Question

Ped-colored Kool-Aid crystals are added to a still glass of hot water. The same amount of crystals is added to a second still glass filled with the same amount of cold water. With no stirring, which would you expect to become uniform in color first: the hot water or the cold water? Why?

Short answer

The hot water will become uniform in color first due to faster diffusion.

Step-by-step solution

Understanding Diffusion

Diffusion is the process by which particles spread out evenly in a fluid due to random motion. In this context, Kool-Aid crystals will dissolve and diffuse through the water, causing the color to spread.

Effect of Temperature on Diffusion

The rate of diffusion increases with temperature. Hot water has more energy, which causes water molecules to move faster and increases the rate at which the Kool-Aid crystals dissolve and spread.

Predicting the Outcome in Hot and Cold Water

Given that diffusion occurs more rapidly at higher temperatures, the Kool-Aid crystals will spread more quickly in hot water compared to cold water, making the hot water become uniform in color first.

Conclusion

Due to the faster molecular movement and increased kinetics in hot water, it will achieve a uniform color before the cold water when Kool-Aid crystals are added.

Key concepts

Temperature effect on diffusion

Diffusion is a fascinating process that occurs when particles spread from an area of high concentration to an area of low concentration. Temperature plays a significant role in this process. When we increase the temperature, particles gain more energy and move more quickly. This increased movement allows them to collide more often and spread out more rapidly.

Consider a glass of hot water and another with cold water. Add the same amount of Kool-Aid crystals to each. The hot water, due to its higher temperature, speeds up the diffusion process. Molecules are moving faster, so the colors mix faster compared to the cold water.

• Higher temperatures increase molecular speed.
• Faster molecules spread substances quicker.
• Diffusion rate increases with temperature.

Thus, the Kool-Aid in hot water will become uniform in color before the cold one.

Molecular motion

At the core of diffusion is molecular motion, which is how molecules move in liquids and gases. These movements are random and constant, and they occur more quickly with additional thermal energy.

In warmer environments, molecules gain energy and jiggle faster. This heightened activity enables them to bump into each other more and spread over a larger area more efficiently.

• Random movement is key to diffusion.
• Increased energy from heat enhances motion.
• More collisions mean faster mixing.

Warm water's molecular motion is more vigorous, making substances like Kool-Aid spread more swiftly.

Dissolution process

Dissolution is the process where solid particles, such as Kool-Aid crystals, integrate into a solvent like water and form a solution. During dissolution, particles interact with the solvent and break away from their solid state.

The process speeds up in hot water as the increased temperature and molecular movement allow more frequent interactions between the solvent (water) and solute (Kool-Aid). This means that the crystals dissolve faster, and their particles spread throughout the solution more swiftly.

• Heat increases the rate of dissolution.
• Temperature promotes solute-solvent interactions.
• Faster dissolution leads to quicker uniformity.

Therefore, the transition from crystal to liquid happens quicker in hot water, resulting in faster color uniformity.

Kinetics in liquids

Kinetics refers to the study of the rate of chemical processes. In liquids, the movement and speed of molecules significantly affect the kinetics of dissolution and diffusion.

In hot water, the increased kinetic energy due to higher temperatures means molecules are more agile and interact frequently. These interactions contribute to a faster diffusion and dissolution process.

• Higher kinetic energy increases reaction rates.
• Faster interactions mean quicker solvent-solute dynamics.
• Kinetics are highly temperature dependent.

When Kool-Aid crystals are added to hot water, the heightened kinetics facilitate speedy integration and diffusion of the crystals, leading to a more rapid attainment of a uniform color.