Calorimetry & Specific Heat practice questions

Question 1

A student dissolves a sample of solid calcium chloride, $\text{CaCl}_2\text{(s)}$, in water contained in an insulated calorimeter. The student observes that the temperature of the water increases from $22.0^\circ\text{C}$ to $31.0^\circ\text{C}$. Which of the following claims and justifications correctly identifies the thermochemical nature of the dissolution process?

Accepted Answer

The process is exothermic because thermal energy flows from the dissolving $\text{CaCl}_2$ (system) to the water (surroundings).

Answer

The process is exothermic because thermal energy flows from the water (surroundings) to the dissolving $\text{CaCl}_2$ (system).

Answer

The process is endothermic because thermal energy flows from the water (surroundings) to the dissolving $\text{CaCl}_2$ (system).

Answer

The process is endothermic because thermal energy flows from the dissolving $\text{CaCl}_2$ (system) to the water (surroundings).

Question 2

A student performs two calorimetry trials in an insulated vessel containing water. In Trial 1, a process transfers heat $q$ to $50.0\text{ g}$ of water, resulting in a temperature change of $\Delta T_1$. In Trial 2, the same process transfers the same amount of heat $q$ to $100.0\text{ g}$ of water, resulting in a temperature change of $\Delta T_2$. Assuming no heat is lost to the surroundings, what is the ratio $\dfrac{\Delta T_1}{\Delta T_2}$?

Accepted Answer

$2$

Answer

$\dfrac{1}{4}$

Answer

$\dfrac{1}{2}$

Answer

$4$

Question 3

Two metal blocks, $\text{Block X}$ and $\text{Block Y}$, are brought into contact inside an insulated container. The initial particulate state of the two blocks is shown in the diagram, where the length of each arrow represents the relative speed of a particle. Which of the following best describes the system after thermal equilibrium is reached?

Accepted Answer

Energy has transferred as heat from $\text{Block X}$ to $\text{Block Y}$, and the average kinetic energy of the particles in $\text{Block X}$ is equal to the average kinetic energy of the particles in $\text{Block Y}$.

Answer

Energy has transferred as heat from $\text{Block Y}$ to $\text{Block X}$, and the average kinetic energy of the particles in $\text{Block X}$ remains greater than that of $\text{Block Y}$.

Answer

Energy has transferred as heat from $\text{Block X}$ to $\text{Block Y}$, and all molecular motion in both blocks has ceased.

Answer

Energy has transferred as heat from $\text{Block X}$ to $\text{Block Y}$ until all particles in $\text{Block X}$ have lower kinetic energy than all particles in $\text{Block Y}$.

Question 4

A student places a sample of hot water with a mass of $50.0 \text{ g}$ at $70.0^\circ\text{C}$ into a calorimeter. The water cools to room temperature, $20.0^\circ\text{C}$. Assuming the specific heat capacity of water is $4.2 \text{ J/(g}\cdot^\circ\text{C)}$, what is the magnitude of the thermal energy transferred from the water as it cools?

Accepted Answer

$10.5 \text{ kJ}$

Answer

$14.7 \text{ kJ}$

Answer

$16.8 \text{ kJ}$

Answer

$18.9 \text{ kJ}$

Question 5

A student performs an experiment to determine the molar enthalpy of combustion, $\Delta H_{comb}$, of ethanol, $\text{C}_2\text{H}_5\text{OH}(l)$. A known mass of ethanol is burned in a spirit burner to heat a measured mass of water in an open metal calorimeter. The student assumes that all heat released by the combustion is absorbed by the water and uses $q = m c \Delta T$ to calculate the experimental molar enthalpy of combustion. However, a portion of the heat released during combustion is transferred to the surrounding air and metal calorimeter cup rather than to the water. Which of the following claims correctly predicts the effect of this heat loss on the calculated magnitude of $\Delta H_{comb}$ and provides the correct justification?

Accepted Answer

The calculated magnitude of $\Delta H_{comb}$ is lower than the actual value because the measured $\Delta T$ of the water is smaller than if all heat were transferred to the water.

Answer

The calculated magnitude of $\Delta H_{comb}$ is higher than the actual value because the heat lost to the surroundings increases the measured final temperature of the water.

