Chapter 5: Problem 2
A closed flask contains water in all its three states: solid, liquid and vapour at \(0^{\circ} \mathrm{C} .\) In this situation the average kinetic energy of the water molecule will be (1) The greater in the vapour state (2) The same in the three states (3) The greatest in the solid state (4) Greater in the liquid than in the vapour state
Short Answer
Expert verified
The same in the three states
Step by step solution
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Phases of Water
Water exists in three distinct phases: solid (ice), liquid (water), and gas (vapor). Each phase has unique properties because of the strength of the intermolecular forces holding the molecules together.
In the solid phase (ice), water molecules are held in a rigid structure with minimal movement. This gives ice its solid shape and structure.
In the liquid phase, water molecules are more loosely packed. They can slide past one another, allowing water to flow and take the shape of its container.
In the gas phase (vapor), water molecules are much farther apart and move freely, filling the entire volume of their container. Understanding these phases is crucial when discussing kinetic energy and temperature’s impact on water.
In the solid phase (ice), water molecules are held in a rigid structure with minimal movement. This gives ice its solid shape and structure.
In the liquid phase, water molecules are more loosely packed. They can slide past one another, allowing water to flow and take the shape of its container.
In the gas phase (vapor), water molecules are much farther apart and move freely, filling the entire volume of their container. Understanding these phases is crucial when discussing kinetic energy and temperature’s impact on water.
Average Kinetic Energy
The average kinetic energy of molecules is directly related to the temperature of the substance. At any given temperature, the average kinetic energy (\text{KE}_{avg}\text{)} can be expressed using the formula:
\[ \text{KE}_{avg} = \frac{3}{2} k_B T \]
where \(k_B\) is the Boltzmann constant, and \(T\) is the temperature in Kelvin. Thus, if the temperature is the same, molecules in different phases have the same average kinetic energy. This is why, in the exercise, the water molecules in solid, liquid, and vapor phases at 0°C have the same average kinetic energy, despite being in different phases.
\[ \text{KE}_{avg} = \frac{3}{2} k_B T \]
where \(k_B\) is the Boltzmann constant, and \(T\) is the temperature in Kelvin. Thus, if the temperature is the same, molecules in different phases have the same average kinetic energy. This is why, in the exercise, the water molecules in solid, liquid, and vapor phases at 0°C have the same average kinetic energy, despite being in different phases.
Temperature Dependence
Temperature plays a critical role in determining the kinetic energy of molecules. As temperature increases, the kinetic energy of molecules also rises, causing molecules to move faster. At higher temperatures, water molecules gain enough energy to overcome the forces holding them in a specific phase and transition to another phase (e.g., ice melting to water or water boiling to vapor). Conversely, lowering the temperature reduces kinetic energy, slowing down molecular movement and potentially causing phase transitions such as water freezing into ice.
The relationship between temperature and kinetic energy is foundational in understanding physical changes and thermodynamic processes in substances like water.
The relationship between temperature and kinetic energy is foundational in understanding physical changes and thermodynamic processes in substances like water.
