Problems with part (b) and (c)

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In summary, the gas with a temperature of 310 K and a pressure of 101 KPa has a volume of 3.19 x 10^-2 m^3 when 1.25 mol of the gas is assumed to be ideal. The fraction of the volume occupied by the gas molecules is 165.155 m^3, which suggests that the assumption of gas molecules as points of zero volume may not be entirely valid for this case.
  • #1
dg_5021
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A gas has a temperature of 310 K and a pressure of 101 KPa. (a) Find the volume occupied by 1.25 mol of the gas, assuming it is ideal. (b) Assuming the gas molecules can be approximated as small spheres of diameter 2.5x10^-10 meters, determine the fraction of the volume found in part (a) that is occupied by the molecules. (c) In determining the properties of an ideal gas, we assume that molecules are points of zero volume. Discuss the validity of this assumption for the case considered here.

(a) PV=NRT V=(NRT)/P V= ((1.25mol x 8.31 J/molxK x 310 K)/1.01 x10^5Pa)
= 3.19 x 10^-2 m^3

(b)

I was able to do part (a) but I don't know what to do for (b) or (c) or how to start it? Can someone please help? Thanks
 
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  • #2
dg_5021 said:
A gas has a temperature of 310 K and a pressure of 101 KPa. (a) Find the volume occupied by 1.25 mol of the gas, assuming it is ideal. (b) Assuming the gas molecules can be approximated as small spheres of diameter 2.5x10^-10 meters, determine the fraction of the volume found in part (a) that is occupied by the molecules. (c) In determining the properties of an ideal gas, we assume that molecules are points of zero volume. Discuss the validity of this assumption for the case considered here.

(a) PV=NRT V=(NRT)/P V= ((1.25mol x 8.31 J/molxK x 310 K)/1.01 x10^5Pa)
= 3.19 x 10^-2 m^3

(b)

I was able to do part (a) but I don't know what to do for (b) or (c) or how to start it? Can someone please help? Thanks

Figure out what "N" means in PV = NRT. You should know the connection between this, and the total number of molecules in the gas. Once you know this number, then finding the volume occupied by the molecules should be a matter of baby algebra since you should know how to find the volume of a sphere.

For the last part, compare the ratio of the occupied volume with the total volume of the gas. If the Ideal Gas assumption is that the gas molecule's occupied volume is negligible, is the ratio that you obtained is consistent with such an assumption?

Zz.
 
  • #3
(2.5x10^-10)/2 = 1.25x10^-10 m

V= (4 x pie x (1.25x10^-10^3)/3 = 8.18123x10^30 m^3


N= (PV)/(RT) = .000193 Molecules

(3.19 x 10^-2 m^3)/(.000193 Molecules) =165.155 m^3

Did I do part (b) right?
 
  • #4
dg_5021 said:
(2.5x10^-10)/2 = 1.25x10^-10 m

V= (4 x pie x (1.25x10^-10^3)/3 = 8.18123x10^30 m^3


N= (PV)/(RT) = .000193 Molecules

(3.19 x 10^-2 m^3)/(.000193 Molecules) =165.155 m^3

Did I do part (b) right?


[tex]pV=\nu RT[/tex]
and
[tex]\nu =\frac{N}{N_A}[/tex]
N-number of molecules
N_A- Avogadro's number
 
  • #5
dg_5021 said:
(2.5x10^-10)/2 = 1.25x10^-10 m

V= (4 x pie x (1.25x10^-10^3)/3 = 8.18123x10^30 m^3


N= (PV)/(RT) = .000193 Molecules

(3.19 x 10^-2 m^3)/(.000193 Molecules) =165.155 m^3

Did I do part (b) right?

Er... take 12 steps back and look at your "number" here. Does it make sense that you have a FRACTION of a molecule in a gas? You have not understood the meaning of "N" in that equation.

Zz.
 

Related to Problems with part (b) and (c)

What is the difference between part (b) and (c)?

Part (b) and (c) refer to different sections or aspects of a problem. Part (b) usually involves finding a solution or answering a question based on given information, while part (c) may require the application of additional concepts or equations.

Why do many people struggle with part (b) and (c) of a problem?

Part (b) and (c) can be challenging because they often require critical thinking and problem-solving skills. These sections may also involve multiple steps and the use of various formulas, requiring a thorough understanding of the problem and its underlying concepts.

What can I do to improve my performance on part (b) and (c) of a problem?

To improve your performance on part (b) and (c) of a problem, it is essential to have a strong understanding of the underlying concepts and equations. Practice problem-solving regularly and review any mistakes or difficulties you encounter. Additionally, seek help from a teacher or tutor if needed.

Are there any tips for approaching part (b) and (c) of a problem?

One helpful tip for approaching part (b) and (c) of a problem is to read the instructions and given information carefully. Identify what is being asked and what information is provided. Then, break the problem down into smaller, more manageable steps and make sure to show all work and calculations.

What should I do if I still have trouble with part (b) and (c) of a problem?

If you still have trouble with part (b) and (c) of a problem, don't be afraid to ask for help. Consult with a teacher, tutor, or classmate for clarification or additional practice problems. Continue to review and practice regularly to improve your understanding and performance.

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