The boiling of water is represented
by the equation H₂O liquid forming H₂O gas. The standard molar entropy of a
material, 𝑆 nought 298, is the molar entropy of the material at 298 Kelvin and 1.00
bar pressure. The value of 𝑆 nought 298 for
liquid water is 70.0 joules per mole Kelvin, and the value for steam is 188.8 joules
per mole Kelvin. Calculate Δ𝑆 nought 298, the
standard molar entropy change for boiling water.
We can calculate the standard molar
entropy change of any reaction by taking the sum of the standard molar entropies of
each product times its stoichiometric coefficient minus the sum of the standard
molar entropies for each reactant times their stoichiometric coefficients.
The only product of this reaction
is H₂O gas, which has a standard molar entropy of 188.8 joules per mole Kelvin. Its stoichiometric coefficient is
one. So, we can multiply by one or just
leave it how it is. Our only reactant is liquid water,
which has a standard molar entropy of 70.0 joules per mole Kelvin. Its stoichiometric coefficient is
also one. If we subtract these numbers, we’ll
find that the standard molar entropy change for the boiling of water is 118.8 joules
per mole Kelvin.
You should note that although we’ve
calculated a positive value for the entropy change for this reaction, we can’t
assume that this process occurs spontaneously. This is because the second law of
thermodynamics tells us that a process is spontaneous if the entropy change of the
universe is positive. And, we’ve only calculated the
entropy change of our system, water boiling.
If we wanted to calculate the total
entropy change for this process, we could add the number that we’ve calculated in
this problem to the entropy change for the surroundings. This is why you don’t see a glass
of water spontaneously boil away at 298 Kelvin, which is room temperature.