Trouble Solving Volume of Condensed Water

[kapatter]

I'm having some trouble getting started on this one:

3.00×10^4 cm^3 of 300 degrees C steam at a pressure of 10.0 atm is cooled until it condenses. What is the volume of the liquid water? Give your answer in cm^3.

I figure you use pV=nRT to solve. I've been trying to rearrange it, but am confused. Any help would be greatly appreciated. Thanks.

 

[Hootenanny]

Firstly, why is this is Quantum Physics?

Secondly, why don't you show us the equation that you get when you rearrange it?

 

[Moetasim]

I understand your struggle with solving the volume of condensed water in this scenario. Let me provide some guidance to help you get started.

First, it is important to note that the ideal gas law, pV = nRT, cannot be directly applied in this situation as the steam is not an ideal gas. Instead, we will need to use the Clausius-Clapeyron equation, which relates the vapor pressure of a substance to its temperature and enthalpy of vaporization.

To begin, we can rearrange the equation to solve for the enthalpy of vaporization (ΔHvap):

ΔHvap = (RTln(P2/P1)) / (1/T2 - 1/T1)

Where P1 and T1 are the initial pressure and temperature of the steam, and P2 and T2 are the final pressure and temperature at which the steam condenses. In this case, P1 = 10.0 atm, T1 = 300 degrees C, and T2 = 100 degrees C (the boiling point of water).

Next, we can calculate the number of moles of water vapor using the ideal gas law:

n = PV/RT

Where V is the initial volume of the steam, which is given as 3.00×10^4 cm^3.

Once we have calculated the enthalpy of vaporization and the number of moles of water vapor, we can use the definition of enthalpy of vaporization (ΔHvap = Q/m) to calculate the amount of heat released when the steam condenses. This heat will be transferred to the surroundings and will cause the steam to condense into liquid water.

Finally, we can use the relationship between heat (Q), mass (m), and density (ρ) to calculate the volume of the liquid water:

V = m/ρ = Q/ρΔHvap

Where ρ is the density of water and can be found in a table or online.

I hope this helps you get started on solving the volume of condensed water in this scenario. Remember to carefully consider the units and conversions throughout the calculations. Good luck!