Question

The latent heat of vaporization for water at room temperature is 2430 J/g. Consider one particular molecule at the surface of a glass of liquid water, moving upward with sufficiently high speed that it will be the next molecule to join the vapor.(b) Find its speed. Now consider a thin gas made only of molecules like that one.

Answer 1

The question involves using the concept of the heat of vaporization to relate to the kinetic energy of a water molecule transitioning from liquid to vapor. However, there is insufficient information provided to calculate the exact speed, as it would require advanced calculations involving the mass of a water molecule and kinetic theory.

Step-by-step explanation:

The question is asking to calculate the speed of a water molecule as it escapes from the liquid phase to the vapor phase, a transition that requires energy known as the heat of vaporization. Given the latent heat of vaporization for water at room temperature as 2430 J/g, we are to find the speed of the molecule as it vaporizes. This involves using the concept of the heat of vaporization and kinetic energy.

The heat of vaporization is the energy required to transform one gram of a liquid into gas without changing the temperature. For water, this process requires breaking the hydrogen bonds between water molecules, which is why water has such a high heat of vaporization. The kinetic energy of a single molecule escaping from the liquid surface can be equated to this energy input.

However, from the given question, there seems to be insufficient information to calculate the exact speed of a single water molecule, because we would need to consider the individual mass of a water molecule and perform calculations assuming ideal behavior and the use of molecular kinetic theory, which is often beyond the scope of basic physics.

Answer 2

The speed of the molecule can be found using the concept of kinetic energy. We use the formula for kinetic energy and relate the mass to the latent heat of vaporization.

Step-by-step explanation:

The speed of the molecule can be found using the concept of kinetic energy. The kinetic energy of the molecule is equal to the latent heat of vaporization, which is 2430 J/g. We can use the formula for kinetic energy:

K.E. = (1/2)mv^2

where m is the mass of the molecule and v is its speed. Since the mass is not given, we need to find a way to relate it to the latent heat of vaporization. We can do this by considering that the latent heat of vaporization for water is about 2250 J/g. So, for every gram of water that vaporizes, the molecule we are interested in has a speed that can be found using the equation:

(1/2)mv^2 = 2250 J/g

Using the given information, we can solve for v, the speed of the molecule.