Problem 28 - Chemistry The Central Science In Si Units

Question

For each of the following processes, does the potential energy of the object(s) increase or decrease? (a) The charge of two oppositely charged particles is increased. (b) \(\mathrm{H}_{2} \mathrm{O}\) molecule is split into two oppositely charged ions, \(\mathrm{H}^{+}\) and \(\mathrm{OH}^{-}\). (c) A person skydives from a height of 600 meters.

Step-by-Step Solution

Answer

(a) Increase, (b) Increase, (c) Decrease.

Step 1: Increase in Charge of Oppositely Charged Particles

When the charge of two oppositely charged particles is increased, the force of attraction between them increases. Consequently, the potential energy increases because more work would be required to separate them, moving them against the attractive force. Thus, the potential energy of the system increases.

Step 2: Splitting of Water Molecule into Oppositely Charged Ions

Upon splitting a water molecule (H_2O) into ions H^+ and OH^-, electrical potential energy in the system increases. Energy must be added to break the molecular bond and separate the charges, leading to an increase in potential energy due to the separation of these oppositely charged ions.

Step 3: Skydiver's Descent

As a person skydives from a height of 600 meters, they move closer to Earth. The gravitational potential energy decreases because potential energy is converted into kinetic energy as the skydiver descends, moving toward the center of gravity.

Key Concepts

Oppositely Charged Particles

When you have two charged particles, the potential energy between them is a key concept in physics.
The potential energy depends massively on the nature and amount of charge. Oppositely charged particles, such as a proton and an electron, are drawn towards each other due to their attractive forces.

• Increasing the amount of charge on these particles escalates the force of attraction.
• The potential energy is therefore increased because more energy is required to separate these attracting charges.

In simpler terms, the greater the charge, the more energy you need to keep them apart. This concept is important in understanding various natural and technological processes.

Water Molecule Splitting

Water molecule splitting is a fascinating process with significant implications. When an \(\text{H}_2 \text{O}\) molecule is split into \(\text{H}^+\) and \(\text{OH}^-\) ions, you're effectively separating oppositely charged ions.
This separation involves a change in potential energy factors:

• Energy must be added to the system to break the chemical bonds holding the water molecule together.
• Once split into \(\text{H}^+\) and \(\text{OH}^-\), the system's potential energy increases because it takes energy to keep the charged ions apart.

Therefore, the act of splitting a water molecule illustrates how changes in chemical structure can influence energy within a system.

Gravitational Potential Energy

Gravitational potential energy is a concept that describes the energy an object possesses due to its height relative to the Earth's surface.
This type of energy is crucial when considering activities such as skydiving.
As a skydiver jumps from a height of 600 meters:

• Their gravitational potential energy is high at the start because they are far from the ground.
• As they fall, this energy is converted to kinetic energy, causing the gravitational potential energy to decrease.

In essence, gravitational potential energy is highest when the position is elevated and decreases as objects move closer to Earth. It's an elegant way of explaining why things accelerate as they fall.