Finding the Volume of an Ideal Gas

In summary, the conversation discusses the use of two different equations to solve a problem and the importance of using the correct units when calculating volume. The equation PV=mRT yields the correct answer of 4.305 m**2, while using the equation Density = Mass/Volume with given values of density and mass results in a volume of 4.08. It is noted that the density of air can vary with temperature and pressure, and the volume of air cannot be 4.305 m2 due to incorrect units.
  • #1
Kajan thana
151
18
Homework Statement
A rigid tank contains 5 kg of air at 100 kPa and 27 °C. The air is now heated until
its pressure doubles. Determine the volume of the air?
Relevant Equations
1) PV= mRT.
2) Denisty = Mass/Volume
Hi,

I tried to do this question in two different approaches one of them was using the equation PV=mRT where I got the right answer which is 4.305 m**2. However, I tried using this Density = Mass/Volume, where I substituted Denisity= 1.225 and Mass equals 5kg to get the volume as 4.08.
Can someone tell me why I can't use the second equation? Is it because the density of the air varies?
 
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  • #2
Kajan thana said:
Is it because the density of the air varies?
Yes. The density of air will vary with temperature and pressure. You are given values for both and should use those values.

The volume of the air is most definitely not 4.305 m2. Can you see why?
 
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  • #3
jbriggs444 said:
Yes. The density of air will vary with temperature and pressure. You are given values for both and should use those values.

The volume of the air is most definitely not 4.305 m2. Can you see why?
Thank you.
It makes sense that the density will vary with temperature and pressure so I have to use the values that is given. But can please explain why 4.305m2 is not also the right answer ( according to marking scheme, it is ) ?
 
Last edited:
  • #4
Hint: the problem is not with the number, but the units.
 
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  • #5
mjc123 said:
Hint: the problem is not with the number, but the units.
Oh thank you.. Yh wrong unit..
 

FAQ: Finding the Volume of an Ideal Gas

What is the ideal gas law and how is it used to find the volume of an ideal gas?

The ideal gas law is a mathematical equation that relates the pressure, volume, temperature, and amount of a gas. It is written as PV = nRT, where P is pressure, V is volume, n is the number of moles of the gas, R is the ideal gas constant, and T is temperature. To find the volume of an ideal gas, we rearrange the equation to V = nRT/P.

What is the difference between an ideal gas and a real gas?

An ideal gas is a theoretical gas that follows the ideal gas law perfectly, meaning that its particles have no volume and do not interact with each other. A real gas, on the other hand, has particles with finite volume and may interact with each other, causing deviations from the ideal gas law at high pressures and low temperatures.

How do you measure the volume of an ideal gas?

The volume of an ideal gas can be measured using various methods, such as a gas syringe, a graduated cylinder, or a burette. These devices allow for the measurement of the volume of gas at a specific pressure and temperature.

What factors affect the volume of an ideal gas?

The volume of an ideal gas is affected by the pressure, temperature, and amount of the gas. According to the ideal gas law, as pressure and temperature increase, the volume of the gas also increases. Additionally, the volume is directly proportional to the number of moles of the gas present.

How does the volume of an ideal gas change with changing pressure and temperature?

According to the ideal gas law, the volume of an ideal gas is directly proportional to the pressure and temperature. This means that as pressure and temperature increase, the volume of the gas also increases. Conversely, as pressure and temperature decrease, the volume of the gas decreases as well.

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