Question

In each of the following pairs, choose the substance with a lower entropy. (a) One mole of \(\mathrm{O}_{2}(g)\) with \(758 \mathrm{~mm}\) Hg pressure, one mole of \(\mathrm{O}_{2}(g)\) with \(493 \mathrm{~mm}\) Hg pressure, both at room temperature (b) glucose \((s),\) glucose \((a q)\) (c) \(\mathrm{Hg}(l), \mathrm{Hg}(g),\) both at room temperature

Short answer

Question: Determine the substance with lower entropy in each of the following pairs: a) 1 mol O2(g) at room temperature and 758 mm Hg pressure or 1 mol O2(g) at room temperature and 493 mm Hg pressure b) 1 mol glucose(s) or 1 mol glucose (aq) c) 1 mol Hg(l) at room temperature or 1 mol Hg(g) at room temperature Answer: a) 1 mol O2(g) at room temperature and 758 mm Hg pressure has lower entropy. b) 1 mol glucose(s) has lower entropy. c) 1 mol Hg(l) at room temperature has lower entropy.

Step-by-step solution

(a) Comparing the entropy of O2(g) at different pressures

Both substances are one mole of O2(g) at room temperature, but at different pressures. In general, higher pressure implies more ordered particles and hence lower entropy. So to find the substance with lower entropy, we will look for the one with higher pressure. In this case, O2(g) with 758 mm Hg pressure has a higher pressure than O2(g) with 493 mm Hg pressure. Thus, the substance with lower entropy is O2(g) with 758 mm Hg pressure.

(b) Comparing the entropy of glucose in solid and aqueous phases

We have to compare the entropy of glucose (s) and glucose (aq). In general, the entropy of a substance increases as it moves from solid to liquid to gas phase. In this case, solid glucose is in a more ordered structure than glucose dissolved in water. Therefore, glucose (s) has lower entropy than glucose (aq).

(c) Comparing the entropy of Hg in liquid and gaseous phases

We have to compare the entropy of Hg(l) and Hg(g), both at room temperature. As mentioned before, the entropy of a substance increases as it moves from solid to liquid to gas phase. In this case, Hg(l) is in a more ordered structure than Hg(g). Thus, Hg(l) has lower entropy than Hg(g).

Key concepts

Thermodynamics

The field of thermodynamics deals with the principles governing energy transformations and the behavior of systems in terms of heat and work. One of the central concepts in thermodynamics is entropy, which is often associated with the level of disorder or randomness in a system.

Entropy is a measure of the number of specific ways in which a thermodynamic system can be arranged, often at a molecular level, and still produce the same energy state. In practical terms, it reflects the amount of energy in a physical system that cannot be used to do work. This concept can be seen in the provided exercise, where students learn to identify substances with lower entropy based on changes in phases and pressures.

Defining Entropy in Thermodynamics

Entropy can be quantified and is denoted by the symbol 'S'. The Second Law of Thermodynamics states that in an isolated system, entropy can only stay the same or increase over time; this implies that processes occur in a direction that increases the total entropy of the universe. The exercises provided help students to understand this by comparing the entropy between different states of matter and under different conditions, solidifying their comprehension of how entropy relates to thermodynamics overall.

States of Matter

The states of matter—solid, liquid, and gas—are distinguished by differences in the structural arrangements and movements of particles. Students often learn about these distinctions early in their chemistry education, but a deeper understanding comes from studying the implications these states have on properties like entropy.

In solids, particles are closely packed in a highly ordered structure, which confines them to vibrate in fixed locations. As a result, solids generally have the lowest entropy. Liquids allow for more particle movement but still maintain a level of structural order, giving them moderate entropy. Gases have particles that are widely spaced and move freely, which corresponds to a higher level of randomness or entropy.

Impact of Phase Changes on Entropy

When a substance changes from solid to liquid (melting) or from liquid to gas (vaporization), it undergoes a phase change which is accompanied by an increase in entropy. This concept is vividly demonstrated in the exercise, where students see that glucose in aqueous solution (representing a higher entropy state) has more disorder than solid glucose and that mercury is more disordered as a gas than as a liquid.

Physical Chemistry

Physical chemistry is the branch of chemistry that deals with the study of how matter behaves on a molecular and atomic level and how chemical reactions occur. It combines principles of physics and chemistry to understand the physical properties of molecules, the forces that act upon them, and the interactions between them.

One of the key areas within physical chemistry is the study of thermodynamics, which includes concepts such as energy, enthalpy, and, importantly for our exercise, entropy. Physical chemistry helps in quantifying how changes in pressure, temperature, or phase can affect the entropy of a substance.

Applying Physical Chemistry Concepts

Physical chemistry can be used to explain the outcomes in the exercise. For example, it can provide the quantitative tools to measure the differences in entropy between oxygen at two different pressures, or to predict the increase in entropy when a substance like mercury transitions from a liquid to a gas. Students use physical chemistry to connect the theoretical underpinnings of entropy with practical examples, enhancing their analytical and predictive skills in chemistry.