Problem 38 - Chemistry: An Atoms-Focused Approach

Question

For each of the reactions given, indicate whether \(\Delta S\) should have a positive sign or a negative sign. If it is not possible to judge the sign of \(\Delta S\) based on the information provided, indicate why that is the case. a. \(2 \mathrm{Na}(s)+\mathrm{Cl}_{2}(g) \rightarrow 2 \mathrm{NaCl}(s)\) b. \(4 \mathrm{H}_{3} \mathrm{PO}_{3}(\ell) \rightarrow \mathrm{PH}_{3}(g)+3 \mathrm{H}_{3} \mathrm{PO}_{4}(\ell)\) c. \(\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g)\) d. \(\mathrm{Ca}(\mathrm{OH})_{2}(s)+\mathrm{CO}_{2}(g) \rightarrow \mathrm{CaCO}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(g)\)

Step-by-Step Solution

Answer

a. \(2 \mathrm{Na}(s)+\mathrm{Cl}_{2}(g) \rightarrow 2 \mathrm{NaCl}(s)\) b. \(4 \mathrm{H}_{3} \mathrm{PO}_{3}(\ell) \rightarrow \mathrm{PH}_{3}(g)+3 \mathrm{H}_{3} \mathrm{PO}_{4}(\ell)\) c. \(\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g)\) d. \(\mathrm{Ca}(\mathrm{OH})_{2}(s)+\mathrm{CO}_{2}(g) \rightarrow \mathrm{CaCO}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(g)\) Answer: a. ∆S is negative. b. ∆S is positive. c. ∆S is indeterminable. d. ∆S is indeterminable.

Step 1: Analyze the change in the number of gas particles

In this reaction, one mole of chlorine gas is used to form two moles of solid sodium chloride. There is a decrease in the number of gas particles.

Step 2: Determine the sign of ∆S

Since the number of gas particles decreases in this reaction, the entropy of the reaction should decrease, and therefore ∆S should have a negative sign. b. \(4 \mathrm{H}_{3} \mathrm{PO}_{3}(\ell) \rightarrow \mathrm{PH}_{3}(g)+3 \mathrm{H}_{3} \mathrm{PO}_{4}(\ell)\)

Step 1: Analyze the change in the number of gas particles

In this reaction, four moles of liquid phosphorous acid react to form one mole of phosphine gas and three moles of liquid phosphoric acid. There is an increase in the number of gas particles.

Step 2: Determine the sign of ∆S

Since the number of gas particles increases in this reaction, the entropy of the reaction should increase, and therefore ∆S should have a positive sign. c. \(\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g)\)

Step 1: Analyze the change in the number of gas particles

In this reaction, one mole of carbon monoxide gas and one mole of water vapor react to form one mole of carbon dioxide gas and one mole of hydrogen gas. The number of gas particles remains the same.

Step 2: Determine the sign of ∆S

Since the number of gas particles does not change in this reaction, it is not possible to determine the sign of ∆S based on the given information. d. \(\mathrm{Ca}(\mathrm{OH})_{2}(s)+\mathrm{CO}_{2}(g) \rightarrow \mathrm{CaCO}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(g)\)

Step 1: Analyze the change in the number of gas particles

In this reaction, one mole of solid calcium hydroxide reacts with one mole of carbon dioxide gas to form one mole of solid calcium carbonate and one mole of water vapor. The number of gas particles remains the same.

Step 2: Determine the sign of ∆S

Since the number of gas particles does not change in this reaction, it is not possible to determine the sign of ∆S based on the given information.

Key Concepts

Entropy

Entropy is a measure of disorder or randomness in a system. In chemistry, it is represented by the symbol \(S\). When we talk about changes in entropy, we're considering how the arrangement of particles is affected during a chemical reaction.

Entropy increases when there is more disorder within a system, such as when solid particles dissolve in liquid or when gas escapes into the air. Conversely, entropy decreases when a system becomes more ordered, like when gases condense into a liquid or when substances form a more structured solid.

• Increase in entropy: More randomness or spread-out energy leads to a positive \(\Delta S\).
• Decrease in entropy: Less randomness or higher order results in a negative \(\Delta S\).

Understanding the changes in entropy helps us predict how a chemical reaction will proceed.

Gas Particles

Gas particles play a crucial role in determining the entropy change during a chemical reaction. Gas molecules have a lot of freedom to move, and hence, they typically increase the entropy of a system significantly.

When a reaction involves a change in the number of gas particles, this often leads to a change in entropy. For example:

• If the number of gas particles increases (more moles of gas are produced than consumed), the entropy generally increases.
• Conversely, if the number of gas particles decreases, the entropy usually decreases.

The behavior of gas particles allows us to predict the direction of entropy change without needing detailed calculations.

Thermodynamics

Thermodynamics is the study of energy transformations in chemical processes. It relies heavily on concepts like energy, entropy, and equilibrium.

In this field, entropy is a key concept. It helps demonstrate how natural processes tend to move towards a state of maximum disorder or randomness. Thermodynamics uses laws such as the Second Law, which states that spontaneous processes in an isolated system have a tendency to increase total entropy.

• The first law (conservation of energy) states energy cannot be created or destroyed, only transformed.
• The second law emphasizes the inevitable increase of overall entropy in isolated systems.

These principles are foundational for understanding chemical reactions and processes.

Chemical Reactions

Chemical reactions involve breaking and forming chemical bonds, leading to a transformation of substances. Often, these reactions are accompanied by changes in energy and entropy.

Here are a few takeaways about how entropy relates to chemical reactions:

• Reactions moving from ordered to more disordered states (like solids dissolving) show increased entropy.
• Reactions becoming more ordered from a disordered state (like gas forming into a solid) usually have decreased entropy.

Evaluating the change in gas particles during a reaction helps predict shifts in entropy, guiding predictions on reaction spontaneity.