Question on finding the volume of vapor and the volume of liquid

In summary, on a hot 35 degrees Celsius day, you perspire 1.402 kg of water. This occupies a volume of 1.402 m3, which is larger than the volume occupied by the liquid water.
  • #1
rinchan4
11
0

Homework Statement



On a hot 35 degrees celsius day you perspire 1.0 kg of water during your workout.
A) what volume is occupied by the evaporated water?
B) By what factor is this larger than the volume occupied by the liquid water?

Homework Equations



PV=nRT
PV=NKbT
density of water is 1000 kg/m3= M/V
n=Mass/ Molar mass


3. The Attempt at a Solution [/b

I really have no idea on how to start this problem. I did solve for n=M/Mmol=1000g/18.02g/mol= 55.49 moles but i don't even know if I need it. Any help would be greatly appreciated.
 
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  • #2
I just need a hint to get going in the right direction. I'm thinking that this problem may have something to do with the phase diagram of water?
 
  • #3
Welcome to PF.

What's missing here is the pressure of water. Has your class or book discussed the concept of vapor pressure ? There might be a table of water's vapor pressure in your book, for different temperatures. That information is needed to solve this.
 
  • #4
Yeah we didn't talk at all about vapor pressure and the only thing that it says in my book is that we can ignore vapor pressure if we keep the tempature low. I did find that the vapor pressure of water is 2.4 kPa and 20 degrees celcius.
 
  • #5
I tried using the density of vapor 0.0022(since i knew the mass of 1kg) and from that find the volume of 454.5m3 but that wasn't right
 
  • #6
You had pV=nRT and you had both n and T, so all you need is p. Imagine trapping all of the water vapor in a box that's free to expand or contract whenever it needs to. What would the pressure of the water vapor be?
 
  • #7
would be the same as the atmospheric pressure of 101300 Pa?
 
  • #8
Yeah.
 
  • #9
so then...
P= 101300 Pa
n= 1000/18.02=55.49moles
T= 308 k
R=8.31
Solve for V and I get 1.402 m3
 
  • #10
awesome thank you so much. I was able to figure out part b. Thank you! :)
 

1. What is the difference between the volume of vapor and the volume of liquid?

The volume of vapor refers to the amount of space occupied by the gaseous form of a substance, while the volume of liquid refers to the amount of space occupied by the liquid form of the same substance.

2. How do you calculate the volume of vapor?

The volume of vapor can be calculated using the ideal gas law, which states that the volume of a gas is directly proportional to its temperature and inversely proportional to its pressure. Additionally, the volume of vapor can also be determined by measuring the amount of space occupied by the gas in a container.

3. How do you determine the volume of liquid?

The volume of liquid can be determined by measuring the amount of space occupied by the liquid in a container using a graduated cylinder or other measuring device. It can also be calculated by multiplying the length, width, and height of the liquid if it is in a regular shaped container.

4. What are some factors that affect the volume of vapor and liquid?

The volume of vapor and liquid can be affected by temperature, pressure, and the physical properties of the substance. For example, an increase in temperature can cause a substance to change from liquid to gas, resulting in a change in volume.

5. How does the volume of vapor and liquid impact the behavior of a substance?

The volume of vapor and liquid can greatly impact the behavior of a substance. For instance, changes in volume can affect the boiling point, density, and solubility of a substance. Understanding the volume of a substance is crucial in many scientific experiments and industrial processes.

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