Problem 45 - Chemistry and Chemical Reactivity

Question

Sodium reacts violently with water according to the equation $$\mathrm{Na}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow \mathrm{NaOH}(\mathrm{aq})+1 / 2 \mathrm{H}_{2}(\mathrm{g})$$ Without doing calculations, predict the signs of \(\Delta_{r} H^{\circ}\) and \(\Delta_{\mathrm{r}} S^{\circ}\) for the reaction. Verify your prediction with a calculation.

Step-by-Step Solution

Answer

\( \Delta_{r} H^{\circ} \) is negative; \( \Delta_{r} S^{\circ} \) is positive.

Step 1: Predict the Sign of Enthalpy Change (ΔrH°)

To predict the sign of \( \Delta_{r} H^{\circ} \) consider the nature of the reactants and products. The given reaction is exothermic because sodium reacts violently with water, releasing energy in the form of heat. Therefore, \( \Delta_{r} H^{\circ} \) is negative.

Step 2: Predict the Sign of Entropy Change (ΔrS°)

The reaction produces a gas, \( 1/2 \mathrm{H}_2(\mathrm{g}) \), from a solid and liquid reactant. This increase in the amount of gas indicates higher disorder in the system. Consequently, the entropy change, \( \Delta_{\mathrm{r}} S^{\circ} \), is positive.

Step 3: Verify Predictions Using the Reaction Equation

Examine the reaction's energetic nature and phase changes involved: \( \mathrm{Na} \) (solid) and \( \mathrm{H}_2\mathrm{O} \) (liquid) form \( \mathrm{NaOH} \) (aqueous) and a gas, \( \mathrm{H}_2(g) \). An exothermic reaction releasing a gas out of a solid-liquid system confirms the predicted signs: \( \Delta_{r} H^{\circ} < 0 \) and \( \Delta_{r} S^{\circ} > 0 \).

Key Concepts

Entropy

Entropy is a measure of the disorder or randomness in a system. When a chemical reaction occurs, it can either increase or decrease the system's entropy based on the changes in molecular motion and arrangement.

In the provided reaction where sodium reacts with water, there is a transition from solid and liquid reactants to an aqueous solution and a gaseous product. Specifically, the production of hydrogen gas (\( 1/2 \mathrm{H}_2(\mathrm{g}) \)) signifies a move from a more ordered state (solid and liquid) to a less ordered state (involving gases).

This shift signifies an increase in disorder, contributing to a positive change in entropy (\( \Delta_{\mathrm{r}} S^\circ > 0 \)). The more freedom the particles have in how they move and interact, the higher the entropy.

When interpreting this in thermodynamic terms:

• Solids typically have low entropy since their particles are tightly packed.
• Liquids have more entropy than solids, considering particle flow is possible.
• Gases represent the highest entropy within this context, due to maximum freedom of movement.

Enthalpy

Enthalpy is the measurement of total heat content in a system under constant pressure. It reflects changes that occur during a reaction, often categorized as either exothermic or endothermic.

For the reaction of sodium with water, we considered whether heat is absorbed or released. In this case, since the reaction proceeds vigorously and releases heat (you might even see sparks fly when sodium hits water), it is classified as exothermic. Therefore, the enthalpy change for the reaction (\( \Delta_{r} H^\circ \)) is negative.

Here's a simpler way to break down the concept of enthalpy:

• Exothermic reactions result in a loss of heat to the surroundings. This is denoted by a negative enthalpy change (\( \Delta H < 0 \)). Common indicators include temperature increase and, in some reactions like this one, visible energetic displays like sparks.
• Endothermic reactions absorb heat from the surroundings, leading to cooling effects, and are denoted by a positive enthalpy change (\( \Delta H > 0 \)).

Understanding the nature and direction of heat flow helps predict other reaction characteristics, such as spontaneity and energy efficiency.

Exothermic Reactions

Exothermic reactions are chemical processes that release energy, usually in the form of heat, light, or sound, as they proceed. They are characterized by a negative energy change (\( \Delta H < 0 \)), which indicates that the energy of the products is lower than that of the reactants.

In our case, the reaction of sodium with water is a classic example of an exothermic reaction. The obvious signs are the violent reaction that occurs upon contact, often accompanied by sparks and even small explosions. This type of reaction is typical when highly reactive metals like sodium come into contact with water.

Consider some of the features of exothermic reactions:

• Reaction tends to occur spontaneously, releasing energy. In terms of thermodynamics, the surrounding environment absorbs this released energy.
• The temperature of the surroundings often increases, serving as an indicator of the exothermic nature.
• These reactions are not only dramatic but often used in practical applications where heat generation is desired, such as in hand warmers or combustion engines.

Understanding exothermic reactions is essential for safely managing energy transformations in both academic and real-world chemical settings.