Question

Identify the following processes as either spontaneous or not spontaneous. (a) Liquid water turns to ice when placed in a freezer at \(-5^{\circ} \mathrm{C}\) (b) Nitrogen gas is compressed to one half its original volume. (c) Sodium reacts with water forming \(\mathrm{H}_{2}(\mathrm{g})\) and \(\mathrm{NaOH}(\mathrm{aq})\) (d) Slightly soluble \(\operatorname{CaSO}_{4}\left(K_{\mathrm{sp}}=4.5 \times 10^{-5}\right)\) dis- solves in water to form a saturated solution.

Short answer

(a) Spontaneous; (b) Not spontaneous; (c) Spontaneous; (d) Not spontaneous.

Step-by-step solution

Understand the Definition of Spontaneity

A process is considered \( \text{spontaneous} \) if it occurs naturally without needing an external input of energy. Spontaneity is often driven by the tendency to minimize free energy in a system.

Evaluate Process (a) Liquid water turns to ice

Liquid water turning to ice in a freezer at \(-5^{\circ} \mathrm{C}\) is spontaneous because it is below the freezing point of water, and at such temperatures, water naturally transitions from liquid to solid.

Evaluate Process (b) Compression of Nitrogen Gas

Compression of nitrogen gas to half its original volume involves doing work on the system. This process is not spontaneous, as external work (energy) must be input to compress the gas.

Evaluate Process (c) Reaction of Sodium with Water

Sodium reacts vigorously with water to produce hydrogen gas and sodium hydroxide spontaneously. This reaction is exothermic and releases energy, making it spontaneous.

Evaluate Process (d) Dissolution of Slightly Soluble CaSO4

The dissolution of \( \text{CaSO}_4 \) in water is not spontaneous in general terms, as \( \text{CaSO}_4 \) is only slightly soluble, and the equilibrium favors the solid rather than a dissolved state. However, once the solution becomes saturated, no further dissolution occurs without altering conditions.

Key concepts

Free Energy

Have you ever wondered why certain reactions or changes happen on their own while others need a push? The reason often lies in a concept called free energy. In chemistry, free energy refers to the energy available to do work. When a system's free energy decreases, the process is more likely to occur spontaneously. This essentially means that the process proceeds without needing any added energy.

• A significant drop in free energy often drives spontaneous changes.
• If a process leads to lower free energy, it is more thermodynamically favorable.
• The formula for change in free energy (\( \Delta G \)) is given by:\[ \Delta G = \Delta H - T \Delta S\]where \( \Delta H \) is the change in enthalpy (heat content), \( \Delta S \) is the change in entropy (disorder), and \( T \) is the temperature in Kelvin.

Understanding free energy helps us predict whether a reaction or process will occur on its own or if it will need external energy input.

Exothermic Reactions

Some reactions release energy into their surroundings, often in the form of heat. These are known as exothermic reactions. When sodium reacts with water, this is what occurs.
During an exothermic reaction:

• The temperature of the surroundings increases because heat is released.
• The change in enthalpy (\( \Delta H \)) is negative, indicating that the system loses heat.
• The released energy can help explain the spontaneity of the reaction.

Exothermic reactions are spontaneous under most conditions because they contribute to a decrease in a system’s total free energy. This is why you might see reactions like fireworks or combustion happen quickly and frequently without much help.

Solubility Equilibrium

Solubility equilibrium refers to the balance between a solid and its dissolved ions in a solution. Not all compounds dissolve completely in water, which is the case with calcium sulfate (\( \text{CaSO}_4 \)). Here is what happens:

• Only a small quantity of \( \text{CaSO}_4 \) dissolves in water until its solubility limit, known as the solubility product constant (\( \text{K}_{ ext{sp}} \)), is reached.
• At this point, no more solid dissolves without changes in temperature or pressure.
• The equilibrium determines the concentration of ions in the solution.

Understanding solubility equilibrium is crucial in predicting whether certain substances will precipitate or dissolve under given conditions, affecting numerous chemical processes and industries.

Compressibility of Gases

Have you ever pressed down on a balloon and noticed it squishing in? This behavior in gases is called compressibility. When considering processes involving gases, like compressing nitrogen, we ponder their ability to occupy less volume under pressure.

• Gases are highly compressible due to the large spaces between their particles.
• Compression requires inputting significant energy to reduce gas volume.
• This is why compressing a gas half its original volume is non-spontaneous.

Understanding the compressibility of gases helps in various applications, from industrial processes to everyday phenomena like filling tires with air.