Answer

The calculated magnitude of $\Delta H_{comb}$ is lower than the actual value because the heat loss causes the calculated mass of ethanol burned to be greater than the actual mass consumed.

Answer

The calculated magnitude of $\Delta H_{comb}$ is higher than the actual value because the unmeasured heat absorbed by the cup is added directly to the calculated heat absorbed by the water.

Question 6

A student dissolves a sample of solid calcium chloride, $\text{CaCl}_2\text{(s)}$, in an insulated calorimeter containing water at room temperature. The student claims that the dissolution of $\text{CaCl}_2\text{(s)}$ is an exothermic process. Which of the following experimental observations provides the best evidence to support the student's claim?

Accepted Answer

The temperature of the aqueous solution increases as the solid dissolves, demonstrating that thermal energy is transferred from the chemical system to the surroundings.

Answer

The temperature of the aqueous solution decreases as the solid dissolves, demonstrating that thermal energy is absorbed by the chemical system from the surroundings.

Answer

The solubility of the solid in water increases when the temperature is raised, demonstrating that thermal energy acts as a reactant in the dissolution process.

Answer

The electrical conductivity of the solution increases as the solid dissolves, demonstrating that thermal energy is produced alongside mobile hydrated ions.

Question 7

A student investigates the thermal properties of three solid metal samples: $\text{Al(s)}$, $\text{Fe(s)}$, and $\text{Ag(s)}$. Each sample has a mass of $10.0 \text{ g}$ and an initial temperature of $25.0^\circ\text{C}$. The student transfers $180 \text{ J}$ of heat to each sample. The specific heat capacities of the three metals are given in the table below.

| Metal | Specific heat capacity ($\text{J/(g}\cdot^\circ\text{C)}$) |
|---|---|
| $\text{Al(s)}$ | $0.90$ |
| $\text{Fe(s)}$ | $0.45$ |
| $\text{Ag(s)}$ | $0.24$ |

Which of the following correctly ranks the metals in order of the magnitude of their temperature change ($\Delta T$), from greatest to least?

Accepted Answer

$\text{Ag(s)} > \text{Fe(s)} > \text{Al(s)}$

Answer

$\text{Al(s)} > \text{Fe(s)} > \text{Ag(s)}$

Answer

$\text{Al(s)} > \text{Ag(s)} > \text{Fe(s)}$

Answer

$\text{Ag(s)} > \text{Al(s)} > \text{Fe(s)}$

Question 8

A student places a sample of an unknown metal with a mass of $100.0\text{ g}$ and an initial temperature of $80.0^\circ\text{C}$ into an insulated cup containing $50.0\text{ g}$ of water at an initial temperature of $20.0^\circ\text{C}$. The specific heat capacity of the metal is $0.42\text{ J/(g}\cdot^\circ\text{C)}$, and the specific heat capacity of water is $4.2\text{ J/(g}\cdot^\circ\text{C)}$. Assuming no heat is lost to the surroundings or the cup, what is the final thermal equilibrium temperature of the system?

Accepted Answer

$30.0^\circ\text{C}$

Answer

$24.0^\circ\text{C}$

Answer

$26.0^\circ\text{C}$

Answer

$50.0^\circ\text{C}$

Question 9

A student conducts an experiment to compare the thermal energy required for phase changes of water, $\text{H}_2\text{O}$. The student measures the thermal energy required to completely melt a $18.0 \text{ g}$ sample of ice at $0^\circ\text{C}$ ($q_{\text{fus}}$) and the thermal energy required to completely vaporize a $18.0 \text{ g}$ sample of liquid water at $100^\circ\text{C}$ ($q_{\text{vap}}$). Which of the following correctly compares $q_{\text{vap}}$ to $q_{\text{fus}}$ and provides the correct molecular explanation?

Accepted Answer

$q_{\text{vap}} > q_{\text{fus}}$, because vaporization requires completely overcoming all intermolecular hydrogen bonds, whereas fusion requires only partially disrupting the hydrogen bonding network.

Answer

$q_{\text{vap}} < q_{\text{fus}}$, because ice has a lower density than liquid water, requiring more energy to expand the crystal structure during melting.

