Question

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.

Answer 1

1)
`kinectic energy=7.26*10^-^2^0J`

2)
`V= 2.0m/s`

3)
`T=3.5*10^3K`

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

Step-by-step 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

`M=(18.02)/(6.02*10^-^2^6)`

`M=3*10^-^2^3g`

Therefore

`kinectic energy=2430J/g*3*10^-^2^3g`

`kinectic energy=7.26*10^-^2^0J`

b)Generally the evaporation speed V is given as
`V= \sqrt{(K.E*2)/(m) }`

Mathematically derived from the equation

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

To Give

`V= \sqrt{(K.E*2)/(m) }`

`V= \sqrt{(7.26*10^-^2^0J*2)/(3*10^-^2^3g) }`

`V= 2.0m/s`

c)Generally the equation for velocity
`Vrms=\sqrt{(3RT)/(M) }`

Therefore

Effective temperature T is given by

`T=(√(v)*m)/(R)`

where

`T=(√(2.0m/s)*6.02*10^-^2^6)/(0.082057 L atm mol-1K-1)`

`T=3.5*10^3K`

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