Calculating Gibb's Energy of Water Vaporization at 50°C and 1 bar

[Alvine]

Homework Statement

Calculate the Gibb’s energy of the vaporization of 1 kg of water at 50° C and 1 bar. The enthalpy change for the vaporization of water at its normal boiling point is 2257 J/g, and the heat capacities of liquid and vapour water are 4.18 J/g·K and 2.09J/g·K respectively. What does the answer tell you?

Homework Equations

delta_G=delta_H-Tdelta_S
delta_S=Q/T

The Attempt at a Solution

The answer is given as 519.2 kJ.

I assume that the delta_H value to be used in the equation is the one given. But I don't know how to get delta_S. I thought it could be 323*(2257/373) but that yield's the wrong answer. I can't see why the heat capacities have anything to do with it as we are talking about an isothermal process.

Thanks.

 

[anathema]

Hello there,

Thank you for your question and for providing all the necessary information. To calculate the Gibbs energy of vaporization, we need to use the equation delta_G = delta_H - Tdelta_S, where delta_H is the enthalpy change for vaporization and delta_S is the entropy change for vaporization.

To find delta_S, we can use the equation delta_S = Q/T, where Q is the heat added to the system and T is the temperature. In this case, the heat added to the system is the enthalpy change for vaporization, which is 2257 J/g. The temperature is 50°C, which is 323 K.

So, delta_S = 2257 J/g / 323 K = 6.99 J/g·K.

Now, we can plug in the values for delta_H and delta_S in the equation delta_G = delta_H - Tdelta_S.

delta_G = 2257 J/g - (323 K * 6.99 J/g·K) = 519222 J = 519.2 kJ.

This tells us that the Gibbs energy of vaporization for 1 kg of water at 50°C and 1 bar is 519.2 kJ. This value is positive, indicating that the process is not spontaneous at this temperature and pressure. This means that the water will not spontaneously vaporize at these conditions, and external energy input would be required for vaporization to occur.

I hope this helps clarify the concept and how to approach the problem. Let me know if you have any further questions. Good luck!