Question

At altitudes above sea level, the boiling point of water is less than \(100^{\circ} \mathrm{C}\). Use collision theory to explain why it takes longer to boil an egg at altitudes higher than sea level.

Short answer

At higher altitudes, the boiling point of water decreases due to lower atmospheric pressure. This results in the egg being cooked at a lower temperature, which in turn means that the egg proteins take longer to denature and coagulate because they are colliding with hot water molecules at a reduced kinetic energy. Therefore, it takes longer to boil an egg at higher altitudes.

Step-by-step solution

Understand the Collision Theory

Collision theory postulates that for a reaction to occur, it is not enough for reactant molecules to collide – they must also have enough kinetic energy, and the correct spatial orientation. In the context of boiling an egg, the egg protein molecules need to collide with water molecules with enough energy to cause them to denature and coagulate.

Understand the effect of atmospheric pressure on boiling point

The boiling point of water decreases with decreasing atmospheric pressure. At higher altitudes, the atmospheric pressure is lower, so water boils at a temperature lower than its usual boiling point at sea level. Thus, at high altitude, water will boil at a temperature lower than \(100^{\circ}C\).

Connect the two concepts

Lower boiling point at high altitude means the egg is cooked at a lower temperature. This means it takes longer time for the protein molecules in the egg to collide with the hot water molecules at the reduced kinetic energy – thus, it takes longer for the egg proteins to denature and coagulate. This is why it takes longer to boil an egg at altitudes higher than sea level.

Key concepts

Collision Theory

The collision theory is crucial in understanding why reactions occur or, in our case, why boiling an egg takes longer at higher altitudes. According to the collision theory, chemical reactions only take place when particles collide with sufficient energy and the correct orientation.

In the process of boiling an egg, we're looking at a physical change where heat energy from boiling water causes the proteins within the egg to denature and coagulate. The heat energy is transferred through collisions between water molecules and the egg. For these proteins to denature, the water must be at or above the egg proteins' denaturation temperature. As water boils at a lower temperature at higher altitudes due to reduced atmospheric pressure, it has less heat energy. Therefore, the frequency and energy of the collisions between water molecules and the egg proteins are reduced, making the denaturation process less efficient and longer.

Atmospheric Pressure

Atmospheric pressure plays a vital role in boiling and cooking. At sea level, atmospheric pressure is measured at 1 atmosphere that stands for a certain amount of weight pressing down due to the air above.

As altitude increases, atmospheric pressure decreases because there is less air above exerting pressure. This has direct consequences on the boiling point of water. Normally, water boils at a temperature of \(100^{\text{\textdegree}}\text{C}\) at sea level, but as you go higher and the pressure decreases, the boiling point drops. This is because it takes less energy to convert the water from liquid to vapor at lower pressure. Therefore, the water boils at a lower temperature, which can affect cooking times for foods such as eggs, which rely on high temperatures to change their structure.

Kinetic Energy

Kinetic energy is essentially the energy of motion. In the case of boiling water, kinetic energy refers to the movement and vibration of water molecules.

At a microscopic level, temperature is directly proportional to the average kinetic energy of molecules. As the temperature of water increases, so does the kinetic energy of its molecules, which move more rapidly and collide more often and with more force. These energetic collisions are what allow water to change from a liquid to a gas during boiling. At higher altitudes, due to the lower atmospheric pressure, water boils at a lower temperature, which means the water molecules have less kinetic energy compared to boiling at sea level. Consequently, the reduced energy of these molecules when they come in contact with egg proteins is less effective for cooking, leading to longer preparation times for boiled eggs.

Protein Denaturation

Protein denaturation is a structural change in proteins that results in the loss of their biological properties. When we boil an egg, the heat causes the proteins to unfold from their natural state and then coagulate, or clump together, forming a solid structure — the firm egg white and yolk we're familiar with when we cook an egg.

Heat is the trigger for this structural transformation, and it's directly affected by the boiling point of water. At higher altitudes, since water boils at a lower temperature, the heat available to denature the egg proteins is less. This reduced heat means the proteins denature more slowly, results in a longer process to achieve the cooked state of an egg. It's an insightful example of how temperature and protein behavior are intertwined, and it shows the delicate balance required to achieve proper food preparation.