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The latent heat of vaporization for water at room temperature is 2430 J/g.

1. How much kinetic energy does each water molecule that evaporates possess before it evaporates?
2. Find the pre-evaporation rms speed of a water molecule that is evaporating.
3. What is the effective temperature of these molecules (modeled as if they were already in a thin gas)?

4. Why do these molecules not burn you

a. These molecules got to be slow-moving in collisions that made other molecules fast-moving; the average molecular energy decreases.
b. These molecules got to be slow-moving in collisions that made other molecules fast-moving; the average molecular energy is unaffected.
c. These molecules got to be fast-moving in collisions that made other molecules slow-moving; the average molecular energy is unaffected.
d. These molecules got to be fast-moving in collisions that made other molecules slow-moving; the average molecular energy increases.

Sagot :

Answer:

1)   [tex]kinectic energy=7.26*10^-^2^0J[/tex]

2)  [tex]V= 2.0m/s[/tex]

3)  [tex]T=3.5*10^3K[/tex]

4)  The Molecules do not burn because of the presences of hydrogen bond in place

Explanation:

From the question we are told that

latent heat of vaporization for water at room temperature is 2430 J/g.

1)Generally in determining the molar mass of water evaporated we have that

-One mole (6.02 x 10. 23 molecules)

-Molar mass of water is 18.02 g/mol

Mathematically the mass of water is give as

   

  [tex]M=\frac{18.02}{6.02*10^-^2^6}[/tex]

  [tex]M=3*10^-^2^3g[/tex]

Therefore

  [tex]kinectic energy=2430J/g*3*10^-^2^3g[/tex]

 [tex]kinectic energy=7.26*10^-^2^0J[/tex]

b)Generally the evaporation speed V is given as[tex]V= \sqrt{\frac{K.E*2}{m} }[/tex]

Mathematically derived from the equation

[tex]\frac{1}{2} mv^2 =K.E[/tex]

To Give

[tex]V= \sqrt{\frac{K.E*2}{m} }[/tex]

[tex]V= \sqrt{\frac{7.26*10^-^2^0J*2}{3*10^-^2^3g} }[/tex]

[tex]V= 2.0m/s[/tex]

c)Generally the equation for velocity   [tex]Vrms=\sqrt{\frac{3RT}{M} }[/tex]

Therefore

Effective temperature T is given by

      [tex]T=\frac{\sqrt{v}*m}{R}[/tex]

where

     [tex]T=\frac{\sqrt{2.0m/s}*6.02*10^-^2^6}{0.082057 L atm mol-1K-1}[/tex]

     [tex]T=3.5*10^3K[/tex]

4) The Molecules do not burn because of the presences of hydrogen bond in place