# Video: Standard Molar Entropy Change for Boiling Water

The boiling of water is represented by the equation H₂O(l) ⟶ H₂O(g). The standard molar entropy of a material, 𝑆_(298) ^(⦵), is the molar entropy of the material at 298 K and 1.00 bar pressure. The value of 𝑆_(298) ^⦵ for liquid water is 70.0 J/mol ⋅ K and the value for steam is 188.8 J/mol ⋅ K. Calculate Δ𝑆_(298) ^⦵, the standard molar entropy change for boiling water.

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### Video Transcript

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.