Question

Explain why $\mathrm{\Delta }H$ is obtained directly from coffee-cup calorimeters, whereas $\mathrm{\Delta }E$ is obtained directly from bomb calorimeters.

Short answer

Coffee-cup calorimeters measure heat changes at constant pressure (isobaric conditions), which is directly related to the enthalpy change (∆H) of the reaction. On the other hand, bomb calorimeters measure heat changes at constant volume (isochoric conditions), which is directly related to the internal energy change (∆E) of the reaction. Therefore, ∆H is obtained directly from coffee-cup calorimeters, whereas ∆E is obtained directly from bomb calorimeters.

Step-by-step solution

Understanding Coffee-cup Calorimeters

Coffee-cup calorimeters are simple, open-system calorimeters that are well insulated to minimize heat exchange with the surroundings. As a result, these calorimeters measure heat changes at constant pressure (isobaric conditions). Hence, the heat change measured by a coffee-cup calorimeter is directly related to the enthalpy change (∆H) of the reaction.

Understanding Bomb Calorimeters

Bomb calorimeters, on the other hand, are closed-system calorimeters that consist of a sealed metal container called a "bomb" in which the reaction takes place, submerged in a known amount of water. The pressure inside the bomb is allowed to increase as the reaction proceeds, but the volume is kept constant. As a result, bomb calorimeters measure heat changes at constant volume (isochoric conditions). The heat change measured at constant volume is directly related to the internal energy change (∆E) of the reaction.

Comparing Coffee-cup and Bomb Calorimeters

To summarize, coffee-cup calorimeters measure heat changes at constant pressure, while bomb calorimeters measure heat changes at constant volume. Since enthalpy changes (∆H) occur at constant pressure and internal energy changes (∆E) occur at constant volume, we can conclude that ∆H is obtained directly from coffee-cup calorimeters and ∆E is obtained directly from bomb calorimeters.

Key concepts

Enthalpy Change

Enthalpy change, denoted as $\mathrm{\Delta }H$, represents the heat absorbed or released during a chemical reaction at constant pressure. It is a crucial concept in thermodynamics because most chemical reactions in laboratories and industry occur at constant pressure.

• When a reaction gives off heat, it is exothermic, and $\mathrm{\Delta }H$ is negative.
• If it absorbs heat, it is endothermic, and $\mathrm{\Delta }H$ is positive.

In real-world applications, enthalpy is preferred because it considers not only the internal energy change but also the work done by the system as it expands or contracts against the atmospheric pressure. This makes enthalpy an essential part of understanding how much energy a reaction releases or consumes.

Internal Energy

Internal energy, symbolized as $\mathrm{\Delta }E$, refers to the total energy change within a system. It includes all forms of energy, like kinetic and potential energy, that contribute to the system's overall energy state.

• In a closed system, the only changes in energy are due to heat exchange and work done.
• Unlike enthalpy, internal energy does not account for pressure-volume work.

This makes internal energy a simpler concept, directly linked to heat in a constant volume setting, providing clarity when experiments are designed in a closed container, like a bomb calorimeter. Here, $\mathrm{\Delta }E$ becomes crucial for understanding how energy is conserved in a reaction.

Constant Pressure

Constant pressure conditions, or isobaric conditions, are used in coffee-cup calorimeters to measure enthalpy changes. Under these conditions, pressure remains unchanged while heat is absorbed or released.

• Common in everyday scenarios, as atmospheric pressure often remains constant.
• Allows for the direct measurement of $\mathrm{\Delta }H$ without needing to adjust for pressure changes.

Operating under constant pressure is practical in experimental setups because it mirrors common laboratory conditions more closely, making data easy to interpret. This makes constant pressure an essential concept when determining the heat dynamics of reactions using simpler calorimeters.

Constant Volume

In constant volume or isochoric conditions, the volume of the system does not change during a reaction. Bomb calorimeters use this setup as their heavy-duty design ensures no expansion or contraction.

• This makes it easier to measure changes in internal energy $\mathrm{\Delta }E$.
• Pressure may vary but does not affect the direct calculation of $\mathrm{\Delta }E$.

Constant volume conditions are ideal for reactions involving gases, where pressure changes would complicate measurements. The robust construction of bomb calorimeters makes them perfect for obtaining precise energy change readings by focusing purely on internal energy shifts.