Question

In an ice calorimeter, a chemical reaction is allowed to occur in thermal contact with an ice-water mixture at \(0^{\circ} \mathrm{C}\). Any heat liberated by the reaction is used to melt some ice; the volume change of the ice-water mixture indicates the amount of melting. When solutions containing \(1.0\) millimole each of \(\mathrm{AgNO}_{3}\) and \(\mathrm{NaCl}\) were mixed in such a calorimeter, both solutions having been pre-cooled to \(0^{\circ} \mathrm{C}\), \(0.20 \mathrm{~g}\) of ice melted. Assuming complete reaction in this experiment, what is \(\Delta H\) for the reaction: \(\mathrm{Ag}^{+}(\mathrm{aq})+\mathrm{Cl}^{-}(\mathrm{aq})\) \(\rightarrow\) AgCl(s)? Latent heat of fusion of ice at \(0{ }^{\circ} \mathrm{C}\) is \(80 \mathrm{cal} / \mathrm{g}\). (a) \(-16 \mathrm{kcal}\) (b) \(+16 \mathrm{kcal}\) (c) \(-16\) cal (d) \(+16\) cal

Short answer

\(-16\) cal

Step-by-step solution

Calculate the heat absorbed to melt the ice

Determine the amount of ice that melted and use the latent heat of fusion to calculate the total heat absorbed. The formula to use is: Heat absorbed \(Q = m \times L_f\), where \(m\) is the mass of the ice melted, and \(L_f\) is the latent heat of fusion.

Convert the calculated heat to calories

The mass of ice melted is given as 0.20 g and the latent heat of fusion of ice is given as 80 cal/g. So the heat absorbed (in calories) will be \(Q = 0.20 \times 80 = 16 \text{cal}\).

Determine the enthalpy change of the reaction

Since the heat released by the reaction is used to melt the ice, the enthalpy change for the reaction will be the negative of the heat absorbed during the melting of ice, resulting in \(\Delta H = -16 \text{cal}\) for the reaction.

Key concepts

Calorimetry

Calorimetry is a technique used to measure the amount of heat energy released or absorbed in a chemical or physical process. This measurement is crucial for understanding energy changes in reactions, which is a fundamental aspect of chemical thermodynamics. By using a calorimeter — a device designed to measure heat changes — the quantity of heat involved in a chemical reaction can be determined through direct or indirect means.

In direct calorimetry, the process occurring within the calorimeter either absorbs or releases heat, which changes the temperature of the surrounding. Recording this temperature change allows for the calculation of the heat change using the known specific heat capacities of the materials involved. Indirect calorimetry, on the other hand, relies on observing a physical change that correlates with heat absorption or release, like the melting of ice in an ice calorimeter as described in the exercise.

Latent Heat of Fusion

Latent heat of fusion is the amount of heat required to change a substance from a solid to liquid phase (or vice versa) at constant temperature and pressure, without changing its temperature. This physical property is essential for substances like ice, where melting or freezing is commonplace.

For ice at 0°C, the latent heat of fusion is typically around 80 calories per gram. This means that each gram of ice absorbs 80 calories of heat energy to convert into water at the same temperature. This concept plays a crucial role in the ice calorimeter experiment, as the amount of ice melted provides a direct measure of the heat generated by the chemical reaction when multiplying by the latent heat of fusion.

Chemical Thermodynamics

Chemical thermodynamics is the study of the interrelation of heat and work with chemical reactions or with physical changes of state within the confines of the laws of thermodynamics. In essence, it focuses on understanding how energy is transferred within systems and how it can be harnessed.

Key elements of chemical thermodynamics include the first law, which states that energy cannot be created or destroyed, and the second law, which deals with the spontaneous direction of heat flow and the concept of entropy. These principles help explain why certain reactions occur spontaneously while others require additional energy, such as the application of heat or pressure.

Enthalpy of Reaction

The enthalpy of reaction, often denoted as \(\Delta H\), is the heat change that occurs during a chemical reaction at constant pressure. It's a thermodynamic quantity used to express the amount of energy, in the form of heat, released or absorbed by a reaction. A negative \(\Delta H\) indicates an exothermic process, where heat is released to the surroundings, while a positive value indicates an endothermic process, where heat is absorbed from the surroundings.

In the context of the exercise, the enthalpy of reaction is calculated by using the heat absorbed to melt the ice, indicative of the heat released during the chemical reaction. With the formula \(Q = m \times L_f\), and the latent heat of fusion value, we can calculate the energy change during the reaction, yielding a negative enthalpy change (\(\Delta H\)), as the reaction is exothermic.