Answer

$q_{\text{vap}} < q_{\text{fus}}$, because melting requires breaking covalent $\text{O-H}$ bonds within $\text{H}_2\text{O}$ molecules, whereas boiling only disrupts intermolecular hydrogen bonds.

Answer

$q_{\text{vap}} > q_{\text{fus}}$, because vaporization requires breaking intramolecular covalent $\text{O-H}$ bonds, whereas fusion requires only overcoming intermolecular hydrogen bonds.

Question 10

A student uses a coffee-cup calorimeter to determine the molar enthalpy of dissolution of solid potassium nitrate, represented by the equation $\text{KNO}_3\text{(s)} \rightarrow \text{K}^+\text{(aq)} + \text{NO}_3^-\text{(aq)}$. The student obtains the following data.

| Measurement | Value |
|---|---:|
| Mass of $\text{KNO}_3\text{(s)}$ | $10.1\text{ g}$ |
| Mass of water | $89.9\text{ g}$ |
| Initial temperature | $25.00^\circ\text{C}$ |
| Final temperature | $16.25^\circ\text{C}$ |

Assume that the solution has a specific heat capacity of $4.00\text{ J/(g}\cdot^\circ\text{C)}$, the calorimeter absorbs negligible heat, and the molar mass of $\text{KNO}_3$ is $101\text{ g/mol}$. What is the molar enthalpy of dissolution of $\text{KNO}_3\text{(s)}$?

Accepted Answer

$+35.0\text{ kJ/mol}$

Answer

$-35.0\text{ kJ/mol}$

Answer

$+350\text{ kJ/mol}$

Answer

$+35{,}000\text{ kJ/mol}$

Question 11

A student evaluates ammonium nitrate, $\text{NH}_4\text{NO}_3$, for use in an instant cold pack by dissolving a known amount of the solid in water. The dissolution is endothermic. Initially, the water, solid, and room are at the same temperature. The student performs the experiment in a covered, thin-walled vessel without an insulating jacket and calculates the enthalpy of dissolution using

$$q_{\text{solution}}=m_{\text{solution}}c_{\text{solution}}(T_f-T_i)$$

and

$$\Delta H_{\text{soln}}=-\dfrac{q_{\text{solution}}}{n_{\text{NH}_4\text{NO}_3}}$$

Assume that heat exchange with the room is the only significant source of error. Compared with the accepted positive value of $\Delta H_{\text{soln}}$, how will the calculated value be affected, and why?

Accepted Answer

It will be too low, because thermal energy enters the colder solution from the room, reducing the magnitude of the measured temperature decrease.

Answer

It will be too high, because thermal energy entering from the room makes $T_f-T_i$ more negative.

Answer

It will be too high, because the calculation counts thermal energy entering from the room as energy absorbed by the dissolution.

Answer

It will be too low, because some thermal energy released by the dissolution is transferred from the solution to the room.

Question 12

To model a neutralization step in wastewater treatment, a student mixes the following solutions in a constant-pressure calorimeter.

| Solution | Volume | Concentration | Initial temperature |
|----------|--------|---------------|---------------------|
| $\text{HNO}_3\text{(aq)}$ | $40.0\text{ mL}$ | $1.50\text{ M}$ | $21.00^\circ\text{C}$ |
| $\text{NaOH(aq)}$ | $50.0\text{ mL}$ | $1.00\text{ M}$ | $21.00^\circ\text{C}$ |

The maximum temperature of the mixture is $28.40^\circ\text{C}$. Assume that the volumes are additive, the density of the mixture is $1.00\text{ g/mL}$, its specific heat capacity is $4.18\text{ J/(g}\cdot^\circ\text{C)}$, and the calorimeter absorbs negligible heat. The reaction is

$\text{HNO}_3\text{(aq)}+\text{NaOH(aq)}\rightarrow\text{NaNO}_3\text{(aq)}+\text{H}_2\text{O(l)}$

What is the magnitude of the experimental enthalpy of neutralization per mole of $\text{H}_2\text{O(l)}$ formed?

Accepted Answer

$55.7\text{ kJ/mol}$

Answer

$0.0557\text{ kJ/mol}$

Answer

$2.78\text{ kJ/mol}$

Answer

$46.4\text{ kJ/mol}$

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