Problem 33 - Chemistry The Central Science

Question

(a) Why is the change in enthalpy usually easier to measure than the change in internal energy? (b) \(H\) is a state function, but \(q\) is not a state function. Explain. (c) For a given process at constant pressure, \(\Delta H\) is positive. Is the process endothermic or exothermic?

Step-by-Step Solution

Answer

(a) The change in enthalpy (\(\Delta H\)) is easier to measure than the change in internal energy (\(\Delta U\)) because most experiments occur at constant pressure, making \(\Delta H\) equal to the heat absorbed or released. Measuring work, which is required to calculate \(\Delta U\), is difficult in practice. (b) Enthalpy (\(H\)) is a state function as it depends only on the system's current state (being the sum of \(U, P,\) and \(V\), all state functions). Heat (\(q\)) is not a state function as it depends on the path taken. (c) A process with a positive change in enthalpy (\(\Delta H > 0\)) at constant pressure is endothermic, as it involves absorption of heat by the system.

Step 1: (a) Comparison between measuring change in enthalpy and change in internal energy

Enthalpy (\(H\)) is a thermodynamic property defined as the sum of the system's internal energy (\(U\)) and the product of its pressure (\(P\)) and volume (\(V\)): \(H = U + PV\). The change in enthalpy (\(\Delta H\)) is usually easier to measure than the change in internal energy (\(\Delta U\)) because most practical experiments and reactions occur at constant pressure. Under constant pressure conditions, the change in enthalpy (\(\Delta H\)) is equal to the heat absorbed or released by the system (\(q_p\)): \(\Delta H = q_p\). However, the change in internal energy (\(\Delta U\)) involves measuring the changes in both heat (\(q\)) and work (\(w\)) done by or on the system, since \(\Delta U = q + w\). Measuring work is quite difficult in practice, especially for chemical reactions, while measuring heat absorbed or released is relatively easier. Therefore, it is more convenient to measure the change in enthalpy than the change in internal energy.

Step 2: (b) Enthalpy as a state function and heat not being a state function

State functions are properties that depend only on the current state of the system and are independent of the path taken to reach that state. Enthalpy (\(H\)) is a state function because it is defined as the sum of the system's internal energy (\(U\), also a state function) and the product of pressure (\(P\), a state function) and volume (\(V\), a state function): \(H = U + PV\). On the other hand, heat (\(q\)) is not a state function because it is a form of energy transfer that depends on the path taken. The amount of heat transferred between two states of a system is not solely determined by the initial and final states but depends on the process through which the system changes.

Step 3: (c) Determining whether a process is endothermic or exothermic based on the change in enthalpy

A process at constant pressure has a positive change in enthalpy (\(\Delta H > 0\)). Based on the definition of enthalpy and its relationship with heat at constant pressure conditions (\(\Delta H = q_p\)), a positive value for \(\Delta H\) implies that the heat has been absorbed by the system from its surroundings. Since endothermic processes involve absorption of heat by the system, a process with a positive change in enthalpy at constant pressure is endothermic.