Energy for one molecule to
escape
14 Matter very hot and cold
To do:
• You will be finding the
energy required to
release one water
molecule from the
liquid. When the
energy is calculated on
the basis of the energy
per kilogram, the
quantity is known as
the specific latent heat
of vaporisation.
A preliminary check
• The first step is to estimate the effective
power output of the kettle.
– Add enough water to the kettle to cover the
element, then add about 100 g more.
Measure the total mass of this water.
– Measure the temperature of the water (or
simply guess that it is around 15–20 °C).
– Time how long it takes for the kettle to bring
the water to a rolling boil.
Calculation
• Use the specific thermal
capacity of the water
(4200 J kg–1 K–1) to
calculate how much
energy must have been
supplied to the kettle.
Divide this energy by the
time taken in seconds to
estimate power supplied
to the water. This value
provides some correction
for energy losses. Where
might the energy go?
The measurement
• This part of the activity produces steam –
be careful!
– Place the kettle on the mass balance and
switch it on.
– Wait for the water to boil and then note the
total mass of kettle plus water. Time how long
it takes for about 50 g of water to boil away.
Measure the actual mass loss as accurately
as you can.
Use your knowledge of the effective power output of the kettle and the time
taken to calculate the energy supplied to boil off this mass of water. Now
calculate the energy to liberate each molecule from the water – here are some
steps to help you:
• The molar mass of water is 18 g. How many moles of
water did you boil off?
• How many molecules of water were transferred from the
liquid to the vapour?
• How much energy was required to release each
molecule into the vapour?
• Make what comments you can about the reliability of
your estimate.
• Now compare this value with the average energy of the
molecules at 100 °C. This is of the order kT, so the
average energy is about 1.38 x 10–23 J K–1 x 373 K = 5.1
x 10–21 J
How much water boiled off?
m( water)  50 g
m(molar )  18 gmol
1
m( water)
 moles ( water)
m(molar )
n  2.8 mol
How much water boiled off?
N  NA n
N  6 10  2.8
23
N  1.7 10
24
How much water boiled off?
W
P
t
W  Pt
W  Pt
Pt
Energy / particle 
1.7 10 24
You have shown that
1. The energy required to evaporate each
molecule is roughly 7 x 10–20 J.
2. The energy required to evaporate one
molecule at 100 °C is about 15 times the
average energy of the molecules (15 kT)
at that temperature.