Problem 65 - 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 \(\Delta_{\mathrm{r}} H^{\circ}\) and \(\Delta_{\mathrm{r}} S^{\circ}\) for the reaction. Verify your prediction with a calculation.

Step-by-Step Solution

Answer

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

Step 1: Predicting the sign of \(\Delta_{\mathrm{r}} H^{\circ}\)

The reaction involves the combination of sodium and water to form sodium hydroxide and hydrogen gas. This process is exothermic because sodium reacts violently with water, releasing energy in the form of heat. Therefore, the sign of \(\Delta_{\mathrm{r}} H^{\circ}\) is predicted to be negative.

Step 2: Predicting the sign of \(\Delta_{\mathrm{r}} S^{\circ}\)

Entropy, \(S^{\circ}\), measures the disorder or randomness in a system. The reaction turns solid sodium (low entropy) and liquid water into aqueous sodium hydroxide and gaseous hydrogen. The increase in disorder due to the production of gas suggests that \(\Delta_{\mathrm{r}} S^{\circ}\) will be positive.

Step 3: Verify by Calculation with \(\Delta_{\mathrm{r}} H^{\circ}\)

Consult a standard table of enthalpies of formation. \[\Delta_{\mathrm{r}} H^{\circ} = \Sigma \Delta_{f} H^{\circ} (\text{products}) - \Sigma \Delta_{f} H^{\circ} (\text{reactants})\] For sodium hydroxide and hydrogen formation, \(\Delta_{f} H^{\circ}(\text{NaOH}) = -470.1 \text{ kJ/mol}\) and \(\Delta_{f} H^{\circ}(\text{H}_2) = 0\). Sodium and water have \(\Delta_{f} H^{\circ}\) values of \(\Delta_{f} H^{\circ}(\text{Na}) = 0\) and \(\Delta_{f} H^{\circ}(\text{H}_2\text{O}) = -285.8 \text{ kJ/mol}\), respectively. Calculating confirms exothermicity with a negative result.

Step 4: Verify by Calculation with \(\Delta_{\mathrm{r}} S^{\circ}\)

Using standard entropies: \[\Delta_{\mathrm{r}} S^{\circ} = \Sigma S^{\circ} (\text{products}) - \Sigma S^{\circ} (\text{reactants})\] Calculate using values such as \(S^{\circ}(\text{NaOH}) = 64.3 \text{ J/K/mol}\), \(S^{\circ}(\text{H}_2) = 130.7 \text{ J/K/mol}\), \(S^{\circ}(\text{Na}) = 51.2 \text{ J/K/mol}\), and \(S^{\circ}(\text{H}_2\text{O}) = 69.9 \text{ J/K/mol}\). The calculation shows increase in entropy, confirming a positive sign.

Key Concepts

Enthalpy Change

In chemical thermodynamics, the term **enthalpy change** refers to the difference in heat content between the products and reactants in a chemical reaction. When we discuss enthalpy change, we are often referring to how much energy is absorbed or released during a reaction.
To predict whether a reaction is exothermic (releases heat) or endothermic (absorbs heat), we look at the sign of the enthalpy change (\(\Delta_{\mathrm{r}} H^{\circ}\)).

• If the enthalpy change is negative, the reaction is exothermic, meaning it releases energy.
• If positive, the reaction is endothermic, indicating energy absorption.

In our case, the reaction of sodium with water is violent and releases heat, suggesting it is an exothermic reaction. Therefore, the sign of \(\Delta_{\mathrm{r}} H^{\circ}\) is negative.

Entropy Change

**Entropy change** (\(\Delta_{\mathrm{r}} S^{\circ}\)) is a concept that measures the change in disorder or randomness within a system during a chemical reaction. Entropy is closely linked with the second law of thermodynamics and provides insight into the viability of a reaction.
For the reaction of solid sodium with liquid water to form sodium hydroxide and hydrogen gas, the change from a more ordered state (solid and liquid) to a less ordered state (aqueous and gaseous) reflects an increase in entropy.

• Solids have low entropy due to their structured arrangement of particles.
• Gases have high entropy due to high particle movement and disorder.

Here, since gas is produced, the entropy of the system increases, resulting in a positive \(\Delta_{\mathrm{r}} S^{\circ}\).Determining entropy change helps predict how feasible a reaction is in nature.

Exothermic Reaction

An **exothermic reaction** is a type of chemical reaction that releases energy through light, sound, or heat. These reactions are ubiquitous in both natural phenomena and industrial processes.
When sodium reacts with water, the reaction is not only violent but also exothermic. This means that it liberates heat into its surroundings, causing the temperature to rise.

• Indicators of exothermic reactions include a rise in temperature of the environment or release of gases.
• Familiar examples include combustion and many oxidation reactions.

For students grasping chemical reactions, understanding whether a reaction is exothermic can help predict outcomes like energy release, temperature changes, and the spontaneous nature of the reaction.

Reaction Prediction

**Reaction prediction** is a vital aspect of chemical sciences, allowing chemists to anticipate the outcomes of reactions without performing experimental trials. Two key factors inform such predictions: enthalpy change and entropy change.
In our example, assessing both the predicted negative enthalpy change and positive entropy change supports the conclusion that the reaction between sodium and water will proceed spontaneously under standard conditions.

• For a quick prediction, one can note the signs of \(\Delta_{\mathrm{r}} H^{\circ}\) and \(\Delta_{\mathrm{r}} S^{\circ}\).
• A negative \(\Delta_{\mathrm{r}} H^{\circ}\) and positive \(\Delta_{\mathrm{r}} S^{\circ}\) typically point to a spontaneous reaction.

By using thermodynamic principles, chemists can effectively predict the behavior and feasibility of chemical reactions.