What gas law explains why hot water diffused the food coloring faster than the cold water?
The gas law that explains why hot water diffused the food coloring faster than cold water is not directly related to gases, but rather to a principle called diffusion. Diffusion is the process by which molecules and particles move from an area of higher concentration to an area of lower concentration until equilibrium is reached.
In the case of hot water, the molecules have higher kinetic energy, meaning they move faster and collide more frequently. This increased movement and collision rate result in faster diffusion. The higher temperature increases the speed of the water molecules, facilitating the movement and mixing of the food coloring throughout the water.
On the other hand, cold water has lower kinetic energy, meaning the water molecules move slower and collide less frequently. As a result, the diffusion process in cold water is slower compared to hot water. The lower temperature reduces the speed of the water molecules, resulting in a slower and less efficient mixing of the food coloring.
To summarize, it is not a gas law, but rather the principle of diffusion that explains why hot water diffused the food coloring faster than cold water.
The gas law that explains why hot water diffuses food coloring faster than cold water is called Graham's Law of Diffusion. Graham's Law states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass.
To understand why this law applies to the diffusion of food coloring in water, we need to consider that when a liquid is heated, its molecules gain kinetic energy and start moving faster. This increased molecular motion leads to more collisions between the water molecules and the food coloring particles.
Now, let's break down the steps to apply Graham's Law to explain why hot water diffuses food coloring faster than cold water:
1. Determine the molar masses of the gases involved: In this case, we consider water as the "gas." The molar mass of water is approximately 18 g/mol.
2. Apply Graham's Law: The rate of diffusion of the food coloring in water is inversely proportional to the square root of their molar masses. Since the molar mass of water is constant, we only need to compare the molar masses of the "hot water" and "cold water" gases.
3. Calculate the square root of the molar mass: Let's assume that the molar mass of hot water is 100 g/mol and the molar mass of cold water is 50 g/mol. The square root of the molar mass of hot water is √100 = 10 g/mol, while the square root of the molar mass of cold water is √50 ≈ 7.07 g/mol.
4. Compare the rates of diffusion: As per Graham's Law, the rate of diffusion is inversely proportional to the square root of the molar mass. Since 10 g/mol > 7.07 g/mol, the rate of diffusion of the food coloring in hot water will be faster than in cold water.
In conclusion, according to Graham's Law of Diffusion, hot water diffuses food coloring faster than cold water due to the increased kinetic energy and faster molecular motion of the hot water molecules.