
    • It quadruples.

    Answer: It quadruples.

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